Factoring Quadratics (a=1 and GCF)

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components, 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 for a quadratic to be factorable?

Back

A quadratic is factorable if it can be expressed as the product of two binomials.

Front

What is the GCF (Greatest Common Factor)?

Back

The GCF is the largest factor that two or more numbers have in common.

Front

How do you factor x² + 12x + 35?

Back

(x + 5)(x + 7) - This is done by finding two numbers that multiply to 35 and add to 12.

Front

How do you factor x² - 12x - 13?

Back

(x + 1)(x - 13) - This is done by finding two numbers that multiply to -13 and add to -12.

Front

What is the factored form of x² - 5x?

Back

x(x - 5) - This is done by factoring out the common term x.

Front

How do you factor x² - 23x - 24?

Back

(x - 24)(x + 1) - This is done by finding two numbers that multiply to -24 and add to -23.

Front

What is the factored form of x² - 9x + 20?

Back

(x - 5)(x - 4) - This is done by finding two numbers that multiply to 20 and add to -9.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.