Unit 5 Test

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Desmos - Graphing
Desmos - Scientific
Quadratic Regression

List of perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
List of perfect cubes:     1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Formulae:
i = \sqrt{-1}
For a standard form quadratic equation, ax^{2}+bx+c=0, x =\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}.
For a, b \neq 0 \in \mathbb{R}:
     a^{2} - b^{2} = (a-b)(a+b)
     a^{2} + b^{2} = (a-bi)(a+bi)
     a^{3}-b^{3} = (a-b)(a^{2}+ab+b^{2})
     a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})

1

Simplify

\frac{(-6x^{2}y^{3})^{4}}{8x^{9}y^{7}\cdot3xy^{5}}

1

Simplify.

(18 - 2x3 + 9x) - (4 - x2 - 3x3 + 11x)

Write your answer as a polynomial in standard form, no spaces.

1

Simplify

(n3 + 2n2)(n2 - 3n + 8)

Write your answer as a polynomial in standard form, no spaces..

1

Simplify.

(2w - 5)3

Write your answer as a polynomial in standard form, no spaces.

1

Simplify.

\frac{-18a^{7}b^{3}+9a^{4}b^{2}-63a^{2}b}{9ab}

Write your answer as a polynomial, no spaces. List terms in order of decreasing powers of a.

4

Match the graphs to their descriptions

Draggable item		Corresponding Item
		polynomial with odd degree; negative leading coefficient
		polynomial with even degree; negative leading coefficient
		polynomial with even degree; positive leading coefficient
		polynomial with odd degree; positive leading coefficient

For problems 9-14,

f(x) = x3 - 12x2 + 45x -54

1

What is the relative maximum of f(x)?

Use (x, y) format, with exactly one space after the comma.

1

Solve by factoring. Simplify all irrational and complex solutions.

8x3 - 98x = 0

Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

1

Solve by factoring. Simplify all irrational and complex solutions.

3x3 + 4x2 = 12x + 16

Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

1

Which of the following represent the solutions to
0 = x3 + 512

Check all that apply.

1

Identify the zeroes of the function.

f(x) = 2x(x + 4)6(3x - 2)3

Use x={#, ...} format, with exactly one space after each comma. List the roots in increasing order.

1

Which of the following are factors of the polynomial below? Check all that apply.

x4 + 216x

1

Which of the following are factors of the polynomial below? Check all that apply.

14x3 - 49x2 + 21x

1

Which of the following are factors of the polynomial below? Check all that apply.

x3 - 5x2 - x + 5

Put factors in order of increasing number of terms. If two factors have the same number of terms, put them in increasing order based on their last terms. There should be no spaces in your answer.

1

Find the quotient by FACTORING.

\frac{9x^{2}-6x-8}{3x+2}

Your answer should be a linear binomial in standard form, no spaces.

1

Find the quotient.

\frac{x^{2}+6x-25}{x-2}

Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

1

Find the quotient.

\frac{x^{3}+3x^{2}-31x-26}{x+7}

Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

1

If f(x) = 5x^{4}-23x^{3}+24x^{2}-7, what is the remainder when f(x) is divided by (x-3)?

Your answer should be an integer, no spaces.

1

The remainder of g(x) when divided by (x + 5) is 18. g(x) must equal 18 for what value of x?

Your answer should be an integer, no spaces.

For 31 through 36:

   f(x) = x2 - x
   g(x) = 9 - 2x
   h(x) = x2 +2x -63

1

Find (f+h)(x).

Your answer should be a trinomial in standard form, no spaces.

1

Unit 5 Test

Simplify\frac{(-6x^{2}y^{3})^{4}}{8x^{9}y^{7}\cdot3xy^{5}}

Simplify.(18 - 2x3 + 9x) - (4 - x2 - 3x3 + 11x)Write your answer as a polynomial in standard form, no spaces.

Simplify(n3 + 2n2)(n2 - 3n + 8)Write your answer as a polynomial in standard form, no spaces..

