Factoring Expressions

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 the greatest common factor (GCF)?

Back

The greatest common factor (GCF) is the largest factor that two or more numbers share.

Front

How do you factor out the GCF from an expression?

Back

To factor out the GCF, identify the GCF of the terms in the expression and divide each term by the GCF, then write the expression as the GCF multiplied by the resulting expression.

Front

What does it mean if an expression cannot be factored?

Back

If an expression cannot be factored, it means that there are no two or more simpler expressions that can be multiplied together to yield the original expression.

Front

What is a linear expression?

Back

A linear expression is an algebraic expression of the first degree, meaning it has no exponents greater than one.

Front

How do you factor a binomial expression?

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

Front

What is the difference of squares?

Back

The difference of squares is a factoring technique used for expressions in the form a^2 - b^2, which can be factored as (a + b)(a - b).

Front

What is a trinomial?

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A trinomial is a polynomial with three terms, often in the form ax^2 + bx + c.

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How do you factor a trinomial?

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To factor a trinomial, look for two numbers that multiply to ac (the product of the coefficient of x^2 and the constant term) and add to b (the coefficient of x).

Front

What is a prime polynomial?

Back

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