Question:
Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x), or not:
$f(x)=2 x^{3}-9 x^{2}+x+13, g(x)=3-2 x$
Solution:
Here, $f(x)=2 x^{3}-9 x^{2}+x+13$
g(x) = 3 - 2x
To prove that g(x) is the factor of f(x),
To prove that g(x) is the factor of f(x),
we should show ⟹ f(3/2) = 0
here, 3 - 2x = 0
⟹ -2x = -3
⟹ 2x = 3
⟹ x = 3/2
Substitute the value of x in f(x)
$f(3 / 2)=2(3 / 2)^{3}-9(3 / 2)^{2}+(3 / 2)+13$
= 2(27/8) − 9(9/4) + 3/2 + 12
= (27/4) − (81/4) + 3/2 + 12
Taking L.C.M
$=\frac{21-81+6+48}{4}$
$=\frac{81-81}{4}$
= 0
Since, the result is 0 g(x) is the factor of f(x)