Factoring - GCF, Difference of Squares, and Trinomials

Front

What is the GCF (Greatest Common Factor)?

Back

The GCF is the largest factor that two or more numbers have in common.

Front

How do you factor a polynomial using the GCF?

Back

1. Identify the GCF of all terms. 2. Divide each term by the GCF. 3. Write the polynomial as the GCF multiplied by the resulting polynomial.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states: a² - b² = (a + b)(a - b).

Front

Factor the expression: x² - 16.

Back

(x + 4)(x - 4) - This is a difference of squares.

Front

What is a trinomial?

Back

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

Front

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

Back

Look for two numbers that multiply to c and add to b. Rewrite the trinomial 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 any polynomial?

Back

Look for the GCF (Greatest Common Factor).

Front

Factor the expression: 3x² - 12.

Back

3(x² - 4) = 3(x + 2)(x - 2) - This includes factoring out the GCF and then applying the difference of squares.

Front

What does it mean for a polynomial to be prime?

Back

A polynomial is prime if it cannot be factored into simpler polynomials with integer coefficients.