Simplify.(2w - 5)3Write your answer as a polynomial in standard form, no spaces.

Simplify.\frac{-18a^{7}b^{3}+9a^{4}b^{2}-63a^{2}b}{9ab}Write your answer as a polynomial, no spaces. List terms in order of decreasing powers of a.

Match the graphs to their descriptions

What is the relative maximum of f(x)?Use (x, y) format, with exactly one space after the comma.

Solve by factoring. Simplify all irrational and complex solutions.8x3 - 98x = 0Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

Solve by factoring. Simplify all irrational and complex solutions.3x3 + 4x2 = 12x + 16Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

Which of the following represent the solutions to 0 = x3 + 512Check all that apply.

Identify the zeroes of the function.f(x) = 2x(x + 4)6(3x - 2)3Use x={#, ...} format, with exactly one space after each comma. List the roots in increasing order.

Which of the following are factors of the polynomial below? Check all that apply.x4 + 216x

Which of the following are factors of the polynomial below? Check all that apply.14x3 - 49x2 + 21x

Which of the following are factors of the polynomial below? Check all that apply.x3 - 5x2 - x + 5Put factors in order of increasing number of terms. If two factors have the same number of terms, put them in increasing order based on their last terms. There should be no spaces in your answer.

Find the quotient by FACTORING. \frac{9x^{2}-6x-8}{3x+2}Your answer should be a linear binomial in standard form, no spaces.

Find the quotient. \frac{x^{2}+6x-25}{x-2}Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

Find the quotient. \frac{x^{3}+3x^{2}-31x-26}{x+7}Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

If f(x) = 5x^{4}-23x^{3}+24x^{2}-7, what is the remainder when f(x) is divided by (x-3)?Your answer should be an integer, no spaces.

The remainder of g(x) when divided by (x + 5) is 18. g(x) must equal 18 for what value of x?Your answer should be an integer, no spaces.

Find (f+h)(x).Your answer should be a trinomial in standard form, no spaces.

Simplify\frac{(-6x^{2}y^{3})^{4}}{8x^{9}y^{7}\cdot3xy^{5}}

Simplify.(18 - 2x3 + 9x) - (4 - x2 - 3x3 + 11x)Write your answer as a polynomial in standard form, no spaces.

Simplify(n3 + 2n2)(n2 - 3n + 8)Write your answer as a polynomial in standard form, no spaces..

Simplify.(2w - 5)3Write your answer as a polynomial in standard form, no spaces.

Simplify.\frac{-18a^{7}b^{3}+9a^{4}b^{2}-63a^{2}b}{9ab}Write your answer as a polynomial, no spaces. List terms in order of decreasing powers of a.

Match the graphs to their descriptions

What is the relative maximum of f(x)?Use (x, y) format, with exactly one space after the comma.

What is the relative minimum of f(x)?Use (x, y) format, with exactly one space after the comma.

As x -> \infty, f(x) approaches what value?As x -> -\infty, f(x) approaches what value?

On what interval(s) does the function increase? Check all that apply.

On what interval(s) does the function decrease? Check all that apply.

What are the roots of f(x)?Check all that apply.

Solve by factoring. Simplify all irrational and complex solutions.8x3 - 98x = 0Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

Solve by factoring. Simplify all irrational and complex solutions.3x3 + 4x2 = 12x + 16Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

Which of the following represent the solutions to 0 = x3 + 512Check all that apply.

Identify the zeroes of the function.f(x) = 2x(x + 4)6(3x - 2)3Use x={#, ...} format, with exactly one space after each comma. List the roots in increasing order.

Which of the following are factors of the polynomial below? Check all that apply.x4 + 216x

Which of the following are factors of the polynomial below? Check all that apply.14x3 - 49x2 + 21x

Which of the following are factors of the polynomial below? Check all that apply.x3 - 5x2 - x + 5Put factors in order of increasing number of terms. If two factors have the same number of terms, put them in increasing order based on their last terms. There should be no spaces in your answer.

