How do you factor polynomials into binomials and trinomials?

Answer 1

Here are the steps to factoring a trinomial of the form x2 + bx + c , with c > 0 . We assume that the coefficients are integers, and that we want to factor into binomials with integer coefficients.

1. Write out all the pairs of numbers which can be multiplied to produce c .
2. Add each pair of numbers to find a pair that produce b when added. Call the numbers in this pair d and e .
3. If b > 0 , then the factored form of the trinomial is (x + d )(x + e) . If b < 0 , then the factored form of the trinomial is (x - d )(x - e) .
4. Check: The binomials, when multiplied, should equal the original trinomial.

Note: Some trinomials cannot be factored. If none of the pairs total b , then the trinomial cannot be factored.