Factoring GCF & Basic Trinomials

Front

What is the GCF (Greatest Common Factor)?

Back

The GCF is the largest factor that divides two or more numbers without leaving a remainder.

Front

How do you factor a trinomial of the form x² + bx + c?

Back

To factor, find two numbers that multiply to c and add to b, then express as (x + m)(x + n) where m and n are those numbers.

Front

Factor the trinomial: x² + 5x + 6

Back

(x + 2)(x + 3)

Front

What is the first step in factoring out the GCF from an expression?

Back

Identify the largest factor that is common to all terms in the expression.

Front

Factor completely: 12x² - 8x

Back

4x(3x - 2)

Front

What does it mean to factor a polynomial completely?

Back

To factor a polynomial completely means to break it down into irreducible factors.

Front

Factor the expression: 2x² + 8x

Back

2x(x + 4)

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + bx + c.

Front

Factor the trinomial: x² - 7x + 10

Back

(x - 5)(x - 2)

Front

What is the relationship between the coefficients and roots of a trinomial?

Back

The sum of the roots is -b/a and the product of the roots is c/a for a trinomial ax² + bx + c.