Use the Factor Theorem to determine whether x-c is a factor of f(x). f(x) = x^4
ID: 3036928 • Letter: U
Question
Use the Factor Theorem to determine whether x-c is a factor of f(x). f(x) = x^4 +11x^3 + 5x^2 +48x-77; x + 11 ______________ List the potential rational zeros of the polynomial function. Do not find the zeros. f(x) = 7x^3 - x^2 + 3 ____________ Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x) = x^3 + 2x^2 - 5x-6 _____________ solve the equation in the real number system. 2x^3-9x^2 +7x +6 = 0 _______________ Use the Intermediate value Theorem to determine whether the polynomial function has a zero in the given interval. f(x) = 10x^3 - 6x^2 - 8x + 3; [1, 2] _____________ solve the problem. The polynomial function f(x) = 6x^3 + 25x^2 + 12x - 7 has exactly one positive zero. Use the Intermediate Value Theorem to approximate the zero correct to 2 decimal places __________________Explanation / Answer
f(x) = x^4 + 11x^3 + 5x^2 + 48x - 77
factor theorem says f(x) at x= -11 must be zero
So, f(-11) = (-11)^4 + 11(-11)^3 + 5(11)^2 + 48(-11) - 77
= 11^4 - 11^4 + 605 - 528 - 77
= 605 - 605
= 0
So, (x+11) is a factor of f(x)
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