5-8 Rational Zero Theorem
Find all of the rational zeros of each function.
3
2
25. f (x) = 4x + x + 16x + 4
SOLUTION: The possible rational zeros are:
Test for some possible zeros using synthetic division.
is one of the zeros of the function and the depressed polynomial is .
Again use the rational root theorem and synthetic division to find the zeros of the depressed polynomial.
The polynomial
doesn’t have rational zeros. Therefore, the rational zeros of the original polynomial are
Find all of the zeros of each function.
3
2
32. f (x) = 6x + 11x – 3x – 2
SOLUTION: The possible rational zeros are:
Test for some possible zeros using synthetic division.
is one of the zeros of the function and the depressed polynomial is Factor the depressed polynomial and find its zeros.
.
eSolutions Manual - Powered by Cognero
Page 1
doesn’t have rational zeros. Therefore, the rational zeros of the original polynomial are
The polynomial
5-8 Rational Zero Theorem
Find all of the zeros of each function.
3
2
32. f (x) = 6x + 11x – 3x – 2
SOLUTION: The possible rational zeros are:
Test for some possible zeros using synthetic division.
is one of the zeros of the function and the depressed polynomial is Factor the depressed polynomial and find its zeros.
.
The zeros of the polynomial are
3
.
2
34. f (x) = 2x – 7x – 8x + 28
SOLUTION: The possible rational zeros are:
Test for some possible zeros using synthetic division.
is one of the zeros of the function and the depressed polynomial is Factor the depressed polynomial and find its zeros.
Manual - Powered by Cognero
eSolutions
.
Page 2
The zerosZero
of theTheorem
polynomial are
5-8 Rational
3
.
2
34. f (x) = 2x – 7x – 8x + 28
SOLUTION: The possible rational zeros are:
Test for some possible zeros using synthetic division.
is one of the zeros of the function and the depressed polynomial is Factor the depressed polynomial and find its zeros.
.
The zeros of the polynomial are
eSolutions Manual - Powered by Cognero
.
Page 3