Math Analysis Honors – Worksheet 18
Real Zeros of Polynomial Functions
Find the real zeros of the function. Write the function in factored form. You may use a calculator to find
enough zeros to reduce your function to a quadratic equation using synthetic substitution.
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f ( x ) = 2x 3 − 13x 2 + 24x − 9
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f ( x ) = x 3 − 8x 2 + 17x − 6
f ( t ) = t 3 − 4t 2 + 4t
f ( x ) = x 4 − x 3 − 20x 2
f ( x ) = 4x 3 + 4x 2 − 7x + 2
f ( x ) = x 4 − x 3 − 6x 2 + 4x + 8
f ( x ) = x 3 + 3x 2 − 3x − 9
f ( x ) = x 3 + x 2 − 8x − 6
Find k such that f ( x ) = x 3 − kx 2 + kx + 2 has a factor of x − 2
What is the remainder when f ( x ) = 2x 20 − 8x10 + x − 2 is divided by x − 1 ? (Hint: Do not use synthetic or
long division)
One solution of the equation x 3 − 8x 2 + 16x − 3 = 0 is 3 . Find the sum of the remaining solutions.
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List the zeros of the polynomial, f ( x ) = x ( x − 2 ) ( x + 1) ( x − 5 ) and their multiplicities. Draw a possible
sketch of f ( x ) .