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Multiplication of Two Polynomials Help

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By and — McGraw-Hill Professional
Updated on Sep 26, 2011

Multiplication of Two Polynomials

Two polynomials can be multiplied by using the distributive property as many times as needed. It is the same as shown for two binomials.

Examples

Example 1

Multiply (x + 2)(x 2 + 5x - 6).

Solution 1

Multiplication of Two Polynomials

Multiplication of polynomials can be performed vertically. The process is similar to multiplying whole numbers.

Example 2

Multiply (x + 2)(x 2 + 5x - 6) vertically.

Solution 2

Multiplication of Two Polynomials

Example 3

Multiply (x 2 + 3x - 8)(3x - 5) vertically.

Solution 3

Multiplication of Two Polynomials

Math Note: Be sure to place like terms under each other when multiplying vertically.

Multiplication of Two Polynomials Practice Problems

Practice

Multiply:

1. (x 2 + 3x + 2)(x + 1)

2. (3x 2 + 2x + 5)(x -6)

3. (2x 2 + 4x -1)(2x - 3)

4. (x 3 - 2x 2 + 2x + 1)(x - 5)

5. (x 2 + 2x + 7)(x 2 - x -6)

Answers

1. x 3 + 4x 2 + 5x + 2

2. 3x 3 - 16x 2 - 7x - 30

3. 4x 3 + 2x 2 - 14x + 3

4. x 4 - 7x 3 + 12x 2 - 9x - 5

5. x 4 + x 3 - x 2 - 19x - 42

Practice problems for these concepts can be found at: Operations With Monomials And Polynomials Practice Test.

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