Question:
If $f(x)=2 x^{3}-13 x^{2}+17 x+12$, Find
1. $f(2)$
2. $f(-3)$
3. $f(0)$
Solution:
The given polynomial is $f(x)=2 x^{3}-13 x^{2}+17 x+12$
1. $f(2)$
we need to substitute the ' 2 ' in $f(x)$
$f(2)=2(2)^{3}-13(2)^{2}+17(2)+12$
$=(2 * 8)-(13 * 4)+(17 * 2)+12$
$=16-52+34+12$
$=10$
therefore $f(2)=10$
2. $f(-3)$
we need to substitute the '(-3)' in f(x)
$f(-3)=2(-3)^{3}-13(-3)^{2}+17(-3)+12$
$=\left(2^{*}-27\right)-\left(13^{*} 9\right)-\left(17^{*} 3\right)+12$
$=-54-117-51+12$
= -210
therefore f(-3) = -210
3. f(0)
we need to substitute the '(0)' in f(x)
$f(0)=2(0)^{3}-13(0)^{2}+17(0)+12$
= (2 * 0) - ( 13 * 0) + (17 * 0) + 12
= 0 - 0 + 0 + 12
= 12
therefore f(0) = 12