5.3 Operations on Polynomial FunctionsObjectives:

Learn to add, sub, multiply polynomial functions

Example 1Add

(5x2 + 3x + 4) + (3x2 + 5)

= 8x2 + 3x + 9

Example 2Add.

(2x4 – 5x2 + 4x + 5) + (5x4 + 7x3 – 2x2 – 2x)

2x4 + 0x3 – 5x2 + 4x + 55x4 + 7x3 – 2x2 – 2x + 0

7x4 + 7x3 – 7x2 + 2x + 5

Practice

1) (-2m3 – 5m2 – 2m – 4) + (m4 – 6m2 + 7m – 10)

Add.

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Example 1Subtract.

(5x2 + 3x - 2) - (2x2 + 1)

= 5x2 + 3x - 2 - 2x2

= 3x2

- 1

+ 3x - 3

Practice

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1) (5x4 + 4) – (2x2 – 1)

Subtract.

2) (-7m3 + 2m + 4) – (-2m3 – 4)

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Example 2Subtract.

(8x3 + 6x2 – 3x + 5) – (5x3 – 3x2 + 2x – 4)

8x3 + 6x2 – 3x + 5-5x3

3x3

+ 3x2 - 2x + 4

+ 9x2 - 5x + 9

Practice

1) (-2m3 – 5m2 – 2m – 4) - (m4 – 6m2 + 7m – 10)

Subtract.

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Example 1Multiply.

(x + 1)(x2 + x + 1)

= (x)(x2 + x + 1)

= (x3 + x2 + x)

= x3

+ (1)(x2 + x + 1)

+ (x2 + x + 1)

+ 2x2 + 2x + 1

Example 2Multiply.

(2x + 3)(x2 + 4x + 5)

= (2x)(x2 + 4x + 5)

= (2x3 + 8x2 + 10x)

= 2x3

+ (3)(x2 + 4x + 5)

+ (3x2 + 12x + 15)

+ 11x2 + 22x + 15

Practice

1) (x2 + 5)(x2 + 3x – 4)

Multiply.

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Example 3Multiply.

(5x2 + 3x + 2)(3x2 + 2x – 1)

15x4

9x3

6x2

15x4

+ 10x3 – 5x2

+ 6x2 – 3x+ 4x - 2

+ 19x3 + 7x2 + x - 2

Practice

1) (3x2 – 2x + 4)(x2 + 5x + 1)

Multiply.

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Assignment

• Pg 349, 350 #3-33 multiples of 3, 59