section 5.5 multiplying polynomials. 5.5 lecture guide: multiplying polynomials objective 1:...
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Section 5.5
Multiplying Polynomials
5.5 Lecture Guide: Multiplying Polynomials
Objective 1: Multiply polynomials.
Multiplying a Monomial Times a Polynomial
Verbally
To multiply a monomial times a polynomial, use the distributive property to multiply the monomial times each ___________ of the polynomial.
Algebraic Example
2
2
3 2
5 2 3 8
5 2 5 3 5 8
10 15 40
x x x
x x x x x
x x x
Multiply the polynomial factors.
2 3 2 25 4ab c a bc 1.
Multiply the polynomial factors.
2. 24 5 3x x
Multiply the polynomial factors.
3. 2 2 22 (2 4 5 )x x xy y
Multiply the polynomial factors.
4. 2 28 3 7 3x xy y y
Multiplying Two Polynomials
To multiply one polynomial times another, multiply each ________________ of the first polynomial times each ________________ of the second polynomial and then combine the like terms.
Multiply the polynomial factors.
3 7x x 5.
Multiply the polynomial factors.
6. 25 2 7x x x
Multiply the polynomial factors.
7. 2 5 2 5x y x y
Multiply the polynomial factors.
8. 25 3 3x x x
Multiply the polynomial factors.
9. 2 22 1 3 3x x x x
Multiply the polynomial factors.
10. 3 2 5x x x
Using the distributive property results in multiplying each term of
Objective 2: Multiply binomials by inspection.
A helpful method for multiplying two binomials is sometimes known as the FOIL method. FOIL is an acronym for First, Outer, Inner, and Last. The logic of the FOIL method is illustrated below for the product 2 5 6 .x x
2 5x times eachterm of 6x .
This product would be simplified to
22 7 30x x
2
2 5 6 2 6 5 6
2 12 5 30
x x x x x
x x x
Think:
First terms,
Outer terms,
Inner terms,
Last terms,
2x x
2 6x
5 x
5 6
Practice using the FOIL method to multiply each pair of binomials as quickly as possible.
11. 6 8x x
Practice using this procedure to multiply each pair of binomials as quickly as possible.
12. 3 5x x
Practice using this procedure to multiply each pair of binomials as quickly as possible.
13. 4 7x x
Practice using this procedure to multiply each pair of binomials as quickly as possible.
14. 9 2x x
Practice using this procedure to multiply each pair of binomials as quickly as possible.
15. 2 5 3 1x x
Practice using this procedure to multiply each pair of binomials as quickly as possible.
16. 4 3 5 2x x
Practice using this procedure to multiply each pair of binomials as quickly as possible.
17. 8 7 2 3x x
Practice using this procedure to multiply each pair of binomials as quickly as possible.
18. 24 5x
19. Write a polynomial for the area of the figure.
4 6 cmx
3 7 cmx
Use the distributive property to expand each expression in the first column and to factor each expression in the second column.
20.
Expand Factor
21. 22 3x x x 28 12x x
Use the distributive property to expand each expression in the first column and to factor each expression in the second column.
Expand Factor
22. 23. 3 4 5xy x 215 25x y xy
Use the distributive property to expand each expression in the first column and to factor each expression in the second column.
Expand Factor
24. 25. 7 2 7x x x 7 2 7x x x
26. A concrete sidewalk of width 5 ft is poured around a circular pool of radius x ft. From the formula
the area covered by the concrete will be Expand and simplify this polynomial.
5 ftx
2A r 2 25 .A x x
27. Revenue = Number of items sold Price per item The price per unit is x and the number of units that will sell at that price is 5000 – 8.75x.
(a) Write a revenue polynomial R x for this product.
(b) Evaluate and interpret 52 .R.