Factoring - GCF, Difference of Squares, and Trinomials

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest positive integer that divides all the coefficients of a polynomial without leaving a remainder.

Front

How do you find the GCF of 12 and 18?

Back

The GCF of 12 and 18 is 6, as it is the largest number that divides both 12 and 18.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).

Front

Factor the expression: x^2 - 16.

Back

(x + 4)(x - 4) using the difference of squares formula.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

Front

How do you factor a trinomial of the form x^2 + bx + c?

Back

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

Front

Factor the trinomial: x^2 + 5x + 6.

Back

(x + 2)(x + 3) because 2 and 3 multiply to 6 and add to 5.

Front

What is the first step in factoring by grouping?

Back

The first step is to group terms that have a common factor.

Front

Factor the expression: 2n^2 + 8n.

Back

2n(n + 4) by factoring out the GCF, which is 2n.

Front

What is the factored form of 3x^2 - 75?

Back

3(x + 5)(x - 5) by factoring out the GCF and recognizing the difference of squares.