§ 5.2 multiplication of polynomials. blitzer, algebra for college students, 6e – slide #2 section...
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Blitzer, Algebra for College Students, 6e – Slide #2 Section 5.2
Multiplying Polynomials
EXAMPLEEXAMPLE
SOLUTIONSOLUTION
Multiply
yxyx 724 36
. 36 724 yxyx
127436 yyxx Rearrange factors
Multiply coefficients andadd exponents
127418 yx
31118 yx Simplify
Blitzer, Algebra for College Students, 6e – Slide #3 Section 5.2
Multiplying Polynomials
EXAMPLEEXAMPLE
SOLUTIONSOLUTION
Multiply . 7536 253 xxx
7536 253 xxx
765636 32353 xxxxx Distribute
Multiply coefficients andadd exponents
358 423018 xxx
Blitzer, Algebra for College Students, 6e – Slide #4 Section 5.2
Multiplying Polynomials
EXAMPLEEXAMPLE
SOLUTIONSOLUTION
Multiply . 22 bababa
22 bababa
2222 bababbabaa Multiply the trinomial by each term of the binomial
Multiply coefficients andadd exponents
2222 bbabbabbaabaaa 322223 babbaabbaa
33 ba
Distribute
Simplify
Note this: We multiply each term of the binomial by each term of the trinomial. We get 6 products in all.
Blitzer, Algebra for College Students, 6e – Slide #5 Section 5.2
Multiplying Polynomials - FOIL
dbcxbdaxcxaxdcxbax
Using the FOIL Method to Multiply Binomials
first
outside
inside
last F O I L
Product of First terms
Product of Outside terms
Product of Inside terms
Product of Last terms
Blitzer, Algebra for College Students, 6e – Slide #6 Section 5.2
Multiplying Polynomials - FOIL
EXAMPLEEXAMPLE
SOLUTIONSOLUTION
Multiply . 1534 xx
1534 xx 13531454 xxxx
Combine like terms
Multiply315420 2 xxx
31920 2 xx
F O I Lfirst
outside
inside
last
Blitzer, Algebra for College Students, 6e – Slide #7 Section 5.2
Multiplying Polynomials – Special Formulas
The Square of a Binomial Sum
22 BABABA
The Square of a Binomial Difference
222 2 BABABA
222 2 BABABA
The Product of the Sum and Difference of Two Terms
Blitzer, Algebra for College Students, 6e – Slide #8 Section 5.2
Multiplying Polynomials – Special Formulas
EXAMPLEEXAMPLE
SOLUTIONSOLUTION
Multiply .4 2yx
24 yx
222 2 BABABA
Use the special-product formula shown.
+ + = Product
+ +
2
Term
First
Terms theof
Product22
Term
Last
24x yx422y 22 816 yxyx
Blitzer, Algebra for College Students, 6e – Slide #9 Section 5.2
Multiplying Polynomials – Special Formulas
EXAMPLEEXAMPLE
SOLUTIONSOLUTION
Multiply . 43 2yx
243 yx
222 2 BABABA
Use the special-product formula shown.
- + = Product
- +
2
Term
First
Terms theof
Product22
Term
Last
23x yx 432 24y22 16249 yxyx
Blitzer, Algebra for College Students, 6e – Slide #10 Section 5.2
Multiplying Polynomials – Special Formulas
EXAMPLEEXAMPLE
SOLUTIONSOLUTION
Multiply . 4343 22 yxyyxy
222 4 3 yxy
22 BABABA
Use the special-product formula shown.
First Term Squared
Second Term Squared
Product- =
= 242 169 yyx
Blitzer, Algebra for College Students, 6e – Slide #11 Section 5.2
Multiplying Polynomials – Special Formulas
EXAMPLEEXAMPLE
SOLUTIONSOLUTION
Multiply . 33 yxyx
92 22 yyxx
2A
We can group the terms so that the formula for the square of a binomial can be applied.
2B(A + B) (A - B) = - 22 333 yxyxyx
92 22 yxyx
Blitzer, Algebra for College Students, 6e – Slide #12 Section 5.2
Multiplying Polynomial Functions
EXAMPLEEXAMPLE
SOLUTIONSOLUTION
following. theofeach Find .10 and 4Let xxgxxf
4062 xx
(a) (fg)(x) = f (x) g(x)
404102 xxx
(a) (fg)(x)(b) (fg)(-1)(c) (fg)(0)
= (x - 4)(x + 10)F O I L
. 4062 xxxfgThus,
Blitzer, Algebra for College Students, 6e – Slide #13 Section 5.2
Multiplying Polynomial Functions
45401611 2 fg
CONTINUECONTINUEDD
(b) We use the product function to find (fg)(-1) – that is, the value of the function fg at -1. Replace x with -1.
40400600 2 fg
(c) We use the product function to find (fg)(0) – that is, the value of the function fg at 0. Replace x with 0.