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

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Warm-Up: Graph the polynomial. Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 x y -2 1 1 4 0 1 1 -2 2 1

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

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

Warm-Up: Graph the polynomial.Warm-Up: Graph the polynomial.

f(x) = x3 – 4x + 1

x y

-2 1

1 4

0 1

1 -2

2 1

Page 2: Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21.

6.3 – Adding, Subtracting, 6.3 – Adding, Subtracting, & Multiplying Polynomials& Multiplying Polynomials

Algebra 2Algebra 2

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

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

Add and subtract polynomials horizontally.Add and subtract polynomials horizontally.

http://graphicshunt.com/images/oranges-13944.htm
Page 4: Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21.

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

Page 5: Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21.

(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

Page 6: Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21.

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

Multiply polynomials horizontally.Multiply polynomials horizontally.

Page 7: Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21.

(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

Horizontal format: Distribute

Page 8: Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21.

(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

Multiplying Three Binomials

Page 9: Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21.

(x + 5)3 =

x3 + 15x2 + 75x + 125

Page 10: Warm-Up: Graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21.

pgs. 341-342 #18-26 even, 30, 33, 36, 47

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