Factoring practice

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 a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

How do you factor out the greatest common factor (GCF)?

Back

To factor out the GCF, identify the largest factor that is common to all terms in the expression, then divide each term by the GCF and write the expression as the product of the GCF and the remaining terms.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial, typically in the form (a + b)² = a² + 2ab + b².

Front

How do you factor a difference of squares?

Back

A difference of squares can be factored using the formula a² - b² = (a + b)(a - b), where a and b are the square roots of the two terms.

Front

What is the factored form of 4x² - 16?

Back

The factored form is 4(x - 2)(x + 2), which is derived from recognizing it as a difference of squares.

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for the greatest common factor (GCF) among the terms.

Front

How do you factor the expression 12x³ + 9x²?

Back

You factor out the GCF, which is 3x², resulting in 3x²(4x + 3).

Front

What does it mean to factor completely?

Back

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

Front

What is the factored form of 17xy² - xy?

Back

The factored form is xy(17y - 1), where xy is the GCF factored out.