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 a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What does it mean to factor completely?

Back

To factor completely means to break down an expression into its simplest factors, such that no further factoring is possible.

Front

What is the difference between a prime polynomial and a composite polynomial?

Back

A prime polynomial cannot be factored into simpler polynomials over the integers, while a composite polynomial can be factored into two or more non-trivial polynomials.

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that two or more numbers or expressions share.

Front

How do you factor a quadratic expression in the form ax² + bx + c?

Back

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

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, in the form a² ± 2ab + b² = (a ± b)².

Front

How do you factor out the GCF from a polynomial?

Back

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

Front

What is the role of the leading coefficient in factoring quadratics?

Back

The leading coefficient (the coefficient of x²) affects the methods used for factoring; if it is 1, simpler methods can be used, while if it is greater than 1, additional steps may be needed.