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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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to or or the coeff of like terms vertical format
To + or - , + or – the coeff. of like terms!Vertical format :
  • Add 3x3+2x2-x-7 and x3-10x2+8.
  • 3x3 + 2x2 – x – 7 + x3 – 10x2 + 8 Line up like terms
  • 4x3 – 8x2 – x + 1
horizontal format combine like terms
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
examples adding subtracting
Examples: Adding & Subtracting
  • (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
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
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
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
some binomial products appear so much we need to recognize the patterns
Some binomial products appear so much we need to recognize the patterns!
  • 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
Last Pattern
  • Cube of a Binomial
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3
  • (a – b)3 = a3 - 3a2b + 3ab2 – b3
example
Example:
  • (x + 5)3 =

a = x and b = 5

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

x3 + 15x2 + 75x + 125