Sample Midterm
1) Add the polynomials:
(4x3y + 7x2y2 – 5y) + (4x3y − 2x2y2 – 3y)
2) Subtract the polynomials:
(9x2 – 4x + 1) – (x2 + 2x – 5)
3) Multiply the following terms:
(6x3y)(-2xy)
4) Multiply the polynomials:
(4x – 1)(2x2 + 5x – 3)
5) Multiply the polynomials:
(3x + 2)(3x – 2)
6) Multiply the polynomials:
(4x – 5)2
7) divide the polynomial by the monomial:
16 x 3  8 x 2  12 x
4x
8) Divide the polynomial by the binomial:
7 x  4 x 2  9  4 x3
2x 1
9) Simplify, using the rules of exponents:
(4x2y)3
10) Simplify, using the rules of exponents, then give the answer using only positive
exponents:
(5x-3y)-2
11) Simplify, using the rules of exponents:
6 x 3 y
2 xy 1
12) Simplify, using the rules of exponents:
8 x5 y 2
2 xy
13) Compute:
6-2
14) Write 6.501 × 1011 as a regular number
15) Write 3.42 × 10-7 as a regular number
16) Write 0.000000401 using scientific notation
17) Give the degree of the polynomial (caution: the polynomial might not be in descending
order):
4x3 + 5x2y2 – 5y
18) Give an example of a trinomial
Directions: for problems 19-27, factor completely (or state that it is prime)
19) x2 – 2x – 15
20) 2x4 – 50
21) x3 + 2x2 – 9x – 18
22) 4x2 + 8x – 5
23) 7y4 + 14y3 + 7y2
24) 21a2 – 35a
25) 24a4b + 60a3b2 + 150a2b3
26) r2 – 36
27) r2 + 36
Directions: Foe problems 28 – 31, solve by factoring:
28) x2 + 8x + 12 = 0
29) 4x2 = 12x – 9
30) x2 = 8x
31) 4x2 = 81
32) A ball is thrown from the top of a building 160 feet high, with an initial speed of 48 feet
per second. The formula:
h = -16t2 +48t + 160
gives the height (above the ground) of the ball t seconds after it was thrown. How long until
the ball hits the ground?
3x2
6x
33) Simplify:
x2  y2
4 y  4x
34) Simplify:
35) Divide:
x2  x
x2 1

x2  4 x2  5x  6
36) Subtract:
2x  5 6x  4

x2
x2