Lesson
Real Zeros for a Polynomial Function
Use the Remainder Theorem to find the remainder when f(x) is divided b
y
x - c.
1) f(x) = x4 + 8x3 + 12x2; x + 1
Use the Factor Theorem to determine whether x - c is a factor of f(x).
2) f(x) = x3 + 8x2 - 18x + 20; x + 10
3) f(x) = x4 - 5x2 - 36; x - 6
4) f(x) = x4 + 8x3 + 9x2 + 69x - 24; x - 8
5) f(x) = 6x3 + 16x2 - 52x - 110; x + 11
3
6) 7x4 + 20x3 - 3x2 + x + 3; x + 3
List the potential rational zeros of the pol
y
nomial function. Do not find the zeros.
7) f(x) = 7x4 - x2 + 3
8) f(x) = -2x3 + 4x2 - 3x + 8
9) f(x) = 2x5 - 6x2 + 2x - 1
Use the Rational Zeros Theorem to find all the real zeros of the pol
y
nomial function. Use the zeros to
factor f over the real numbers.
10) f(x) = x3 + 2x2 - 9x - 18
11) f(x) = 2x3 - 11x2 + 2x + 15
12) f(x) = 3x3 - 4x2 + 15x - 20
13) f(x) = 4x4 - 9x3 + 25x2 - 45x + 25
Find the intercepts of the function f(x).
14) f(x) = x3 + 3x2 - 4x - 12
CollegeAlgebra
