Algebra

Factoring Trinomials Incorrectly

Students pick two numbers for a trinomial without checking both the sum and the product.

Quick check

Why students make it

They focus on the middle term and forget that multiplying the binomials must recreate every term. The numbers must match the constant term too, or acac when the leading coefficient is not 11.

The rule done right

For x2+bx+cx^2+bx+c, find numbers mm and nn so that m+n=bm+n=b and mn=cmn=c. For ax2+bx+cax^2+bx+c, use numbers whose product is acac and whose sum is bb, then factor by grouping.

Related resources

factoringtrinomialsquadratics