5.11 multiplying polynomials goal: multiply any two polynomials

5.11 Multiplying Polynomials

• Goal: Multiply any two polynomials

To Multiply Polynomials…….

Multiply each term of one polynomial by every term of the other, then add the results

You may either use arrows or the chart to multiply

(2x)(3x2 – 4x + 2)

6x3

+-8x2

+4x

(2x + 3)(4x + 2)

8x2

+4x

+12x

+ 6

8x2 + 16x + 6

(2x2 + 5)(3x2 – 4x + 2)

6x4

-8x3 +4x2+15x

2-20x

+106x4 – 8x3 + 19x2 –20x

+10

(2x + 3)(x2 + 4x + 5)2x3 + 8x2 + 10x

3x2 + 12x + 152x3 + 11x2 + 22x + 15

(b2 + 5)(b2 + 3b – 4)Chart method

b4 + 3b3 -4b2 + 5b2 + 15b+ - 20

b2 5

b2

3b

-4

b4 5b2

3b3 15b

-4b2 -20

=b4 + 3b3 +b2 +15b -20

(3x + 4y)(2x – 3y + 5)you choose your method

6x2 +- xy +– 12y2 + 15x + 20y

Rules for Multiplying PolynomialsA polynomial and a monomial:• Distribute the mono by the polyTwo binomials• (A +B) (A+B) = (A+B) ² = A² +2AB +B²• (A- B) (A-B) = (A –B)² = A² -2AB +B²• (A-B) (A+B) = (A² -B²)• Any two terms you may FOIL or use a chartAny two polynomials:• Multiply each term of one poly by the other poly

AssignmentPage 251

(2-50) even