Chapter 8.6, Problem 16PPS

To determine

To factor: The polynomial $40-22x+x^2$ . Confirm your answer using a graphing calculator.

Answer to Problem 16PPS

  $\left(x-20\right)\left(x-2\right)$

Explanation of Solution

Given:

  $40-22x+x^2$

Calculation:

The given polynomial is $40-22x+x^2$

Write this is standard form

  $x^2-22x+40$

Rewrite the middle term as $-22x=-20x-2x$ . So, the polynomial becomes

  $x^2-20x-2x+40$

Make group as shown below

  $\left(x^2-20x\right)+\left(-2x+40\right)$

Factor out the GCF from each of the group

  $x\left(x-20\right)-2\left(x-20\right)$

Finally, factored out the common factor

  $\left(x-20\right)\left(x-2\right)$

Therefore, the factored form of the given polynomial is $\left(x-20\right)\left(x-2\right)$

Now, using a graphing calculator, the factor of the polynomial is given by

  $\left(x-20\right)\left(x-2\right)$

So, the answer is verified.