MJ2A

Ch 13.4 – Multiplying a Polynomial by a Monomial

Bellwork

• Simplify each expression

1. (x)(3x)2. (2y)(4y)3. (t2)(6t)4. (4m)(m2)

Solutions

3x2

6t3

8y2

4m3

Assignment Review

• Text p. 680 # 10 – 25

Before we begin…

• Please take out your notebook and get ready to work…

• In the last two lessons we looked at adding and subtracting polynomials…

• In today’s lesson we will look at multiplying a polynomial by a monomial…

• We will use the distributive property here…you are required to recognize and know how to work with the distributive property!

Objective 13.4

• Students will multiply polynomials by monomials

Background Knowledge

• At this point you should all know that the rules for multiplying are not the same as adding…

• For example you cannot add polynomials unless you have like terms…

• That doesn’t apply to multiplying…• I can multiply a ● b to get ab• Also, at this point you should know that if

you multiply a ● a you get a2

Strategy

• When multiplying monomials and polynomials a good strategy is to segment the parts…

• What that means is you do a step by step process doing the coefficients first, then the variables, then the exponents, and finally the sign of the terms…

• This strategy is effective because it minimizes errors…

• Let’s look at an example…

Example Multiply- 2a2 (- 3a)

1. Multiply the coefficients to get 6

62. Multiply the variables to

get a3 a3

3. Multiply the signs – negative times negative = positive

+

In this example the solution is +6a3

Distributive Property• When multiplying a polynomial by a

monomial you will use the distributive property…

• That is you will multiply what on the outside of the parenthesis with EACH term on the inside of the parenthesis

• Let’s look at an example…

Example #1

(2x – 6)(3x)

6x2– 18x2. Then multiply 3x times – 6 to get – 18x

1. Multiply 3x times 2x to get 6x2

6x2 – 18x is the solution

Example #2

(3a)(a2 + 2ab -4b2)

3a3+6a2b

2. Then multiply 3a ● 2ab to get + 6a2b

1. Multiply 3a ● a2 to get 3a3

3a2 + 6a2b – 12ab2 is the solution

-12ab2

3. Then multiply 3a ● -4b2 to get -12ab2

Your Turn

• In the notes section of your notebook write and multiply the polynomial by the monomial.

1. (5y – 4)32. (3x – 7)4x3. -5( 3x2 – 7x + 9)

Solutions

15y - 12

-15x2 + 35x - 45

12x2 – 28x

Summary

• In the notes section of your notebook summarize the key concepts covered in today’s lesson

• Today we discussed:• Multiplying polynomials by monomials• What methodology will you use?• What strategy will you use?

Assignment

• Text p. 685 # 11 – 24Reminder

• This assignment is due tomorrow• I do not accept late assignments• You must show how you got your answer

(no work = no credit)