Factoring quadratics

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 is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0.

Front

What is the purpose of factoring quadratics?

Back

Factoring quadratics allows us to solve quadratic equations, simplify expressions, and analyze the properties of quadratic functions.

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor is the largest factor that divides two or more numbers or 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, divide each term by the GCF, and express the original expression as the product of the GCF and the resulting expression.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that applies to expressions of the form a² - b², which can be factored as (a + b)(a - b).

Front

What is the factoring method for a quadratic expression in the form ax² + bx + c?

Back

To factor a quadratic expression in the form ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers to factor by grouping.

Front

What is the factored form of the expression 12x + 9?

Back

The factored form is 3(4x + 3).

Front

What is the factored form of the expression 6x² + 9x?

Back

The factored form is 3x(2x + 3).