Basic Factoring

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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 expressions before factoring.

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, divide each term by the GCF, and write the expression as the GCF multiplied by the simplified expression.

Front

Factor the expression: 24c^5 - 12c^3

Back

12c^3(2c^2 - 1)

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax^2 + bx + c, where a, b, and c are constants.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b. Rewrite the expression using these numbers to factor by grouping.

Front

Factor the expression: x^2 + 3x - 40

Back

(x + 8)(x - 5)

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a^2 - b^2 = (a + b)(a - b).

Front

Factor the expression: x^2 - 9

Back

(x + 3)(x - 3)

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as a^2 + 2ab + b^2 = (a + b)^2.