P5.5: Solving Polynomial Equations

Instructions

For more review on solving by factoring, watch this video (and the videos in the sidebar).

When giving multiple solutions...

Use x={#, #...} format, with one space after each comma.  List the real solutions first, in increasing order, then the imaginary solutions, in increasing order.  Simplify all solutions.

1

See the directions below.

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Resequence the numbers below according to the directions.

-3+3i\sqrt{3}
-3-3i\sqrt{3}
-8/5
5
-1

1

Solve by factoring.

4x^{3}-7x^{2}=3x^{2}

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

1

Solve by factoring.

5x^{5}-80x=0

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

1

Solve by factoring.

8x^{5}+5x^{2}=4x^{2}

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

This one will involve ugly fractions.

1

Solve by factoring.

81x^{3}=3

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

1

Solve by factoring.

81x^{4}=16

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

1

Solve by factoring.

2x^{6}-10x^{4}-48x^{2}=0

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

1

Solve by factoring.

2x^{3}-5x^{2}+40x=100

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

1

Solve by factoring.

2x^{3}-3x^{2}=32x-48

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

1

The population of a species is modeled by the equation p(t) = -t4 + 72t2 + 225, where t is the number of years. Find the approximate number of years until the species is extinct.

Enter your answer as a number rounded to two decimal places.

1

REVIEW

A certain polynomial has an negative leading coefficient and an odd degree. What are the end behaviors of the polynomial?

1

REVIEW

Consider the polynomial

f(x) = 3x - x^{4} + 5

What are the end behaviors of the polynomial?

1

REVIEW
Consider the function below.

The function has a domain of __________ and a range of __________
As x approaches infinity, y approaches __________.
The function is decreasing on the interval __________.
The function is increasing on the interval __________.
The function has a relative maximum at __________.

P5.5: Solving Polynomial Equations

See the directions below.Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.Resequence the numbers below according to the directions.

Solve by factoring. 4x^{3}-7x^{2}=3x^{2}Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.5x^{5}-80x=0Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.8x^{5}+5x^{2}=4x^{2}Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.This one will involve ugly fractions.

Solve by factoring.81x^{3}=3Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.81x^{4}=16Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.2x^{6}-10x^{4}-48x^{2}=0Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.2x^{3}-5x^{2}+40x=100Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.2x^{3}-3x^{2}=32x-48Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

The population of a species is modeled by the equation p(t) = -t4 + 72t2 + 225, where t is the number of years. Find the approximate number of years until the species is extinct. Enter your answer as a number rounded to two decimal places.

REVIEWA certain polynomial has an negative leading coefficient and an odd degree. What are the end behaviors of the polynomial?

REVIEWConsider the polynomial f(x) = 3x - x^{4} + 5 What are the end behaviors of the polynomial?

See the directions below.Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.Resequence the numbers below according to the directions.

Solve by factoring. 4x^{3}-7x^{2}=3x^{2}Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.5x^{5}-80x=0Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.8x^{5}+5x^{2}=4x^{2}Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.This one will involve ugly fractions.

Solve by factoring.81x^{3}=3Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.81x^{4}=16Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.2x^{6}-10x^{4}-48x^{2}=0Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.2x^{3}-5x^{2}+40x=100Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.2x^{3}-3x^{2}=32x-48Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

The population of a species is modeled by the equation p(t) = -t4 + 72t2 + 225, where t is the number of years. Find the approximate number of years until the species is extinct. Enter your answer as a number rounded to two decimal places.

REVIEWA certain polynomial has an negative leading coefficient and an odd degree. What are the end behaviors of the polynomial?

REVIEWConsider the polynomial f(x) = 3x - x^{4} + 5 What are the end behaviors of the polynomial?

See the directions below.

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Resequence the numbers below according to the directions.

Solve by factoring.

4x^{3}-7x^{2}=3x^{2}

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

5x^{5}-80x=0

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

8x^{5}+5x^{2}=4x^{2}

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

This one will involve ugly fractions.

Solve by factoring.

81x^{3}=3

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

81x^{4}=16

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

2x^{6}-10x^{4}-48x^{2}=0

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

2x^{3}-5x^{2}+40x=100

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

2x^{3}-3x^{2}=32x-48

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

The population of a species is modeled by the equation p(t) = -t4 + 72t2 + 225, where t is the number of years. Find the approximate number of years until the species is extinct.

Enter your answer as a number rounded to two decimal places.

REVIEW

A certain polynomial has an negative leading coefficient and an odd degree. What are the end behaviors of the polynomial?

REVIEW

Consider the polynomial

f(x) = 3x - x^{4} + 5

What are the end behaviors of the polynomial?

See the directions below.

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Resequence the numbers below according to the directions.

Solve by factoring.

4x^{3}-7x^{2}=3x^{2}

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

5x^{5}-80x=0

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

8x^{5}+5x^{2}=4x^{2}

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

This one will involve ugly fractions.

Solve by factoring.

81x^{3}=3

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

81x^{4}=16

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

2x^{6}-10x^{4}-48x^{2}=0

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

2x^{3}-5x^{2}+40x=100

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

Solve by factoring.

2x^{3}-3x^{2}=32x-48

Use x={#, #...} format, with one space after each comma. List the real solutions first, in increasing order, then the imaginary solutions, in increasing order. Simplify all solutions.

The population of a species is modeled by the equation p(t) = -t4 + 72t2 + 225, where t is the number of years. Find the approximate number of years until the species is extinct.

Enter your answer as a number rounded to two decimal places.

REVIEW

A certain polynomial has an negative leading coefficient and an odd degree. What are the end behaviors of the polynomial?

REVIEW

Consider the polynomial

f(x) = 3x - x^{4} + 5

What are the end behaviors of the polynomial?