 # 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.

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