Factoring Quadratics

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 is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

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 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.

Front

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

Back

To factor x² + bx + c, 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

What is the difference of squares?

Back

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

Front

How do you factor a quadratic expression of the form ax² + bx + c?

Back

For ax² + bx + c, use the method of grouping or the quadratic formula to find the roots, then express it as a(x - r1)(x - r2), where r1 and r2 are the roots.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as a² + 2ab + b² = (a + b)².

Front

Factor the expression: 3v² - 4v - 7

Back

(3v - 7)(v + 1)