Chapter 8.6, Problem 4CYU

To determine

To factor: The polynomial $m^2-15m+50$ . Confirm your answer using a graphing calculator.

Answer to Problem 4CYU

  $\left(m-10\right)\left(m-5\right)$

Explanation of Solution

Given:

  $m^2-15m+50$

Calculation:

The given polynomial is $m^2-15m+50$

Rewrite the middle term as $-15m=-10m-5m$ . So, the polynomial becomes

  $m^2-10m-5m+50$

Make group as shown below

  $\left(m^2-10m\right)+\left(-5m+50\right)$

Factor out the GCF from each of the group

  $m\left(m-10\right)-5\left(m-10\right)$

Finally, factored out the common factor

  $\left(m-10\right)\left(m-5\right)$

Therefore, the factored form of the given polynomial is $\left(m-10\right)\left(m-5\right)$

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

  $\left(m-10\right)\left(m-5\right)$

So, the answer is verified.