July 16th ClassNotes

Algebra: Polynomial Multiplication

Monomial * Polynomial

Expand out the monomial

Example:

3x² (2x⁴ + 4x²)

= 6x⁶ + 12x⁴

Binomial * Binomial

Use the FOIL method

First - Multiply the first term in each set of parentheses

Outer - Multiply the outer term in each set of parentheses

Inner - Multiply the inner term in each set of parentheses

Last  - Multiply the last term in each set of parentheses

Example:

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

= 2x * 5x + 2x * (-2) + 3 * 5x + 3 * (-2)

= 10x² +  -4x + 15x + -6

= 10x² + 11x - 6

                                            

Binomial * Polynomial

Expand each term of binomial to polynomial

Example:

(8x – 4) (6x² + 3x -9)

= 8x(6x² + 3x -9) – 4 (6x² + 3x -9)

= 48x³ + 24x² - 72x – 24x² – 12x + 36

= 48x³ – 84x + 36

Dividing by a Monomial

Divide each term by the monomial

Example:

(18x⁴ – 12x³ + 24x²) / 6x²

= 3x² – 2x + 4

Division by a Binomial

Use long Division

Example:

(12x³ + 23x²  + 16x + 4) / (3x + 2)

                                           4x² 5x + 2

     3x + 2 / 12x³ + 23x²  + 16x + 4

                 - (12x³ + 8x²)

                                15x² + 16x

                             -(15x² + 10x) 

                                                6x + 4

                                             -(6x + 4)

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