Factoring Quadratics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

What does it mean to solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring means to express the equation in the form (px + q)(rx + s) = 0 and then set each factor equal to zero to find the values of x.

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 ≠ 0.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Front

How do you factor the expression 3x² - 17x + 10?

Back

The expression factors to (x - 5)(3x - 2).

Front

What are the steps to factor a quadratic expression?

Back

1. Identify a, b, and c from ax² + bx + 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 quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean if a quadratic has no real roots?

Back

If a quadratic has no real roots, it means the discriminant (b² - 4ac) is less than zero, indicating that the graph does not intersect the x-axis.

Front

How do you find the factors of 5x² + 20x + 20?

Back

The expression factors to 5(x + 2)(x + 2).