Review the following concepts if needed:
 Polynomial Functions Help
 Sketching Graphs of Polynomials Help
 Polynomial Division Help
 Synthetic Division Help
 Factoring Polynomials Help
 Descartes Rule of Signs Help
 Complex Numbers Help
 Complex Solutions to Quadratic Equations Help
 The Fundamental Theorem of Algebra Help
Polynomial Functions Practice Test
Problems

What are the x intercepts of f(x) = x ^{2} ( x + 3)( x − 2)?
(a) −3 and 2 (b) 3 and −2 (c) 0, −3, and 2 (d) 0, 3, and −2

The graph in Figure 7.20 is the graph of which function?
(a) f(x) = 2 x ^{2} ( x − 1)( x + 2) = 2 x ^{4} + 2 x ^{3} − 4 x ^{2}
(b) f(x) = −2 x ^{2} ( x − 1)( x + 2) = −2 x ^{4} − 2 x ^{3} + 4 x ^{2}
(c) f(x) = 2 x ( x − 1)( x + 2) = 2 x ^{3} + 2 x ^{2} − 4 x
(d) f(x) = −2 x ( x − 1)( x + 2) = −2 x ^{3} − 2 x ^{2} + 4 x

What is the quotient and remainder for
(a) The quotient is x − 1, and the remainder is − 3 x − 3.
(b) The quotient is x − 1, and the remainder is − x + 3.
(c) The quotient is x + 1, and the remainder is x + 3.
(d) The quotient is x + 1, and the remainder is 3 x + 3.

Use synthetic division to find the quotient and remainder for (2 x ^{3} − x ^{2} + 2 x + 4) ÷ ( x − 3).
(a) The quotient is 2 x ^{2} + x + 5, and the remainder is 19.
(b) The quotient is 2 x ^{2} + 5 x + 7, and the remainder is 29.
(c) The quotient is 2 x ^{2} + 5 x + 17, and the remainder is 55.
(d) The quotient is 2 x ^{2} + x + 3, and the remainder is 7.

What is the quotient for ( x ^{4} + x ^{3} − 3 x + 5) ÷ (−2 x ^{2} + x − 6)?

Completely factor P ( x ) = 4 x ^{3} + 4 x ^{2} − x − 1.
(a) ( x − 1) ^{2} (4 x + 1)
(b) ( x + 1)(2 x − 1)(2 x + 1)
(c) ( x + 1) ^{2} (4 x − 1)
(d) ( x − 1)(2 x − 1)(2 x + 1)

Find all solutions for x ^{2} + 2 x + 4 = 0.

What is the quotient for ?

According to the Rational Zero Theorem, which is NOT a possible rational zero for f(x) = 4 x ^{5} − 6 x ^{3} + 2x ^{2} − 6 x − 9?
(a) −4 (c) 3 (d) −9

According to Descartes’ Rule of Signs, how many positive zeros does f(x) = 4 x ^{5} − 6 x ^{3} + 2 x ^{2} − 9 have?
(a) 3 (b) 2 or 0 (c) 2 (d) 3 or 1

Find all zeros for f(x) = x ^{3} − 6 x ^{2} + 13 x − 10.
(a) −2, 2 ± i (b) 2, 2 ± i (c) 2, 1 ±2 i (d) −2, 1 ±2 i
Solutions
 C
 A
 B
 C
 D
 B
 A
 D
 A
 D
 B
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