MATH 1050 SECTION 2 QUIZ 1
FALL 2009
1. Simplify
p
75x2 y −4 so that all exponents are positive.
solution.
√
√
√ √
75 x2
3 25|x|
5 3|x|
p
=
.
=
=
y2
y2
y4
Note that we could have put |y 2 | in the denominator. This is not strictly necessary since y 2 is already
positive. We do need absolute value brackets around x since x could be positive or negative.
s
p
75x2 y −4
75x2
=
y4
√
2. Completely factor and simplify:
3(3 − 4x)2 − 8(3 − 4x)(5x − 1).
solution.
3(3 − 4x)2 − 8(3 − 4x)(5x − 1) = 3(3 − 4x)(3 − 4x) − 8(3 − 4x)(5x − 1)
= (3 − 4x)(3(3 − 4x) − 8(5x − 1)) = (3 − 4x)(9 − 12x − 40x + 8) = (3 − 4x)(17 − 52x).
3. Factor 3x2 − 5x + 2.
solution. There are several ways to factor this polynomial. Any method is acceptable so long as you
get the right answer. We’ll factor by grouping:
3x2 − 5x + 2 = 3x2 − 3x − 2x + 2 = 3x(x − 1) − 2(x − 1) = (x − 1)(3x − 2).
Remember that it is always good to check your answer by multiplying out the factorization and
verifying that you get back the original polynomial.
4. Complete the subtraction and simplify:
3
− 5.
x−1
solution.
3
3
5(x − 1)
3 − 5x + 5
8 − 5x
−5=
−
=
=
.
x−1
x−1
x−1
x−1
x−1
1