Answer
$-15x^3+3x^2+3x+2$
Work Step by Step
Removing the parenthesis and then combining like terms, the given expression, $
(-14x^3-x+2)+(-x^3+3x^2+4x)
,$ is equivalent to
\begin{array}{l}\require{cancel}
-14x^3-x+2-x^3+3x^2+4x
\\=
(-14x^3-x^3)+3x^2+(-x+4x)+2
\\=
-15x^3+3x^2+3x+2
.\end{array}
Let
\begin{array}{l}\require{cancel}Y_1=
(-14x^3-x+2)+(-x^3+3x^2+4x)
,\\Y_2=
-15x^3+3x^2+3x+2
.\end{array}
Using a graphing calculator, the graphs of $Y_1$ (dotted graph) and $Y_2$ (solid graph) are shown below. Since the graphs overlap, then $Y_2$ is the correct simplification of $Y_1.$
