How to Factor a Trinomial When a is Not 1 Explained! (AC Method)

On this lesson on factoring trinomials, you will learn how to factor a trinomial when a is not 1. When the leading coefficient is greater than one, the factoring process (the AC method) is a bit different--let's see why!

This lesson answers the questions: How do I factor a quadratic when a is not 1? How do I solve a trinomial? How do I solve a quadratic? How do I find factors? What is a trinomial? What is a leading coefficient? How do I find the zeros of a function? How do I find the factors of a number?

[zoarfreeman]

This is the best explanation I found to help with my grandaughter's homework. The teacher's explanation was so confusing

[criseastman]

Thanks so much. I have an exam tonight and I was confused until watching your video. You are a lifesaver!

[Maddiecat]

Thanks I just needed someone to explain it to me again when I wasn't half asleep at 7 in the morning.

[tomburt]

Literally said to myself "it can't be that easy." This helped so much especially with studying for finals!

[yassineo]

dude u deserve a nobel prize or sumn this saved me

[shawnremy]

Great video, Anthony. I am the only teacher in my department who teaches it this way. Having the benefit of an interactive whiteboard, I color code the steps, which I appreciated in your video. The process has many names, but I refer to it as the AC B method to help students better recall the first few steps. This is my new go-to supplemental video for this topic. Thanks!

[TrueNorthGaming]

I'm relearning math for university and this was helpful for my first assignment. Thank you!

[pxnkskittles]

thank you so much, i’ve been stuck because i got quarantined and this really helped!

[froggy]

What happens if you CAN pull a GCF on the first step?

[mariebourgoyne]

I checked out your AC method of factor quadratics with leading coefficients other than one. I was impressed. It was very coherent and pretty easy to follow. It was one of the better videos that I have ever seen. One suggestion for improve is to use a visual model to help students to see these common factors, using a four corner box, with the top right containing the leading term, the lower right containing the last term, and the other two box containing the split terms. Then, have students factor out the common factors to the outside of the box, which will show the final factored quantities. If you had that element, it will reach more students.

Keep up the great work. I will tell my fellow math teachers about your channel. Good luck and thank you for the resource,

[SchlundaLeslie]

You have just taught me something that I have been trying to figure out for years!! Thank you much!!

[schoolwithapril]

OMG thank you! I hate the box method, they never remember it properly. I never realized this method involved factoring by grouping. Love your formatting and color coding, truly helps!

[toobrokentolove]

You just saved my homework grade from tomorrow

[xoppa]

Why does this method work? We can show it works by looking at the problem backwards, starting with the final factored form.
Assume your quadratic trinomial factors into two linear binomial factors, without loss of generality (ax + b)(cx + d).
This expands and simplifies to acx^2 + (ad + bc) x + bd.
But note that ac*bd = ad*bc, by the commutative property, and ad + bc happens to be the coefficient of the x term. So it is sufficient to find two factors of the product of the first and last coefficient, i.e. ac and bd, that add to the coefficient of the x term. This guarantees factoring over the integers.

[PresidentNathan]

What if there is no GCF in step 3? Do I just do 1(a+b)? (a and b are just substitutes for numbers)

[gabe]

im in differential equations and had to look this up :')

[GoblinCorn]

skip to 5:21 if you dont want to sit through the whole video

[trenttabor]

Good job and thank you for your help. Wish me luck in boosting my E in math.

[maxonrelaxon]

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[HayesWorldofMath]

Like the informal tone and graphics - you have a great start.

I have taught factoring this way before. Biggest question is this: CCSS stresses understanding the hows and whys things work, not just doing a process. Does this work? Yes. Does it really help students understand why the process works? Not really.

Do I have a better way of doing things that stresses the conceptual side instead of falling into a series of steps? Not really. Many of my videos fell into step-driven methods that I'm trying to get out of. Just trying give some feedback. :) Good luck with the project!