Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21.

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Presentation transcript:

Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy

6.3 – Adding, Subtracting, & Multiplying Polynomials Algebra 2

In order to add and subtract polynomials horizontally, just combine like terms. Add and subtract polynomials horizontally.

Horizontal format: Combine like terms (8x 3 – 3x 2 – 2x + 9) – (2x 3 + 6x 2 – x + 1) = (8x 3 – 2x 3 ) + (-3x 2 – 6x 2 ) + (-2x + x) + (9 – 1) = 6x x 2 + -x + 8 = 6x 3 – 9x 2 – x + 8

(9x 3 – 2x + 1) + (5x x -4) = 9x 3 + 5x 2 – 2x + 12x + 1 – 4 = 9x 3 + 5x x – 3 (2x 2 + 3x) – (3x 2 + x – 4) = 2x 2 + 3x – 3x 2 – x + 4 = 2x 2 - 3x 2 + 3x – x + 4 = -x 2 + 2x + 4

In order to multiply horizontally, distribute all terms in the first polynomial to the second polynomial. Multiply polynomials horizontally.

(x – 3)(3x 2 – 2x – 4)= (x – 3)(3x 2 ) + (x – 3)(-2x) + (x – 3)(-4) = (3x 3 – 9x 2 ) + (-2x 2 + 6x) + (-4x + 12) = 3x 3 – 9x 2 – 2x 2 + 6x – 4x +12 = 3x 3 – 11x 2 + 2x + 12 Horizontal format: Distribute

(x – 1)(x + 4)(x + 3) = FOIL the first two: (x 2 – x + 4x – 4)(x + 3) = (x 2 + 3x – 4)(x + 3) = Then multiply the trinomial by the binomial: (x 2 + 3x – 4)(x) + (x 2 + 3x – 4)(3) = (x 3 + 3x 2 – 4x) + (3x 2 + 9x – 12) = x 3 + 6x 2 + 5x - 12 Multiplying Three Binomials

(x + 5) 3 = x x x + 125

pgs #18-26 even, 30, 33, 36, 47 DEFEAT YOUR HOMEWORK TONIGHT: CHUCK NORRIS STYLE Assignment