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 Depdendent Variable

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 Dependent Variable

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# Factoring Trinomials

## Factoring a Trinomial of the Form ax2+ bx+ c

To factor a trinomial of the form ax2 + bx + c, we can use the grouping method.

Procedure â€” To Factor ax2+ bx+ c Using the Grouping Method

Step 1 Factor out common factors (other than 1 or -1).

Step 2 Identify the values of a, b, and c.

Then find two integers whose product is ac and whose sum is b. If no two such integers exist, then the trinomial does not factor using integers.

Step 3 Replace the middle term, bx, with a sum or difference using the two integers found in Step 2.

Step 4 Factor by grouping.

Note:

Here is an example of a trinomial that does not factor using integers:

2x2 + x + 3

Here, a = 2, b = 1, and c = 3.

So, ac = 2 Â· 3 = 6.

Thus, we need to find two integers whose product ac = 6 and whose sum b = 1.

Here are the possible integer factorizations for 6:

 Factors 1 Â· 6 2 Â· 3 -1 Â· -6 -2 Â· -3 Sum 7 5 -7 -5
Since none of the sums is the required 1, we know that 2x2 + x + 3 does not factor using integers.

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