5.5 Multiplying and Dividing a Polynomial by a Constant

Distributive Property To determine the product of multiplying a binomial or trinomial by a constant, we use the distributive property. Multiply each term in brackets by the term outside of brackets. (*Watch the signs*) -5(4e 2 – 5e + 3) = (-5)(4e 2 ) -5(4e 2 – 5e + 3) + (-5)(-5e) + (-5)(3)

= -20e e + (-15) = -20e e -15 After we have multiplied each term by (-5), we simplify. = (-5)(4e 2 ) + (-5)(-5e) + (-5)(3)

Try these: 1) Multiply. Write the product. 2 (-2b 2 – b + 3) 2(-2b 2 ) +2(-b) + 2(3) -4b 2 – 2b + 6

-3m mn – 21n 2 -3 Write the quotient expression as the sum of 3 fractions. Each term of the trinomial has to be divided by the denominator. -3m mn - 21n Simplify each fraction. m 2 + (-5mn) + 7n 2 = m 2 – 5mn + 7n 2

2) Divide. Write the quotient. 7x 2 -7x x 2 – 7x x 2 + 1x – 3

Multiplying with Algebra tiles 3(-2m + 4) We display the expression in brackets 3 times. There are 6 “–m” tiles and 12 1-tiles. Therefore, 3(-2m +4) = -6m + 12

Dividing with Algebra tiles 6x ÷ 3 To model 6x ÷ 3, we arrange six x-tiles in 3 rows. Each row contains two x-tiles. So, 6x ÷ 3 = 2x

Dividing binomials and trinomials by a constant using tiles 1) 4s 2 – 8 4 In each row there is one s 2 tile and two - 1tiles. = s 2 -2

Assignment: p.246 #3, 4, 5a, 6, 7a, 8a, 15ace, 16ace, 18ac, 22, 23, then 9ab, 20ab

Try these: 1) Sketch algebra tiles to multiply. Write the product. 2 (-2b 2 – b + 3) 2) Divide. 7x 2 -7x