Factoring

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

Front

What is the factored form of a perfect square trinomial?

Back

The factored form of a perfect square trinomial, such as a² - 2ab + b², is (a - b)² or (a + b)².

Front

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

Back

To factor a quadratic expression of the form ax² + bx + c, look for two numbers that multiply to ac and add to b. Rewrite the expression using these numbers and factor by grouping.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for a common factor in all the terms.

Front

How do you factor the expression 3x² + 5x - 12?

Back

To factor 3x² + 5x - 12, find two numbers that multiply to (3 * -12 = -36) and add to 5. The numbers are 9 and -4. Rewrite the expression as 3x² + 9x - 4x - 12, then factor by grouping.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, 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 - 25?

Back

The factored form of x² - 25 is (x - 5)(x + 5), which is an example of the difference of squares.

Front

What is the significance of the leading coefficient in factoring quadratics?

Back

The leading coefficient (the coefficient of x²) affects the methods used for factoring. If it is 1, factoring is often simpler.