Flashcard Factoring a=1

Front

What is the process of factoring a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials. This is often done by finding two numbers that multiply to the constant term and add to the coefficient of the linear term.

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 for a quadratic to be factored completely?

Back

A quadratic is factored completely when it is expressed as a product of irreducible factors, meaning it cannot be factored further over the set of real numbers.

Front

What is the GCF (Greatest Common Factor) and how is it used in factoring?

Back

The GCF is the largest factor that divides all terms in a polynomial. It is factored out first to simplify the expression before further factoring.

Front

How do you factor the expression x² - 6x - 16?

Back

To factor x² - 6x - 16, find two numbers that multiply to -16 and add to -6. The factors are (x - 8)(x + 2).

Front

What are the steps to factor a quadratic expression?

Back

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

Front

What is the factored form of x² + x - 30?

Back

The factored form is (x + 6)(x - 5).

Front

How do you factor x² + 3x - 40?

Back

To factor x² + 3x - 40, find two numbers that multiply to -40 and add to 3. The factors are (x + 8)(x - 5).

Front

What is the factored form of x² + 17x + 72?

Back

The factored form is (x + 9)(x + 8).

Front

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

Back

The leading coefficient (a) affects the shape of the parabola and can influence the factoring process, especially if a ≠ 1.