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*3³
72 = 2*2*2*3*3 = 2³*3²

The powers of 2 are 2¹ and 2³. The smallest
power is 2¹.
The powers of 3 are 3³ and 3². The smallest
power is 3².
Taking the smallest powers gives a GCF of
2¹*3² = 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 x³,x¹, x². 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 x⁵ and x³. The smallest
power is x³.
The GCF is 6x³. Factoring the GCF from both
terms gives
18x⁵+ 6x³= 6x³(3x² + 1)

b. The only common factor of 21 and 15 is 3.
The powers of x are x² and x¹. The smallest
poweris x¹.
The powers of y are y³ and y⁴. The smallest
power is y³.
The GCF is 3xy³. 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

Slope-intercept form

When an equation is in slope-intercept form
the slope is the coefficient of x . The

b. To find the x-intercept substitute 0 for y and
solve for x .

5x+6y=70
5x + 6 * 0 = 70
5x = 70
x=14

The x-intercept= (14,0).
The constant is 35/3 so the

The distance between the two points is 13.