6.3 Adding, Subtracting, & Multiplying Polynomials

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6.3 Adding, Subtracting, & Multiplying Polynomials - PowerPoint PPT Presentation

6.3 Adding, Subtracting, & Multiplying Polynomials. p. 338. To + or - , + or – the coeff. of like terms! Vertical format :. Add 3x 3 +2x 2 -x-7 and x 3 -10x 2 +8. 3x 3 + 2x 2 – x – 7 + x 3 – 10x 2 + 8 Line up like terms 4x 3 – 8x 2 – x + 1.

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6.3 Adding, Subtracting, & Multiplying Polynomials

p. 338

• 3x3 + 2x2 – x – 7 + x3 – 10x2 + 8 Line up like terms
• 4x3 – 8x2 – x + 1
Horizontal format : Combine like terms
• (8x3 – 3x2 – 2x + 9) – (2x3 + 6x2 – x + 1)=
• (8x3 – 2x3)+(-3x2 – 6x2)+(-2x + x) + (9 – 1)=
• 6x3 + -9x2 + -x + 8 =
• 6x3 – 9x2 – x + 8
• (9x3 – 2x + 1) + (5x2 + 12x -4) =
• 9x3 + 5x2 – 2x + 12x + 1 – 4 =
• 9x3 + 5x2 + 10x – 3
• (2x2 + 3x) – (3x2 + x – 4)=
• 2x2 + 3x – 3x2 – x + 4 =
• 2x2 - 3x2 + 3x – x + 4 =
• -x2 + 2x + 4
Multiplying Polynomials: Vertically
• (-x2 + 2x + 4)(x – 3)=
• -x2 + 2x + 4 * x – 3

3x2 – 6x – 12 -x3 + 2x2 + 4x -x3 + 5x2 – 2x – 12

Multiplying Polynomials : Horizontally
• (x – 3)(3x2 – 2x – 4)=
• (x – 3)(3x2)
• + (x – 3)(-2x)
• + (x – 3)(-4) =
• (3x3 – 9x2) + (-2x2 + 6x) + (-4x + 12) =
• 3x3 – 9x2 – 2x2 + 6x – 4x +12 =
• 3x3 – 11x2 + 2x + 12
Multiplying 3 Binomials :
• (x – 1)(x + 4)(x + 3) =
• FOIL the first two:
• (x2 – x +4x – 4)(x + 3) =
• (x2 + 3x – 4)(x + 3) =
• Then multiply the trinomial by the binomial
• (x2 + 3x – 4)(x) + (x2 + 3x – 4)(3) =
• (x3 + 3x2 – 4x) + (3x2 + 9x – 12) =
• x3 + 6x2 + 5x - 12
• Sum & Difference (S&D):
• (a + b)(a – b) = a2 – b2
• Example: (x + 3)(x – 3) = x2 – 9
• Square of Binomial:
• (a + b)2 = a2 + 2ab + b2
• (a - b)2 = a2 – 2ab + b2
Last Pattern
• Cube of a Binomial
• (a + b)3 = a3 + 3a2b + 3ab2 + b3
• (a – b)3 = a3 - 3a2b + 3ab2 – b3
Example:
• (x + 5)3 =

a = x and b = 5

x3 + 3(x)2(5) + 3(x)(5)2 + (5)3 =

x3 + 15x2 + 75x + 125