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How do we factor trinomials?

I don't understand the steps of how to do it. Do we add first or multiply? Why do we have to make a chart? How do we find our answer?

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Amy P. | Top Tutor with Advanced Degree!Top Tutor with Advanced Degree!
4.7 4.7 (29 lesson ratings) (29)

Example of Factoring a Trinomial
Factor x2 + 5x + 4
1) identify a,b, and c in the trinomial
ax2 + bx+c a= 1
b= 5
c= 4
2) write down all factor pairs of 4

(Note: since 5 is positive we only need to think about pairs that are either both positive or both negative. Remember a negative times a negative is a positve. As the chart on the right shows you -2*-2 is positive we do have to consider these two negative factors. This is probabily easier to understand if you watch our video lesson factoring trinonmials)
3) identify which factor pair from the previous step sums up to c
4) Substitute that factor pair into two binomials (x +4)(x+1)
5) If you'd like, you can check your work by multiplying the two binomials and verify that you get the original trinomial (x +4)(x+1) = x2 + 5x + 4

Miles A. | An enthusiastic game designer with experience teaching childrenAn enthusiastic game designer with exper...
5.0 5.0 (2 lesson ratings) (2)

There are several resources on the internet that can help you out. You can begin by watching this video on youtube:

You can read a tutorial here:

Here is an alternative video: