Solving Quadratics by Factoring

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 and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials, if possible, such that ax² + bx + c = (px + q)(rx + s).

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 factor the expression 49x² - 100?

Back

49x² - 100 can be factored as (7x - 10)(7x + 10) using the difference of squares method.

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Set the equation to zero. 2. Factor the quadratic expression. 3. Apply the zero-product property. 4. Solve for the variable.

Front

Solve the equation 4x² + 11x - 3 = 0 by factoring.

Back

The solutions are x = 1/4 and x = -3.

Front

What is the factored form of x² - 16?

Back

The factored form of x² - 16 is (x - 4)(x + 4), which is also a difference of squares.

Front

How do you solve x² + 3x - 18 = 0 by factoring?

Back

Factor the expression to get (x - 3)(x + 6) = 0, leading to solutions x = 3 and x = -6.

Front

What is the solution to the equation 16a² - 9 = 0?

Back

The solutions are a = -3/4 and a = 3/4.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring technique used for expressions of the form a² - b², which factors to (a - b)(a + b).