Find the quotient by FACTORING. \frac{9x^{2}-6x-8}{3x+2}Your answer should be a linear binomial in standard form, no spaces.

Find the quotient. \frac{x^{2}+6x-25}{x-2}Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

Find the quotient. \frac{x^{3}+3x^{2}-31x-26}{x+7}Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

If f(x) = 5x^{4}-23x^{3}+24x^{2}-7, what is the remainder when f(x) is divided by (x-3)?Your answer should be an integer, no spaces.

The remainder of g(x) when divided by (x + 5) is 18. g(x) must equal 18 for what value of x?Your answer should be an integer, no spaces.

Find (f+h)(x).Your answer should be a trinomial in standard form, no spaces.

Find (g\cdot f)(x):Your answer should be a trinomial in standard form, no spaces.

The domain of (\frac{g}{h})(x) is all real numbers except which numbers?

Find (f\circ g)(x).Your answer should be a trinomial in standard form, no spaces.

Evaluate (h-g)(4).Your answer should be an integer, no spaces.

Evaluate (g\circ h)(-1).Your answer should be an integer, no spaces.

What is the relative minimum of f(x)?Use (x, y) format, with exactly one space after the comma.

As x -> \infty, f(x) approaches what value?As x -> -\infty, f(x) approaches what value?

On what interval(s) does the function increase? Check all that apply.

On what interval(s) does the function decrease? Check all that apply.

What are the roots of f(x)?Check all that apply.

Find (g\cdot f)(x):Your answer should be a trinomial in standard form, no spaces.

The domain of (\frac{g}{h})(x) is all real numbers except which numbers?

Find (f\circ g)(x).Your answer should be a trinomial in standard form, no spaces.

Evaluate (h-g)(4).Your answer should be an integer, no spaces.

Evaluate (g\circ h)(-1).Your answer should be an integer, no spaces.

Simplify

\frac{(-6x^{2}y^{3})^{4}}{8x^{9}y^{7}\cdot3xy^{5}}

Simplify.

(18 - 2x3 + 9x) - (4 - x2 - 3x3 + 11x)

Write your answer as a polynomial in standard form, no spaces.

Simplify

(n3 + 2n2)(n2 - 3n + 8)

Write your answer as a polynomial in standard form, no spaces..

Simplify.

(2w - 5)3

Write your answer as a polynomial in standard form, no spaces.

Simplify.

\frac{-18a^{7}b^{3}+9a^{4}b^{2}-63a^{2}b}{9ab}

Write your answer as a polynomial, no spaces. List terms in order of decreasing powers of a.

What is the relative maximum of f(x)?

Use (x, y) format, with exactly one space after the comma.

Solve by factoring. Simplify all irrational and complex solutions.

8x3 - 98x = 0

Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

Solve by factoring. Simplify all irrational and complex solutions.

3x3 + 4x2 = 12x + 16

Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

Which of the following represent the solutions to
0 = x3 + 512

Check all that apply.

Identify the zeroes of the function.

f(x) = 2x(x + 4)6(3x - 2)3

Use x={#, ...} format, with exactly one space after each comma. List the roots in increasing order.

Which of the following are factors of the polynomial below? Check all that apply.

x4 + 216x

Which of the following are factors of the polynomial below? Check all that apply.

14x3 - 49x2 + 21x

Which of the following are factors of the polynomial below? Check all that apply.

x3 - 5x2 - x + 5

Put factors in order of increasing number of terms. If two factors have the same number of terms, put them in increasing order based on their last terms. There should be no spaces in your answer.

Find the quotient by FACTORING.

\frac{9x^{2}-6x-8}{3x+2}

Your answer should be a linear binomial in standard form, no spaces.

Find the quotient.

\frac{x^{2}+6x-25}{x-2}

Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

Find the quotient.

\frac{x^{3}+3x^{2}-31x-26}{x+7}

Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

If f(x) = 5x^{4}-23x^{3}+24x^{2}-7, what is the remainder when f(x) is divided by (x-3)?

Your answer should be an integer, no spaces.

