Factoring Quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of two binomials.

Front

What is the factored form of the quadratic expression x² + 5x + 6?

Back

(x + 2)(x + 3)

Front

How do you factor a quadratic expression of the form x² + bx + c?

Back

To factor, find two numbers that multiply to c and add to b.

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 the greatest common factor (GCF)?

Back

The GCF 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, divide each term of the expression by the GCF and write it outside the parentheses.

Front

What is the factored form of 2x² + 8x?

Back

2x(x + 4)

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the significance of the discriminant in the quadratic formula?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.