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Exponents and Factoring
Section 6.2
1.
3.
5.
7.a
b. Factoring 54 and 72 with a factor tree, we
have
54 = 2*3*3*3 = 2*3^{3}
72 = 2*2*2*3*3 = 2^{3}*3^{2}
The powers of 2 are 2^{1} and 2^{3}. The smallest
power is 2^{1}.
The powers of 3 are 3^{3} and 3^{2}. The smallest
power is 3^{2}.
Taking the smallest powers gives a GCF of
2^{1}*3^{2} = 18
54y + 72 = 18(3y + 4)
c. The GCF of 14,7, and 42 is 7.
Only the variable x appears in all three terms
of the polynomial .
The powers of x are x^{3},x^{1}, x^{2}. The smallest
power is x.
This gives a GCF of 7*x =7x. Factoring, we
have
d.
the
factorization checks
9. a. The GCF of 18 and 6 is 6.
The powers of x are x^{5} and x^{3}. The smallest
power is x^{3}.
The GCF is 6x^{3}. Factoring the GCF from both
terms gives
18x^{5}+ 6x^{3}= 6x^{3}(3x^{2} + 1)
b. The only common factor of 21 and 15 is 3.
The powers of x are x^{2} and x^{1}. The smallest
poweris x^{1}.
The powers of y are y^{3} and y^{4}. The smallest
power is y^{3}.
The GCF is 3xy^{3}. Factoring the GCF from
both terms gives
11. surface area =
13. a. The terms of an expression are separated by
addition or subtraction and we do not count
extra terms inside grouping symbols . This
gives two terms (x + 3)*4y and (x + 3)*9.
Common to both terms is the binomial
(x + 3).
b. (x + 3)(4y + 9)
15.
Skills and Review 6.2
part = percent*whole,
or solute = percent*solution
solute = .25*2 L
solute = .5 L; there is .5 L of alcohol in the
solution .
21.
This is one of several correct proportions. For
help, see setting up proportions on page 180 of
the text.
Let w = the width of the enlargement in inches,
then w + 6 = length of the enlargement.
The width of the enlargement is 9 inches and the
length is 9 + 6 or 15 inches.
23.a. Solving the equation for y in terms of x puts
the equation in slope intercept form and this
gives the slope and y intercept.
5x + 6y =70 Standard form
Slopeintercept form
When an equation is in slopeintercept form
the slope is the coefficient of x. The
b. To find the xintercept substitute 0 for y and
solve for x .
5x+6y=70
5x + 6 * 0 = 70
5x = 70
x=14
The xintercept= (14,0).
The constant is 35/3 so the
The distance between the two points is 13.
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