Mth 95 First Exam

last firstSummer 2011 Name:

(1) (3 points) Factor completely. If a polynomial is prime, state this.a. 9y2 49

b. x4 + x3 x 1

c. 36 + x4

(2) (2 points) Solve.

5

t 1 +1

t + 2=

2

3

(3) (2 points) For what values of x, if any, is this expression undefined:

x 93x x2

(4) (2 points) The length of a rectangle is 2 m more than the width. The area of therectangle is 48 m2. Find the length and width.

(5) (2 points) Divide and simplify your answer.

x2 + 3x 28x2 + 14x + 49

8 2xx + 7

2(6) (2 points) Subtract and, if possible, simplify.

2x 5x 2

x 72 x

(7) (2 points) Add and, if possible, simplify.

1

x3 + 8+

5

x2 2x + 4

(8) (2 points) Simplify.3y2 + 7

y

y 3y3

(9) a. (3 points) Suppose one painter can paint the entire house in 20 hours, and thesecond painter takes 14 hours. How long would it take the two painters together topaint the house?

b. (2 points bonus) If the two painters worked together for the first 5 hours, butthen the first painter left. How long will take the second painter to finish paintingthe house?