Question

given f(x) and g(x), chris attempted to find g(x) - f(x). he did so incorrectly. what was his mistake? what should he have done differently? what is the correct answer?
perform the indicated operation:
g(x)=3x - 2 f(x)=x^3 - 3x^2
find g(x)-f(x)
3x - 2 - x^3 - 3x^2
-x^3 - 3x^2+3x - 2

Explanation:

Step1: Write the subtraction expression

$g(x)-f(x)=(3x - 2)-(x^{3}-3x^{2})$

Step2: Distribute the negative sign

$3x - 2 - x^{3}+3x^{2}$

Step3: Rearrange the terms in standard form

$-x^{3}+3x^{2}+3x - 2$

Chris's mistake was that when subtracting $x^{3}-3x^{2}$ from $3x - 2$, he did not distribute the negative sign correctly to the $- 3x^{2}$ term. He should have changed the sign of each term in $x^{3}-3x^{2}$ when subtracting.

Answer:

The correct answer is $-x^{3}+3x^{2}+3x - 2$. The mistake was incorrect distribution of the negative sign. He should have changed the sign of each term in $x^{3}-3x^{2}$ when subtracting it from $3x - 2$.