### Home > CCAA8 > Chapter 5 Unit 6 > Lesson CCA: 5.3.3 > Problem5-120

5-120.

For the function $g(x) = x^{3} + x^{2} − 6x$, find the value of each expression below.

1. $g(1)$

Substitute $1$ for $x$ in the given equation and then evaluate.

$g(1)=(1)^3+(1)^2-6(1)$

$g(1)=1+1-6$

$g(1)=-4$

1. $g(−1)$

$6$

1. $g(−2)$

$8$

1. $g(10)$

1. Find at least one value of $x$ for which $g(x) = 0$.

Let $g(x) = 0$ in the original equation and then solve for $x$.

$0=x^3+x^2-6x$
$0=x(x^2+x-6)$
$0=x(x+3)(x-2)$

$x = −3$, $0$, $2$

1. If $f(x) = x^{2} − x + 3$, find $g(x) − f(x)$.

$g(x) − f(x) = \left(x^{3} + x^{2} − 6x\right) − \left(x^{2} − x + 3\right)$

Remove parentheses. Pay attention to the minus sign in front of $f(x)$. Combine like terms.