Question

In the following exercise, find the difference of the polynomials.

Find the difference of $\left(z^2-3z-18\right)$ and$\left(z^2+5z-20\right)$

Short answer

$\text{Thedifferenceof}\left(z^2-3z-18\right)\text{and}\left(z^2+5z-20\right)\text{is}-8z+2.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionsare}\\ \left(z^2-3z-18\right)\text{and}\left(z^2+5z-20\right)\\ \text{Wehavetofindthedifference}\\ i.e\text{Tofind:}\left(z^2-3z-18\right)-\left(z^2+5z-20\right)\end{array}$

Step 2. Calculating the difference

$\begin{array}{l}\Rightarrow \left(z^2-3z-18\right)-\left(z^2+5z-20\right)\\ =z^2-3z-18-z^2-5z+20\left[\text{Rewritewithoutparentheses}\right]\\ =z^2-z^2-3z-5z-18+20\left[\text{Combinetheliketerms}\right]\\ =-8z+2\left[\text{Simplify}\right]\end{array}$