chapter 6 – polynomials and polynomial functions 6.4 – multiplying and dividing polynomials

Chapter 6 – Polynomials and Polynomial Functions

6.4 – Multiplying and Dividing Polynomials

6.4 – Multiplying and Dividing PolynomialsToday we will be learning how to:

Multiply and divide polynomials


To multiply two polynomials, you multiply each term of the first polynomial by each term of the second polynomial.

You can use a vertical or a horizontal format.


Example 1 - verticallyFind the product of (3x2 + 3x + 5)(2x + 3)


Example 2 - horizontallyFind the product of

(x – 5)(x2 – 2x + 3)

(x + 3)(x – 4)(x + 5)


Special ProductsSum and Difference

(a + b)(a – b) = a2 – b2

(x + 4)(x – 4) = x2 – 16

Square of a binomial (a + b)2 = a2 + 2ab + b2

(x + 3)2 = x2 + 6x + 9 (a – b)2 = a2 – 2ab + b2

(3x – 4)2 = 9x2 – 24x + 16


Special Products continuedCube of a binomial

(a + b)3 = a3 + 3a2b + 3ab2 + b3

(x + 2)3 = x3 + 6x2 + 12x + 8

(a – b)3 = a3 – 3a2b + 3ab2 – b3

(x – 2)3 = x3 – 6x2 + 12x – 8


Example 3Find the product of (5y – 3)(5y + 3)


Example 4Find the product of (4a + 7)2


Example 5 Find the product of (m – 6)3


HOMEWORK

6.4 Worksheet

#1 - 18


Dividing PolynomialsYou can divide polynomials using

polynomial long divisionYou follow the same steps to divide

polynomials as you do to divide whole numbers

divide, multiply, subtract and bring downBefore dividing polynomials, make sure the

dividend and divisor are in standard form


Example 6Find the quotient of 875 ÷ 31


Example 7Find the quotient of (3x3 + 17x2 + 21x – 11)

÷ (x + 3)


HOMEWORK

6.4 Worksheet

#21 – 29

chapter 6 – polynomials and polynomial functions 6.4 – multiplying and dividing polynomials

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