Factoring Quadratics

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

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 are the factors of a quadratic expression?

Back

The factors of a quadratic expression are the binomials that multiply together to give the original quadratic expression.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

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

How do you factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to ac (the product of a and c) and add to b.

Front

What is the difference of squares?

Back

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

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as a² + 2ab + b² = (a + b)².

Front

What are the steps to factor x² - 10x + 24?

Back

1. Identify a, b, c: a=1, b=-10, c=24. 2. Find two numbers that multiply to 24 and add to -10: -4 and -6. 3. Factor: (x - 4)(x - 6).

Front

What is the factored form of 3x² - 17x + 10?

Back

(x - 5)(3x - 2).