Question

Show that x+3 is a factor of f(x)=3x^4-3x^3-36x^2

Answer 1

f(x) = 3x^4 - 3x³ - 36x²
f(x + 3) = 3(x + 3)^4 - 3(x + 3)³ - 36(x + 3)²
f(x + 3) = 3((x + 3)(x + 3)(x + 3)(x + 3)) - 3((x + 3)(x + 3)(x + 3)) - 36((x + 3)(x + 3))
f(x + 3) = 3((x² + 6x + 9)(x² + 6x + 9)) - 3(x² + 6x + 9)(x + 3) - 36(x² + 6x + 9)
f(x + 3) = 3(x^4 + 12x³ + 54x² + 108x + 81) - 3(x³ + 9x² + 27x + 27) - 36(x² + 6x + 9)
f(x + 3) = 3x^4 + 33x³ + 99x² + 27x - 162