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 and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

To factor a quadratic expression, look for two numbers that multiply to ac and add to b. Rewrite the expression using these numbers and factor by grouping.

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, including any common factors and irreducible polynomials.

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

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

Back

First, factor out the greatest common factor (3), then factor the quadratic: 3(x² - 12x + 32) = 3(x - 4)(x - 8).

Front

What is the significance of the discriminant in the quadratic formula?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you solve a quadratic equation by factoring?

Back

Set the equation to zero, factor the quadratic expression, and then set each factor equal to zero to solve for the variable.

Front

What is the factored form of 2x² + 22x + 60?

Back

The factored form is 2(x + 5)(x + 6).

Front

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

Back

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