Chapter 8.6, Problem 2CYU

To determine

To factor: The polynomial $y^2-7y-30$ . Confirm your answer using a graphing calculator.

Answer to Problem 2CYU

  $\left(y-10\right)\left(y+3\right)$

Explanation of Solution

Given:

  $y^2-7y-30$

Calculation:

The given polynomial is $y^2-7y-30$

Rewrite the middle term as $-7y=-10y+3y$ . So, the polynomial becomes

  $y^2-10y+3y-30$

Make group as shown below

  $\left(y^2-10y\right)+\left(3y-30\right)$

Factor out the GCF from each of the group

  $y\left(y-10\right)+3\left(y-10\right)$

Finally, factored out the common factor

  $\left(y-10\right)\left(y+3\right)$

Therefore, the factored form of the given polynomial is $\left(y-10\right)\left(y+3\right)$

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

  $\left(y-10\right)\left(y+3\right)$

So, the answer is verified.