Download Simplify. 22. (z – 3z + 2z – 4z + 4)(z – 1) SOLUTION: 23. (x – 4x + 4x

5-2 Dividing Polynomials
Simplify.
4
3
2
–1
22. (z – 3z + 2z – 4z + 4)(z – 1)
27. SOLUTION: 5
3
SOLUTION: 2
23. (x – 4x + 4x ) ÷ (x – 4)
SOLUTION: 4
2
25. (g – 3g – 18) ÷ (g – 2)
SOLUTION: 28. SOLUTION: 27. SOLUTION: 3
2
29. (2b – 6b + 8b) ÷ (2b + 2)
SOLUTION: Synthetic division:
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5-2 Dividing Polynomials
3
2
6
29. (2b – 6b + 8b) ÷ (2b + 2)
5
3
31. (10y + 5y + 10y – 20y – 15)(5y + 5)
SOLUTION: −1
SOLUTION: Synthetic division:
6
4
32. CCSS REASONING A rectangular box for a new
product is designed in such a way that the three
dimensions always have a particular relationship
defined by the variable x. The volume of the box can
–1
2
30. (6z + 3z – 9z )(3z – 6)
SOLUTION: 3
2
be written as 6x + 31x + 53x + 30, and the height is
always x + 2. What are the width and length of the
box?
Synthetic division:
SOLUTION: Divide the function by the height (x + 2) to find the
length and width. Use synthetic division.
6
5
3
31. (10y + 5y + 10y – 20y – 15)(5y + 5)
−1
SOLUTION: The depressed polynomial is
.
Since the volume of the box is the product of length,
width and height, the width and length of box are (2x
+ 3)(3x + 5).
33. PHYSICS The voltage V is related to current I and
power P by the equation
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32. CCSS REASONING A rectangular box for a new
. The power of a
3
2
generator is modeled by P(t) = t + 9t + 26t + 24. If
the current of the generator is I = t + 4, write anPage 2
expression that represents the voltage.
SOLUTION: Since the volume of the box is the product of length,
width and height, the width and length of box are (2x
+ 3)(3x +Polynomials
5).
5-2 Dividing
33. PHYSICS The voltage V is related to current I and
power P by the equation
35. BUSINESS The number of magazine subscriptions
. The power of a
sold can be estimated by
generator is modeled by P(t) = t + 9t + 26t + 24. If
the current of the generator is I = t + 4, write an
expression that represents the voltage.
3
the amount of money the company spent on
advertising in hundreds of dollars and n is the number
of subscriptions sold.
SOLUTION: a. Perform the division indicated by
2
,where a is
.
b. About how many subscriptions will be sold if
$1500 is spent on advertising?
SOLUTION: Synthetic division:
a.
35. BUSINESS The number of magazine subscriptions
sold can be estimated by
,where a is
b. There are 15 hundreds in 1500. Substitute a = 15.
the amount of money the company spent on
advertising in hundreds of dollars and n is the number
of subscriptions sold.
a. Perform the division indicated by
.
b. About how many subscriptions will be sold if
$1500 is spent on advertising?
SOLUTION: a.
Therefore, about 2423 subscriptions will be sold.
Simplify.
4
4
36. (x – y ) ÷ (x – y)
SOLUTION: b. There are 15 hundreds in 1500. Substitute a = 15.
3 2
2
37. (28c d – 21cd ) ÷ (14cd)
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3 2
2
–1
5-2 Dividing Polynomials
3 2
2
37. (28c d – 21cd ) ÷ (14cd)
SOLUTION: 3 2
2
38. (a b – a b + 2b)(–ab)
–1
SOLUTION: 41. SOLUTION: 44. CHALLENGE If a polynomial is divided by a
binomial and the remainder is 0, what does this tell
you about the relationship between the binomial and
the polynomial?
SOLUTION: If a polynomial divided by a binomial has no
remainder, then the polynomial has two factors: the
binomial and the quotient.
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