warm-up: graph the polynomial. f(x) = x 3 – 4x + 1 xy -21 14 01 1 21
TRANSCRIPT
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
6.3 – Adding, Subtracting, 6.3 – Adding, Subtracting, & Multiplying Polynomials& Multiplying Polynomials
Algebra 2Algebra 2
• In order to add and subtract polynomials horizontally, just combine like terms.
Add and subtract polynomials horizontally.Add and subtract polynomials horizontally.
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
• In order to multiply horizontally, distribute all terms in the first polynomial to the second polynomial.
Multiply polynomials horizontally.Multiply 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
Horizontal format: Distribute
(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
(x + 5)3 =
x3 + 15x2 + 75x + 125
pgs. 341-342 #18-26 even, 30, 33, 36, 47
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