In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
f(x) = 2x³-9x²+x+12, g(x) = 3-2x

Question

In each of the following, use factor theorem to find whether polynomial g ( x ) is a factor of polynomial f ( x ) or, not: f ( x ) = 2 x 3 -9 x 2 + x +12, g ( x ) = 3-2 x

Philoid · Accepted Answer

We have,

f(x) = 2x³-9x²+x+12 and g(x) = 3-2x

In order to find g (x) = 3 – 2x = 2 (x - ) is a factor of f (x) or not, it is sufficient to prove that f () = 0

Now,

f(x) = 2x³-9x²+x+12

f () = 2 ()³ – 9 ()² + + 12

= - + + 12

=

= 0

Hence, g (x) is a factor of f (x).

In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:f(x) = 2x3-9x2+x+12, g(x) = 3-2x

In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
f(x) = 2x³-9x²+x+12, g(x) = 3-2x