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.

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, b, and c are constants.

Front

What does it mean to factor a quadratic expression?

Back

To factor a quadratic expression means to express it as a product of two binomials.

Front

What is the factored form of x² - 9?

Back

(x + 3)(x - 3) - This is an example of the difference of squares.

Front

What is the difference of squares?

Back

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

Front

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

Back

To factor, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers.

Front

What is the factored form of x² + 5x + 6?

Back

(x + 2)(x + 3) - The numbers 2 and 3 multiply to 6 and add to 5.

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, e.g., a² + 2ab + b² = (a + b)².

Front

What is the factored form of 4x² - 12x + 9?

Back

(2x - 3)(2x - 3) - This is a perfect square trinomial.