AA
7-6 Rational Zero Theorem
Rational Zero Theorem:
n
n-1
* Given P(x) = a0x + a1x
+... an,
(a polynomial in standard form)
then possible factors are p ,
q
where p is a factor of an and q is a factor
of a0.
P(x) = 3x4 + 2x3 - 5x2 + 8
Integral Zero Theorem:
* If the coefficients of a polynomial
function are integers such that a0 = 1
and a ≠ 0, any rational zeros of the
n
function must be factors of a .
n
1. List all of the possible rational zeros of
each function.
4 3
a. f(x) = 3x - x + 4
4
3
b. f(x) = x + 7x - 15
You do not need to test all of the possible
zeros, once you find a factor, use the
depressed polynomial to find another
factor.
2. The volume of a rectangular solid is
1,120 cubic feet. The width is 2 feet
less than the height, and the length is 4
feet more than the height. Find the
dimensions of the solid.
3. Find all of the zeros of
f(x) = x4 + x3 - 19x2 + 11x + 30.
Lesson 7 - 6
pg. 380 - 382
#3, 13, 14, 18, 20, 21, 30, 31, 34 - 36,
37 - 38, 46, 49, 50, 52, 57, 59
(19 problems)