P5.8 - Remainder Theorem & Factoring Review

Last updated about 4 years ago

9 questions

Note from the author:

Instructions

P5.8 - Remainder Theorem & Factoring Review

Last updated about 4 years ago

9 questions

Note from the author:

Watch this video for a review of the Remainder Theorem.
Watch this video for a review of applying the Remainder Theorem.
Watch this video for more applications.

Instructions

Watch this video for a review of the Remainder Theorem.
Watch this video for a review of applying the Remainder Theorem.
Watch this video for more applications.

When the polynomial p(x) is divided by (x-5), there is a remainder of 7.

For what value of x must p(x) = 7?

When the polynomial q(x) is divided by (x+3), there is a remainder of 15.

What is q(-3)?

m(x) is a polynomial, and m(4) = 5.

What is the remainder when m(x) is divided by (x-4)?

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.

Solve by factoring.

8x3 - 2x2 = 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.

2x4 = 18x2

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.

2x3 + 1024 = 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.

x4 + 7x2 = 4x2 + 4

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.

x3 + 7x2 - 4x = 28

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.

P5.8 - Remainder Theorem & Factoring Review

P5.8 - Remainder Theorem & Factoring Review

When the polynomial p(x) is divided by (x-5), there is a remainder of 7.For what value of x must p(x) = 7?

When the polynomial q(x) is divided by (x+3), there is a remainder of 15.What is q(-3)?

m(x) is a polynomial, and m(4) = 5.What is the remainder when m(x) is divided by (x-4)?

Solve by factoring.8x3 - 2x2 = 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.2x4 = 18x2Use 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.2x3 + 1024 = 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. x4 + 7x2 = 4x2 + 4Use 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.x3 + 7x2 - 4x = 28Use 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.

When the polynomial p(x) is divided by (x-5), there is a remainder of 7.For what value of x must p(x) = 7?

When the polynomial q(x) is divided by (x+3), there is a remainder of 15.What is q(-3)?

m(x) is a polynomial, and m(4) = 5.What is the remainder when m(x) is divided by (x-4)?

The roots of the polynomial g(x) are {-1, 5, 7}. Which of the following binomials divides evenly into g(x) - that is, the remainder is 0?Check all that apply.

Solve by factoring.8x3 - 2x2 = 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.2x4 = 18x2Use 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.2x3 + 1024 = 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. x4 + 7x2 = 4x2 + 4Use 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.x3 + 7x2 - 4x = 28Use 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.

When the polynomial p(x) is divided by (x-5), there is a remainder of 7.

For what value of x must p(x) = 7?

When the polynomial q(x) is divided by (x+3), there is a remainder of 15.

What is q(-3)?

m(x) is a polynomial, and m(4) = 5.

What is the remainder when m(x) is divided by (x-4)?

Solve by factoring.

8x3 - 2x2 = 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.

2x4 = 18x2

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.

2x3 + 1024 = 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.

x4 + 7x2 = 4x2 + 4

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.

x3 + 7x2 - 4x = 28

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.

When the polynomial p(x) is divided by (x-5), there is a remainder of 7.

For what value of x must p(x) = 7?

When the polynomial q(x) is divided by (x+3), there is a remainder of 15.

What is q(-3)?

m(x) is a polynomial, and m(4) = 5.

What is the remainder when m(x) is divided by (x-4)?

The roots of the polynomial g(x) are {-1, 5, 7}. Which of the following binomials divides evenly into g(x) - that is, the remainder is 0?

Check all that apply.

Solve by factoring.

8x3 - 2x2 = 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.

2x4 = 18x2

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.

2x3 + 1024 = 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.

x4 + 7x2 = 4x2 + 4

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.

x3 + 7x2 - 4x = 28

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.