Question

One of the zeros of the polynomial function is 5. f(x) = x⁴ - 4x³ - 21x² + 100x - 100 What is the factored form of the function? (a) f(x) = (x - 5)(x + 5)(x - 2)(x + 2) (b) f(x) = (x - 5)(x + 5)(x - 2)² (c) f(x) = (x - 2)²(x - 5)² (d) f(x) = (x - 2)(x + 2)(x - 5)²

Answer 1

To find the factored form of the polynomial function f(x) = x⁴ - 4x³ - 21x² + 100x - 100 with one zero at 5, we can use synthetic division. By dividing the polynomial by (x - 5), we find that the quotient is x³ + x² - 16x + 20. Then, we can factor the cubic polynomial to get f(x) = (x - 5)(x + 2)(x - 2)(x + 5). Therefore, the factored form of the function is (d) f(x) = (x - 2)(x + 2)(x - 5)².

Step-by-step explanation:

To find the factored form of the polynomial function f(x) = x⁴ - 4x³ - 21x² + 100x - 100 with one zero at 5, we can use synthetic division. By dividing the polynomial by (x - 5), we find that the quotient is x³ + x² - 16x + 20. Then, we can factor the cubic polynomial to get f(x) = (x - 5)(x + 2)(x - 2)(x + 5). Therefore, the factored form of the function is (d) f(x) = (x - 2)(x + 2)(x - 5)²