# 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

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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