Chapter 7.6, Problem 83STP

To determine

The value of $p\left(-4\right)\text{and }p\left(x+h\right)$ for the function $p\left(x\right)=x^2-x$ .

Answer to Problem 83STP

The value of $p\left(-4\right)\text{and }p\left(x+h\right)$ are $20$ and $x^2+2xh+h^2-x-h$ respectively.

Explanation of Solution

Given information: The given function is,

  $p\left(x\right)=x^2-x\mathrm{......}\left(1\right)$

Calculation: The value of $p\left(-4\right)\text{and }p\left(x+h\right)$ can be evaluated using (1) as,

  $\begin{array}{c}p\left(x\right)={\left(-4\right)}^2-\left(-4\right)\mathrm{......}\left(\text{Pluggingy }x=-4\right)\\ =16+4\\ =20\\ \text{And, }p\left(x+h\right)={\left(x+h\right)}^2-\left(x+h\right)\mathrm{......}\left(\text{Pluggingy }x=x+h\right)\\ =x^2+2xh+h^2-x-h\\ =x^2+2xh+h^2-x-h\end{array}$