Factoring Expressions

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 greatest common factor (GCF)?

Back

The greatest common factor (GCF) is the largest factor that two or more numbers share. It is used in factoring to simplify expressions.

Front

How do you factor out the GCF from an expression?

Back

To factor out the GCF, identify the largest factor common to all terms in the expression, divide each term by the GCF, and express the original expression as the product of the GCF and the simplified expression.

Front

What is the difference between factoring and expanding an expression?

Back

Factoring is breaking down an expression into its factors, while expanding is multiplying out the factors to get back to the original expression.

Front

What is a binomial expression?

Back

A binomial expression is a polynomial with exactly two terms, such as a + b or 3x - 5.

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What is a trinomial expression?

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A trinomial expression is a polynomial with exactly three terms, such as x^2 + 5x + 6.

Front

How do you factor a binomial expression?

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To factor a binomial, look for common factors or apply special factoring formulas, such as the difference of squares or sum/difference of cubes.

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What is the difference of squares formula?

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The difference of squares formula states that a^2 - b^2 = (a - b)(a + b). This is used to factor expressions that fit this form.

Front

What is the process for factoring a trinomial?

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To factor a trinomial, find two numbers that multiply to the constant term and add to the coefficient of the linear term, then rewrite the trinomial as a product of two binomials.

Front

What does it mean to factor completely?

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Factoring completely means breaking down an expression into its simplest factors, such that no further factoring is possible.