Question

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

f(x) = $3x^4+17x^3+9x^2$ - 7x - 10; g(x) = x + 5

Answer 1

f(x) = $3x^4+17x^3+9x^2$ - 7x - 10; g(x) = x + 5

Let x + 5 = 0, then x = - 5

$\therefore$ Remainder = f(-5) = $3(-5{)}^4+17(-5{)}^3+9(-5{)}^2$-7(-5)-10

=$3\times 625+17\times (-125)+9\times \left(25\right)-7\times (-5)-10$

=1875 - 2125 + 225 + 35 - 10

=2135 - 2135 = 0

$\because$ Remainder = 0

$\therefore$ (x + 5) is a factor of f(x)