Guided Lesson: Factoring Trinomials where a does not Equal 1

What is step 1 of factoring trinomials where “a” does not equal 1?

Identify the values of a, b, and c.

What is the second step of factoring trinomials where “a” does not equal 1?

Factor out GCF if possible.

What is the third step of factoring trinomials where “a” does not equal 1?

Multiply a and c, then list the factors of ac.

What is the fourth step of factoring trinomials where “a” does not equal 1?

What combination of the numbers will multiply to ac, and add to b?

What is the fifth step of factoring trinomials where “a” does not equal 1?

Rewrite the trinomial keeping a and c terms the same, but the b term should be “split” into the factors you found in the previous step.

What is the sixth step of factoring trinomials where “a” does not equal 1?

Group the first two terms together with parentheses; group the second two terms together with parentheses.

What is the seventh step of factoring trinomials where “a” does not equal 1?

Factor out the GCF from each group of parentheses (HINT: what is left inside each group of parentheses should MATCH; if they don’t something is off!)

What is the final step of factoring trinomials where “a” does not equal 1?

The GCF’s you factored out become one binomial, what is left inside each set of parentheses is your other binomial.

What is the quadratic formula in algebra?

ax²+bx+c

What makes expressions equivalent?

If they have the same value no matter what number is substituted in for each of the variables.

What is the Greatest Common Numeric Factor?

The greatest coefficient that can be divided equally between a group of coefficients.

What is the Greatest Common Variable Factor?

The smallest variable(s) within a group of polynomials that can be divided without getting a negative exponent.

What is the Greatest Common Monomial Factor?

Both the Greatest Common Numeric Factor and the Greatest Common Variable Factor Combined.

A rectangle in algebra tiles represent what?

x

A big square in algebra tiles represents what?

x²

The blue, small squares in algebra tiles represent what?

1

The red, small squares in algebra tiles signify what?

-1

Creating an accurate algebra tile for a trinomial or binomial involves what?

The factors of the constant term and the number of x’s in the middle term.

What is a quadratic expression or equation?

A polynomial expression or equation that contains a term of degree 2, but no term of higher degree.

FOIL when multiplying binomials means what?

First, Outer, Inner, Last

1 is always a factor of what numbers?

All numbers