Use the Factor Theorem to determine whether x c is a factor

Use the Factor Theorem to determine whether x - c is a factor of f(x). F(x) = 8x^4 + 31 x^3 - 4x^2 + x - 4; x + 4 Yes No

Solution

f(x)= 8x⁴+31x³-4x²+x-4 , x+4

f(-4)= 8(-4)⁴+31(-4)³-4(-4)²-4 -4= 2048 - 1984-64 -8=-8

Since on plugging x=-4 in f(x), the result is not 0. Hence x+4 is not a factor of f(x)