Multiplying Polynomials

January 29, 2009

Page 416-417 #10-38 even10) terms: 5x3, x;

coefficients: 5, 112) term: 7x2; coeff: 714) monomial16) monomial18) Not a polynomial20) Not classified

(quadnomial)22) binomial24) 3x3 + 5x2+4, degree is 326) x2 –x+4, degree is 2

28) x17 -3x4, degree is 1730) 15, 032) 5, -1534) 34, 3436) -1, 1938) 0, 0

Objectives

• Find the product of a monomial and a polynomial.

• Find the product of two polynomials.• Square a binomial.• Find the product of two binomials that differ

on in sign.

Multiplying a polynomial by a monomial

• Use the distributive property to multiply each term in the polynomial by the monomial.

x(2x+1)2x2+x

Multiplying polynomials

Method 1: The Distributive Property1. Distribute the first binomial over the second

binomial.2. Multiply.3. Combine like terms.(2x+1)(x-5)= 2x(x-5)+1(x-5)= 2x2-10x+x-5= 2x2-9x-5

Multiplying polynomialsMethod 2: FOIL (only works for binomials)1. Multiply the FIRST term of each binomial.2. Multiply the OUTER term of each binomial.3. Multiply the INNER term of each binomial.4. Multiply the LAST term of each binomial.5. Combine like terms.(3x-1)(2x+2)F O I L6x2 +6x -2x -2= 6x2+4x-2

Multiplying PolynomialsMethod 3:Completing the square.1. Write each binomial along the sides of a square…2. Multiply each item…3. Add the items together…4. Combine like terms.(3x+4)(2x+1)6x2+8x+3x+46x2+11x+4

6x2 8x

3x 4

Multiplying polynomialsMethod 4: Vertical Method1. Line up the polynomials.2. Multiply each term, like compound multiplication.3. Add.4. Combine like terms.

x2 +3x +5 x -2 .

-2x2 -6x -10x3 +3x2 +5x .x3 +x2 -x -10