Chapter 8.6, Problem 44HP

To determine

To state: If either of Jerome or Charles is correct? Explain your reasoning.

Answer to Problem 44HP

Both of them are incorrect.

Explanation of Solution

Given:

Jerome and Charles have factored $x^2+6x-16$

Below are their works

Jerome: $x^2+6x-16=\left(x+2\right)\left(x-8\right)$

Charles: $x^2+6x-16=\left(x+2\right)\left(x+8\right)$

Calculation:

The given polynomial is $x^2+6x-16$

Find the factored form of this polynomial

Write the middle as

  $x^2+8x-2x-16$

Make group as shown below

  $\left(x^2+8x\right)+\left(-2x-16\right)$

Now, factored out the GCF from each group

  $x\left(x+8\right)-2\left(x+8\right)$

Now, factored out the common term

  $\left(x+8\right)\left(x-2\right)$

So, both of them are incorrectly found the factored form of the given polynomial.