The remainder of g(x) when divided by (x + 5) is 18. g(x) must equal 18 for what value of x?

Your answer should be an integer, no spaces.

Find (f+h)(x).

Your answer should be a trinomial in standard form, no spaces.

Simplify

\frac{(-6x^{2}y^{3})^{4}}{8x^{9}y^{7}\cdot3xy^{5}}

Simplify.

(18 - 2x3 + 9x) - (4 - x2 - 3x3 + 11x)

Write your answer as a polynomial in standard form, no spaces.

Simplify

(n3 + 2n2)(n2 - 3n + 8)

Write your answer as a polynomial in standard form, no spaces..

Simplify.

(2w - 5)3

Write your answer as a polynomial in standard form, no spaces.

Simplify.

\frac{-18a^{7}b^{3}+9a^{4}b^{2}-63a^{2}b}{9ab}

Write your answer as a polynomial, no spaces. List terms in order of decreasing powers of a.

What is the relative maximum of f(x)?

Use (x, y) format, with exactly one space after the comma.

What is the relative minimum of f(x)?

Use (x, y) format, with exactly one space after the comma.

As x -> \infty, f(x) approaches what value?

As x -> -\infty, f(x) approaches what value?

What are the roots of f(x)?

Check all that apply.

Solve by factoring. Simplify all irrational and complex solutions.

8x3 - 98x = 0

Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

Solve by factoring. Simplify all irrational and complex solutions.

3x3 + 4x2 = 12x + 16

Use x={#, ...} format, with exactly one space after each comma. List solutions in increasing order.

Which of the following represent the solutions to
0 = x3 + 512

Check all that apply.

Identify the zeroes of the function.

f(x) = 2x(x + 4)6(3x - 2)3

Use x={#, ...} format, with exactly one space after each comma. List the roots in increasing order.

Which of the following are factors of the polynomial below? Check all that apply.

x4 + 216x

Which of the following are factors of the polynomial below? Check all that apply.

14x3 - 49x2 + 21x

Which of the following are factors of the polynomial below? Check all that apply.

x3 - 5x2 - x + 5

Put factors in order of increasing number of terms. If two factors have the same number of terms, put them in increasing order based on their last terms. There should be no spaces in your answer.

Find the quotient by FACTORING.

\frac{9x^{2}-6x-8}{3x+2}

Your answer should be a linear binomial in standard form, no spaces.

Find the quotient.

\frac{x^{2}+6x-25}{x-2}

Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

Find the quotient.

\frac{x^{3}+3x^{2}-31x-26}{x+7}

Your answer should have no spaces. Use the variable from the problem, and list terms in order of decreasing powers of the variable.

If f(x) = 5x^{4}-23x^{3}+24x^{2}-7, what is the remainder when f(x) is divided by (x-3)?

Your answer should be an integer, no spaces.

The remainder of g(x) when divided by (x + 5) is 18. g(x) must equal 18 for what value of x?

Your answer should be an integer, no spaces.

Find (f+h)(x).

Your answer should be a trinomial in standard form, no spaces.

Find (g\cdot f)(x):

Your answer should be a trinomial in standard form, no spaces.

Find (f\circ g)(x).

Your answer should be a trinomial in standard form, no spaces.

Evaluate (h-g)(4).

Your answer should be an integer, no spaces.

Evaluate (g\circ h)(-1).

Your answer should be an integer, no spaces.

What is the relative minimum of f(x)?

Use (x, y) format, with exactly one space after the comma.

As x -> \infty, f(x) approaches what value?

As x -> -\infty, f(x) approaches what value?

What are the roots of f(x)?

Check all that apply.

Find (g\cdot f)(x):

Your answer should be a trinomial in standard form, no spaces.

Find (f\circ g)(x).

Your answer should be a trinomial in standard form, no spaces.

Evaluate (h-g)(4).

Your answer should be an integer, no spaces.

Evaluate (g\circ h)(-1).

Your answer should be an integer, no spaces.