Factoring Trinomials with a ≠ 1 – Practice Problems

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Do you need help? Watch the Video Lesson for this Practice Problem. Factoring Trinomials with a ≠ 1

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

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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.