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 its linear factors.

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 difference of squares?

Back

The difference of squares is a special factoring pattern expressed as a² - b² = (a + b)(a - b).

Front

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

Back

To factor x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n).

Front

What is the process for factoring a trinomial?

Back

To factor a trinomial, identify a, b, and c, find two numbers that multiply to ac and add to b, and rewrite the expression.

Front

What is the significance of the leading coefficient in factoring quadratics?

Back

The leading coefficient (a) affects the shape of the parabola and can complicate factoring if it is not 1.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form a² ± 2ab + b², which factors to (a ± b)².

Front

How do you factor by grouping?

Back

To factor by grouping, split the expression into two parts, factor out the common factor from each part, and then factor the resulting expression.

Front

What is the role of the discriminant in factoring quadratics?

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.