Factoring and Quadratic Formula

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 the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you factor the expression 3x² - 36x + 96?

Back

3(x - 4)(x - 8) is the complete factorization of the expression.

Front

What are the roots of the equation 2x² - 8x - 24 = 0?

Back

The roots are x = 6 and x = -2.

Front

What does it mean to find the zeros of a function?

Back

Finding the zeros of a function means determining the values of x for which the function equals zero.

Front

How do you apply the quadratic formula to the equation y = -x² - 5x + 12?

Back

Using the quadratic formula, the solutions are approximately x = -6.77 and x = 1.77.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x - 2)² = x² - 4x + 4.

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated root.