There are no factors of 20 whose sum is 3. For example, consider the trinomial x 2 + 3 x + 20 and the factors of 20: Keep in mind that some polynomials are prime. However, if a guess is not correct, do not get discouraged just try a different set of factors. If we choose the factors wisely, then we can reduce much of the guesswork in this process. Now the check shows that this factorization is correct. This time we choose the factors −2 and 12 because − 2 + 12 = 10. Since the last term in the original expression is negative, we need to choose factors that are opposite in sign. In this case, the middle term is correct but the last term is not. When we multiply to check, we find the error. Then we have the following incorrect factorization:Ī 2 + 10 a − 24 = ? ( a + 4 ) ( a + 6 ) I n c o r r e c t F a c t o r i z a t i o n Suppose we choose the factors 4 and 6 because 4 + 6 = 10, the coefficient of the middle term. The first term of this trinomial, a 2, factors as a ⋅ a.
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