Factoring and Solving Quadratics

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 a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants.

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. They can be found using factoring, completing the square, or the quadratic formula.

Front

How do you factor the expression x² + 7x + 12?

Back

The expression factors to (x + 3)(x + 4).

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you solve the equation m² - 100 = 0?

Back

To solve m² - 100 = 0, factor it as (m - 10)(m + 10) = 0, giving solutions m = 10 and m = -10.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a - b)(a + b).

Front

How do you find the solutions of (x - 5)(x + 6) = 0?

Back

Set each factor to zero: x - 5 = 0 gives x = 5, and x + 6 = 0 gives x = -6. The solutions are {5, -6}.

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 does it mean to complete the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q.