[PDF] 8 6 practice factoring quadratic trinomials

When to factor A trinomial into a product of binomials?

If the trinomial has a greatest common factor, then it is a best practice to first factor out the GCF before attempting to factor it into a product of binomials. If the leading coefficient of a trinomial is negative, then it is a best practice to factor that negative factor out before attempting to factor the trinomial.

What is the leading coefficient of factoring quadratics?

Factoring quadratics: leading coefficient = 1 Factoring quadratics as (x+a)(x+b) (example 2) More examples of factoring quadratics as (x+a)(x+b) Practice: Factoring quadratics intro

How can we verify the correct factorization of A trinomial?

We can multiply to verify that this is the correct factorization. As we have seen before, the product of the first terms of each binomial is equal to the first term of the trinomial. The middle term of the trinomial is the sum of the products of the outer and inner terms of the binomials.

How to factor polynomials in reverse order?

If we rewrite the equations in the reverse order, we will have patterns for factoring polynomials of the form a^2pm2ab+b^2 a2 ±2ab+b2. We can apply the first pattern to factor x^2+10x+25 x2 +10x +25. Here we have blueD a=blueD x a = x and greenD b=greenD 5 b = 5. Expressions of this form are called perfect square trinomials.