3.2 Factor by Grouping Exit ticket

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What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors and then factoring out the common factors.

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How do you identify pairs for grouping in a polynomial?

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Look for terms in the polynomial that can be grouped together based on common factors. Typically, you can group the first two terms and the last two terms.

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What is the first step in factoring by grouping?

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The first step is to rearrange the polynomial if necessary, and then group the terms into pairs.

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What do you do after grouping the terms?

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Factor out the greatest common factor (GCF) from each group.

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What is the significance of the common binomial factor in grouping?

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After factoring out the GCF from each group, the remaining binomial factors should be the same, allowing you to factor them out as well.

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Example: Factor 7r³ - 8r² + 42r - 48 by grouping.

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(r² + 6)(7r - 8) is the factored form.

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Example: Factor 20x³ - 25x² + 4x - 5 by grouping.

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(5x² + 1)(4x - 5) is the factored form.

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

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What is a common factor?

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

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What is the greatest common factor (GCF)?

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The GCF is the largest factor that two or more numbers or expressions share.