college algebra

Question

Find a polynomial of degree 3 with only real coefficients and zeros of −4​, 1​, and 0 for which f(4)=−1.Choose the correct polynomial of degree 3 with only real coefficients and zeros of −4, 1, and 0 for which f(4)=−1.

A.

​f(x)=−118x3−518x3+118x3+3

B.

​f(x)=196x3+132x2−124x

C.

​f(x)=−118x3−518x3+118x3

D.

​f(x)=−196x3−132x2+124x

Answer 1

x(x+4)(x-1) = x(x^2 +3x-4 = x^3 +3x^2 - 4x has the right zeroes

but f(4) = 4(8)3) = 96 Not -1

(-1/96(4(8)(3) = -1

(-1/96)(x)(x+4)(x-1) ==-(1/96)x^3 - (1/32)x^2 + (1/24)x

C has only a zero of 0 with multiplicity 3

plus 4 into D: -196(64) -132(16) + 124(4) which doesn't = -1

plug 4 into B: 196(64) + 132(16) - 124(40 doesn't = -1

plug 4 into A -158(64)+3 doesn't = -1

none of the choices are correct, Not A, B, C or D