Consider the function f(x) = x3 + 8x2 - 24x + 470. What is the remainder if f(x) is divided by (x - 12)? Do not include (x - 12) in your answer. Provide your answer below: remainder:Given that the degree of the polynomialflIx) is 8, which of the following most accurately describes the number ofx intercepts thatf'(.t) has? Select the correct answer below: 0 x) has at least 9x-intercepts. 0 x) has at least '3' xintercepts. 0 x) has at least Sxintercepts. 0 x) has at most 7" xintercepts. 0 x) has at most 9 x-intercepts. 0 x) has at most 3 xintercepts. Describe the end behavior of the function f(x) = -6x(x - 3)(x + 7)(4x + 1)? Provide your answer below: As x goes to oo , f (x ) goes to As x goes to -oo , f (x ) goes toGiven that the polynomial f(x) has degree 4, which of the following most accurately describes the number of turning points of f(x)? Select the correct answer below: O The graph of f(x) has at least 5 turning points. O The graph of f(x) has at least 4 turning points. O The graph of f(x) has at most 5 turning points. O The graph of f(x) has at most 3 turning points. O The graph of f(x) has at most 4 turning points. O The graph of f(x) has at least 3 turning points