Factoring Quadratics

Front

What is factoring in mathematics?

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 share. It is used to simplify expressions before factoring.

Front

Factor the expression completely: 3x^2 + 18x + 15. What is the first step?

Back

The first step is to factor out the GCF, which is 3, resulting in 3(x^2 + 6x + 5).

Front

What is the factored form of x^2 + x?

Back

The factored form is x(x + 1).

Front

How do you factor a quadratic expression of the form x^2 + bx + c?

Back

To factor, find two numbers that multiply to c and add to b, then express the quadratic as (x + m)(x + n) where m and n are those numbers.

Front

Factor the expression: x^2 + 5x - 24. What is the factored form?

Back

The factored form is (x + 8)(x - 3).

Front

What is a difference of squares?

Back

A difference of squares is an expression of the form a^2 - b^2, which can be factored as (a - b)(a + b).

Front

Factor the expression: x^2 - 64. What is the factored form?

Back

The factored form is (x - 8)(x + 8).

Front

What does it mean if a quadratic expression is prime?

Back

A quadratic expression is prime if it cannot be factored into simpler expressions with integer coefficients.

Front

Factor the expression: 3a^2 + 4a + 1. What is the factored form?

Back

The factored form is (3a + 1)(a + 1).