1) Give an example of each:
a) quadratic monomial
b) cubic trinomial
c) quintic binomial
d) monic polynomial
d) perissodactyl ungulate
2) Classify each polynomial. Be as specific as possible. If an expression is not a
polynomial, say so.
a) 5x 2 + 3x ! 2
b) 7x 4
c) x 2 + 5x ! 3
3) In the expression 5 x ! 7x 2 + 6x , what are the coefficients?
4) Do all the arithmetic and simplify completely:
a) 3(x 2 ! 5x ! 8) ! 4(x 2 ! 6x + 12) + (x + 3) 2
b) (x 2 ! 5x ! 8)(x 2 ! 6x + 12)
c) (2x ! 3)(x + 2)(x ! 5)
d) (2x + 3) 2
e) (2x + 3) 3
f) (3 + 2 7) 2
5) Factor each polynomial completely. If a polynomial is prime, say so.
a) x 2 ! 5x + 6
b) x 2 ! 5x ! 6
c) 4 x 3 ! 9x
d) 6x 2 + 5x + 1
e) x 4 ! 81
f) x 2 + 9
6) Solve each equation:
a) x 2 ! 5x = 0
b) (x ! 3) 2 + 7 = (x + 4) 2
c) x 2 ! x ! 6 = 0
7) Rationalize each denominator:
3
3
a)
b)
2 7
2+5 7
8) Simplify each fraction completely. If a fraction is in lowest terms, say so:
2x + 6
2x + 6
x2 ! 4
a)
b)
c) 2
x!3
2x ! 6
x + 10x + 16