# Factoring Trinomials with a ≠ 1 – Practice ProblemsHaving fun while studying, practice your skills by solving these exercises!

#### This exercise will soon be on your smartphone!

For now, Practice Problems are only available on tablets and desktop computers. Please log in on one of these devices.

Do you need help? Watch the Video Lesson for this Practice Problem.

This video lesson will present a more systematic way of factoring trinomials with a≠1; just follow the following steps:

1) Factor out the GCF, if there’s any, and make sure that the trinomial is written in standard form; i.e. ax² + bx + c.

2) Multiply the leading coefficient a and the constant c.

3) Find m and n such that m*n=ac and m+n=b.

4) Rewrite the trinomial by splitting the middle term into two terms; in other words,
ax²+bx+c = ax²+mx+nx+c.

5) Group like terms or use the box method.

Let’s look at an example, 12x² + 34x + 10. We have:
1. 12x² + 34x + 10 = 2 (6x² + 17x + 5)

2. a=6 and c=5. So 6x5=30.

3. 15x2=30. So m=15 and n=2.

4. 2 (6x2 + 17x + 5) = 2 (6x2 + 15x + 2x + 5)
= 2 [(6x2 + 15x) + (2x + 5)]
= 2[3x(2x + 5) + 1(2x + 5)]
= 2(2x + 5)(3x + 1)

Factor a quadratic expression to reveal the zeros of the function it defines.

CCSS.MATH.CONTENT.HSA.SSE.B.3.A

Exercises in this Practice Problem
 Factor the quadratic function: $h(x) = 2x^2 + 4x - 6$. Determine when a ball will land by using a quadratic function. Use the box method to factor $h(x)=4x^2 + 7x - 2$. Factor the quadratic function $h(x) = -3x² + 4x + 4$. Identify the standard form of a quadratic function. Find the factored form of each function written in standard form.