Factoring Quadratics a=1

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 factored form of x² - 10x - 24?

Back

(x - 12)(x + 2)

Front

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

Back

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

Front

What is the factored form of x² + 7x + 12?

Back

(x + 3)(x + 4)

Front

What is the greatest common factor (GCF) and how is it used in factoring?

Back

The GCF is the largest factor that divides all terms in an expression. It is used to factor out common terms from polynomial expressions.

Front

How do you factor the expression 17xy - x?

Back

Factor out the common term x to get x(17y - 1).

Front

What is the factored form of 7w³ - 14w?

Back

7w(w² - 2) is the factored form.

Front

What is the difference between factoring and expanding an expression?

Back

Factoring is breaking down an expression into simpler components (products), while expanding is multiplying out the components to form a single expression.

Front

What are the steps to factor a quadratic expression?

Back

1. Identify a, b, and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the expression using these numbers. 4. Factor by grouping if necessary.