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 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 and a ≠ 0.

Front

What does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers or expressions.

Front

How do you find the GCF of two terms?

Back

To find the GCF of two terms, identify the common factors of the coefficients and the variables, then multiply the common factors together.

Front

Factor the quadratic expression: 3a² + 4a + 1

Back

(3a + 1)(a + 1)

Front

Factor the quadratic expression: x² - 14x + 24

Back

(x - 12)(x - 2)

Front

Factor the quadratic expression: 2x² - 7x + 6

Back

(x - 2)(2x - 3)

Front

What is the first step in factoring a trinomial?

Back

The first step is to identify the coefficients of the quadratic term, linear term, and constant term.

Front

What is the relationship between the roots and factors of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, and they correspond to the factors of the quadratic expression.

Front

Factor the expression: 22x³ + 11x²

Back

11x²(2x + 1)