SECTION 5.4
Multiplying Polynomials
MULTIPLYING POLYNOMIALS

We just extend the distributive property.
First
terms
Last terms
Inner
terms
Outer
terms

In the case of two binomials, its usually called
the FOIL method.
EXAMPLE 1
Find each product.
4
a. −3𝑎 4 + 𝑎
b.
(2𝑚 + 6)(5𝑚 − 3)
EXAMPLE 2
2𝑦 5 (𝑦 − 8)(𝑦 + 2)
EXAMPLE 3
(4𝑧 + 2)(𝑧 2 − 3𝑧 − 5)
DIFFERENCE OF TWO SQUARES PATTERN
 What
happens below?
𝑥+𝑦 𝑥−𝑦 =
EXAMPLE 4
a.
b.
𝑦+2 𝑦−2
(5𝑟 + 4𝑠)(5𝑟 − 4𝑠)
DIFFERENCE OF TWO SQUARES PATTERN
 What
happens below?
(𝑥 + 𝑦)2 =
EXAMPLE 5
(5𝑟 − 7𝑠)2
SECTION 5.5
Dividing Polynomials
THINK BACK TO FRACTIONS . . .

What happens below?
1 4
+ =
6 6
EXAMPLE 1
27𝑚4 −18𝑚3 +9𝑚
a.
9
12𝑎𝑏2 𝑐 + 10𝑎2 𝑏𝑐 +18𝑎𝑏𝑐 2
b.
6𝑎2 𝑏𝑐
THINK BACK TO LONG DIVISION . . .
24 33482
EXAMPLE 2
(𝑥2 + 14𝑥 + 45) ÷ (𝑥 + 9)
EXAMPLE 3
8𝑚3 − 18𝑚2 + 37𝑚 − 13
2𝑚2 − 3𝑚 + 6
WHAT HAPPENS IF WE HAVE MISSING TERMS?
 What
happens with 1001 ÷ 5?
 Write
the polynomial in standard form.
 If
any power is missing, use a zero to
hold the place of that term.
EXAMPLE 4
2𝑥4 + 3𝑥3 – 7𝑥 − 10
𝑥2 – 2𝑥
EXAMPLE 5
9𝑘4 + 12𝑘3 – 4𝑘 − 1
3𝑘2 – 1
QUESTIONS???
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