math basic algebra work sheets 12 work sheets

Math 090 Wk 7 TU Individual Sheet

1. Multiply.

14x2y3(−2x5y) 5r3(2r2 + 3r + 4) (2y − 5)(3y + 4)

m3(3m + 7)(3m − 7) (2x + 5)2

2. Divide.

64x3 − 72x2 + 12x 8x3

p3 + 3p2 − 4 p + 2

3. Divide. If there is a remainder, write your solution in the form P (x)

D(x) = Q(x) +

R(x)

D(x) where P (x) is the

dividend; D(x) is the divisor; Q(x) is the quotient; and R(x) is the remainder.

(3k3 + 9k − 14) ÷ (k − 2)

4. Given f(x) = x2 − 2x, g(x) = x − 3, and h(x) = x3 − 2x2 − 9, find the following. (fg)(x) = f(x) · g(x) (fg)(−1)

(f ◦ g)(x) = f(g(x)) f(g(−1))

( h

g

) (x) =

h(x)

g(x)

( h

g

) (−1)

5. For P (x) = x3 − 4x2 + 3x − 5 and D(x) = x + 1, find the following. P (x)

D(x)

P (−1) note this is x = −1, which comes from setting x + 1 = 0 and solving for x. Compare this with your remainder above. What does this suggest?