Polynomials Lesson 3: Multiplying and Factoring Polynomials using the
Distributive Method
Todays Objectives:
 Students will be able to demonstrate an understanding of the multiplication of
polynomial expressions, including:
 Generalize and explain a strategy for multiplication of polynomials
 Identify and explain errors in a solution for a polynomial expression
 Generalize and explain strategies used to factor a trinomial
 Express a polynomial as a product of its factors
Multiplying Polynomials
 Today we will look at a strategy for multiplying and factoring polynomials:
 _____________ ______________
 When binomials have ______________ terms, it is difficult to show their product
using algebra tiles, but we can use a rectangle diagram or the
__________________ property.
 Algebra tiles are limited to multiplying 2 _______________. The distributive
property can be used to multiply any ________________.
Distributive Property
 Consider the following example: (8 − 𝑏)(3 − 𝑏)
 First we multiply each term in the first brackets by both terms in the second
bracket. We call this “distributing”
 (8 – 𝑏)(3 – 𝑏) =
 =
 Next, we combine _______ _________
 Like terms are terms that have the same _____________ which have the
same ___________, or ______________
 In this case _____and _____are like terms. Both terms have the variable
“b”, with the same degree, or exponent (1). ____ is not a like term
because “b” has an exponent, or degree of 2
 =
Example (You do)
 Use the distributive property to find the product of the binomials (𝑐 + 3)(𝑐 + 5)
Solution:
 Notice from the trinomial:
 8 is the _______ of 3 and 5
 15 is the __________ of 3 and 5
 The leading _______________ of the trinomial is 1, as are the leading
coefficients of the binomial factors
Example
 Factor the trinomial x2 – 4x – 21 into two binomials.
 Answer will be in the form (x + a)(x + b), where we know the following:
 
 
 So we need to find two numbers that ______ to -4, and ______________ to -21
 Find all factors of -21
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 Find one set of factors that add to -4

 So, a = ___, b = ___
Example (You do)
 Factor the trinomial z2 – 12z + 35
Solution:
Example
 List all the factors for the polynomial 2x2 – 10x + 12
 Solution: First, remove the _______
 *you must include the factored out 2 as a factor in your final answer!
 Now, factor the trinomial:

 Find all the factors of +6 
 Find one set of factors that add to – 5 
 So, a = ____, b = _____ Factors of the polynomial 2x2 – 10x + 12 are:

Example (You do)
 Factor -4t2 – 16t + 128
Solution:
The _____________ ___________ can be used to perform any polynomial multiplication.
Each term of one polynomial must be ____________ by each term of the other
polynomial.
Using the distributive property to multiply two polynomials
Multiply (2h + 5)(h2 + 3h – 4)
Solution:Multiply each term in the trinomial by each term in the binomial. Write the
terms in a list.
 = (2ℎ)(ℎ2 + 3ℎ – 4) + 5(ℎ2 + 3ℎ – 4)
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Example:(-3f2 + 3f – 2)(4f2 – f – 6)
Solution:
Use the distributive property. Multiply each term in the 1st trinomial by each term in the
2nd trinomial. ______like terms.
Check:One way to check that your product is correct is to ________ a ________ for the
___________ in both your answer and the original question. If both sides are _______,
then your answer is correct. For this example, let’s let f = 1.
Since the left side _________ the right side, the product is likely correct.
Example (You do)
Use the distributive property to multiply.
(3x – 2y)(4x – 3y + 5)
Solution:
Example:Simpify (2c – 3)(c + 5) + 3(c – 3)(-3c + 1)
Solution:
Use the ________ ___________ ________. Multiply before adding and subtracting.
Then, ____________ like terms.
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Example (You do): (3x + y – 1)(2x – 4) – (3x + 2y)2
Solution:
Homework: pg. 186-187, # 5,7,9,11,15-17, 21