Factoring x² + 5x + 6

Algebra 1 · Axiom Academy

EXAMPLE Factoring x^2 + 5x + 6 Factor the trinomial with the find-two-numbers method, then see why it works using an area model. Factor the trinomial x^2 + 5x + 6 into a product of two binomials. Nice work. You factored a trinomial two ways — by finding the right pair of numbers, and by reading the side lengths off an area model. Find the factor pairs: list every pair of numbers whose product is the constant term c . Match the middle term: keep the pair that also adds to the coefficient of x , here b = 5 . The area model proves it: a rectangle of area x^2 + 5x + 6 has side lengths (x+2) and (x+3) . Always verify: expand (x+2)(x+3) and confirm you land back on x^2 + 5x + 6 . This product-and-sum method works for any trinomial x^2 + bx + c with a leading coefficient of 1. A different leading coefficient calls for an extended technique.

This is the written version of the interactive lesson above. See the full Algebra 1 course.