Factor Quadratic Trinomials with Leading Coefficient Other than 1: example 7.41

Factor: $10 y^{2} - 55 y + 70$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor: $16 x^{2} - 32 x + 12$ .

How did it go?

Is there a greatest common factor? Yes. The GCF is 5.
Factor it. Be careful to keep the factor of 5 all the way through the solution!
The trinomial inside the parentheses has a leading coefficient that is not 1.
Factor the trinomial.
Check by mulitplying all three factors.
$5 (2 y^{2} - 2 y - 4 y + 14)$
$5 (2 y^{2} - 11 y + 14)$
$10 y^{2} - 55 y + 70 ✓$

Is there a greatest common factor? Yes. The GCF is 5.
Factor it. Be careful to keep the factor of 5 all the way through the solution!
The trinomial inside the parentheses has a leading coefficient that is not 1.
Factor the trinomial.
Check by mulitplying all three factors.
$5 (2 y^{2} - 2 y - 4 y + 14)$
$5 (2 y^{2} - 11 y + 14)$
$10 y^{2} - 55 y + 70 ✓$