Rewrite the quadratic as ax 2 + hx + kx + cĤ. H + k = b ( h and k add to give the coefficient of x)ģ. Hk = ac ( h and k are factors of the product of the coefficient of x 2 and the constant term) Given a general quadratic trinomial ax 2 + bx + c That means we can factor out a common factor
Write the 7 x as the sum of –5 x and 12 x: Think of two factors of –60 that add up to 7: That means we can factor out a common factor of (5 x + 1): Notice that the two quantities in parentheses are now identical. Write the 11 x as the sum of 1 x and 10 x: Think of two factors of 10 that add up to 11:
When this happens, the trial and error method becomes very tedious.įactoring by grouping is best demonstrated with a few examples. However, it works quite well when the factors are not immediately obvious, such as when you have a very large number of candidate factors. Factoring by grouping can be a bit more tedious and is often not worth the trouble if you can find the correct factors by some quick trial and error. Factoring a Quadratic Trinomial by GroupingĪnother method for factoring these kinds of quadratic trinomials is called factoring by grouping.
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