5.2.3 Factoring when A doesn't equal 1

Front

What is the general form of a quadratic equation?

Back

The general 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 significance of the leading coefficient (A) in factoring quadratics?

Back

The leading coefficient (A) affects the shape of the parabola and the methods used for factoring when A ≠ 1.

Front

What is the first step in factoring a quadratic expression when A ≠ 1?

Back

The first step is to multiply A (the leading coefficient) by C (the constant term) to find the product.

Front

How do you find two numbers that multiply to AC and add to B in factoring?

Back

You need to identify two integers that, when multiplied together, equal AC and, when added together, equal B.

Front

What is the process of grouping in factoring quadratics?

Back

Grouping involves rearranging the terms of the quadratic expression and factoring by pairs.

Front

What is the difference between factoring completely and factoring partially?

Back

Factoring completely means breaking down the expression into its simplest factors, while factoring partially may leave some factors intact.

Front

What is the role of the zero product property in solving quadratic equations?

Back

The zero product property states that if the product of two factors equals zero, at least one of the factors must equal zero.

Front

How can you check if your factored expression is correct?

Back

You can check by expanding the factored expression to see if it equals the original quadratic expression.

Front

What is the factored form of the expression 4n² - 17n - 15?

Back

The factored form is (n-5)(4n+3).