Factoring Completely

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What is factoring completely?

Back

Factoring completely is the process of breaking down an expression into its simplest factors, such that when multiplied together, they yield the original expression.

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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)?

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

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that applies to expressions of the form a² - b², which can be factored as (a - b)(a + b).

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What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + 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 x² and the constant term) and add to b (the coefficient of x). Use these numbers to split the middle term and factor by grouping.

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What is the quadratic formula?

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The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

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What does it mean for an expression to be prime?

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An expression is considered prime if it cannot be factored further into simpler expressions with integer coefficients.

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How do you factor a polynomial with four terms?

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To factor a polynomial with four terms, use grouping: group the terms into pairs, factor out the common factors from each pair, and then factor out the common binomial.

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What is the role of coefficients in factoring?

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Coefficients are the numerical factors in front of variables in a polynomial. They play a crucial role in determining the GCF and in the overall factoring process.