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1. f(x) = π₯ 3 β π₯ 2 β 8 x + 12

2. h(x) = 2π₯ 3 β 3π₯ 2 β 2 x + 3

3. g(x) = 36π₯ 4 β 13 π₯ 2 + 1

4. g(x) = π₯ 3 + 3π₯ 2 β 6 x β 8

NAME _____________________________________________ DATE ____________________________ PERIOD _____________
2-4 Practice
Zeros of Polynomial Functions
List all possible rational zeros of each function. Then determine which, if any, are zeros.
1. f(x) = π₯ 3 β π₯ 2 β 8x + 12
2. h(x) = 2π₯ 3 β 3π₯ 2 β 2x + 3
3. g(x) = 36π₯ 4 β 13π₯ 2 + 1
4. g(x) = π₯ 3 + 3π₯ 2 β 6x β 8
Solve each equation.
5. 2π₯ 4 + 9π₯ 3 β 87π₯ 2 β 49x + 45 = 0
6. π₯ 3 β 5π₯ 2 β 17x = β21
7. Determine an interval in which all real zeros of f(x) = π₯ 4 + π₯ 3 β 7π₯ 2 β x + 6 must lie. Explain your reasoning using
the upper and lower bound tests. Then find all real zeros.
8. Describe the possible real zeros of f(x) = π₯ 4 + 2π₯ 3 β 13π₯ 2 β 14x + 24.
Write a polynomial function of least degree with real coefficients in standard form that has the given zeros.
9. β5,
1+ β11π 1β β11π
2
,
2
10. 1, β1, β3i, β β3i
Use the given zero to find all real zeros of each function. Then write the linear factorization of p(x).
11. p(x) = π₯ 4 β 5π₯ 3 + 8π₯ 2 β 20x + 16; 2i
12. p(x) = π₯ 4 + 4π₯ 3 β 2π₯ 2 β 4x + 16; 1 + i
13. DRIVING An automobile moving at 12 meters per second on level ground begins to decelerate at a rate of 1.6
1
meters per second squared. The formula for the distance an object has traveled is d(t) = π£0 t + ππ‘ 2 , where π£0 is the
2
initial velocity and a is the acceleration. For what value(s) of t does d(t) = 40 meters?
Chapter 2
23
Glencoe Precalculus
...

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