Chapter 8.6, Problem 5BGP

To determine

To factor: The polynomial $10y^2-35y+30$

Answer to Problem 5BGP

  $5\left(y-2\right)\left(2y-3\right)$

Explanation of Solution

Given:

  $10y^2-35y+30$

Calculation:

The given polynomial is $10y^2-35y+30$

Rewrite the middle term as $-35y=-20y-15y$ . So, the polynomial becomes

  $10y^2-20y-15y+30$

Make group as shown below

  $\left(10y^2-20y\right)+\left(-15y+30\right)$

Factor out the GCF from each of the group

  $10y\left(y-2\right)-15\left(y-2\right)$

Finally, factored out the common factor

  $\left(y-2\right)\left(10y-15\right)$

This can be further factored as

  $5\left(y-2\right)\left(2y-3\right)$

Therefore, the factored form of the given polynomial is $5\left(y-2\right)\left(2y-3\right)$