3.4 Fundamental Theorem of Algebra
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2. Find all the zeros of the polynomial function and write the polynomial Hint: First determine the as a product of its leading coefficient and its linear factors. (
rational zeros.) P(x) = 4x4 − x3 − 8x2 + 18x − 4 x = Factor the polynomial.
P(x) = 2
3. Find all the zeros of the polynomial function and write the polynomial Hint: First determine the as a product of its leading coefficient and its linear factors. (
rational zeros.) P(x) = 6x3 − 17x2 + 34x − 20 x = Factor the polynomial.
P(x) = 3
5. Use the given zero to find the remaining zeros of each polynomial function. (Enter your answers as a comma­separated list. Enter all answers including repetitions.) P(x) = 2x3 − 5x2 + 6x − 2; (1 + i) 4
6. Use the given zero to find the remaining zeros of each polynomial function. (Enter your answers as a comma­separated list. Enter all answers including repetitions.) P(x) = x3 + 8x2 + x + 8; −i
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9. Find a polynomial function of lowest degree with integer coefficients that has the given zeros. 3, −6, 2
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10. Find a polynomial function of lowest degree with integer coefficients that has the given zeros. 0, i, −i 7
Find a polynomial function P with real coefficients that has the indicated zeros and satisfies the given conditions. Zeros: −1, 2, 3; degree 3; P(1) = 20 8