P5.5: Solving Polynomial Equations

Akwankyerɛ

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}
5
-1
-8/5

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?

x\rightarrow\infty, f(x)\rightarrow\infty

x\rightarrow\infty, f(x)\rightarrow -\infty

x\rightarrow -\infty, f(x)\rightarrow\infty

x\rightarrow -\infty, f(x)\rightarrow -\infty

Impossible to determine, not enough information.

1

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

x\rightarrow\infty, f(x)\rightarrow\infty

x\rightarrow\infty, f(x)\rightarrow -\infty

x\rightarrow -\infty, f(x)\rightarrow\infty

x\rightarrow -\infty, f(x)\rightarrow -\infty

Impossible to determine, not enough information.

1

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?