If f(x) = 2x3 − 13x2

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