Factoring

Front

What is factoring in algebra?

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 does it mean to factor completely?

Back

To factor completely means to break down an expression into its simplest factors, such that no further factoring is possible.

Front

What is the factored form of x² - 16?

Back

(x - 4)(x + 4) - This is an example of a difference of squares.

Front

What is the first step in factoring a quadratic expression?

Back

The first step is to identify the coefficients a, b, and c in the expression ax² + bx + c.

Front

How do you factor the expression 3x² + 10x - 8?

Back

You can factor it as (3x - 2)(x + 4).

Front

What is the significance of the zero product property in factoring?

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

What is the factored form of x² + 9x - 36?

Back

(x + 12)(x - 3).

Front

What is the method to factor x² + 7x - 30?

Back

Look for two numbers that multiply to -30 and add to 7; the factors are (x + 10)(x - 3).

Front

What is a prime polynomial?

Back

A prime polynomial is a polynomial that cannot be factored into simpler polynomials with real coefficients.