Question

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x)

f(x) = $x^5+3x^4-x^3-3x^2$ + 5x + 15, g(x) = x + 3

Answer 1

f(x) = $x^5+3x^4-x^3-3x^2$ + 5x + 15, g(x) = x + 3

Let x + 3 = 0, then x = - 3

$\therefore$ Remainder = f(-3)

$=(-3{)}^5+3(-3{)}^4-(-3{)}^3-3(-3{)}^2+5(-3)+15$

= - 243 + 3$\times$ 81 -(-27) - 3 $\times$ 9 + 5 (-3) + 15

=-243 + 243 + 27 -27 - 15 + 15

=285-285 = 0

$\therefore$ Remainder = 0

$\therefore$ (x + 3) is a factor fo f(x)