Factoring (GCF, Trinomials)

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest factor that two or more numbers have in common. It is used to simplify fractions and factor expressions.

Front

How do you factor out the GCF from an expression?

Back

To factor out the GCF, identify the largest factor common to all terms in the expression, then divide each term by the GCF and write the expression as the GCF multiplied by the resulting expression.

Front

Factor the expression using GCF: 8n^3 + 2n^2

Back

2n^2(4n + 1)

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 a trinomial of this form, find two numbers that multiply to c and add to b, then express the trinomial as (x + m)(x + n), where m and n are the two numbers.

Front

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

Back

(x + 2)(x + 3)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring case where an expression is in the form a^2 - b^2, which can be factored as (a + b)(a - b).

Front

Factor the expression: x^2 - 16

Back

(x + 4)(x - 4)

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, look for two numbers that multiply to ac (the product of a and c) and add to b, then rewrite the expression using these numbers.