Factor By Grouping Polynomials - 4 Terms, Trinomials - 3 Terms, Algebra 2
The Organic Chemistry Tutor・2 minutes read
Factor by grouping involves identifying the greatest common factor for the first two terms and the last two terms of an expression, then factoring out the common factor to obtain the final answer. By following the steps of identifying the GCF, factoring out the common factors, and adjusting the polynomial if necessary, you can effectively factor expressions using the grouping method.
Insights
- The key to factoring by grouping is ensuring that the ratios of coefficients in the first two terms match those in the last two terms, allowing for the extraction of a common factor that simplifies the expression.
- By identifying the greatest common factor (GCF) for the initial and final terms, one can effectively factor out common elements, simplifying complex polynomials into more manageable expressions.
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Recent questions
How do you factor by grouping?
Identify common factors in pairs of terms.
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Summary
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Factoring Polynomials by Grouping: A Guide
- To factor by grouping, ensure the first two coefficients' ratio matches the last two coefficients' ratio.
- Identify the greatest common factor (GCF) for the first two terms, which is x, resulting in x + 4.
- Determine the GCF for the last two terms, which is 5, leading to x + 4.
- Factor out the common factor x + 4, leaving x and 5, resulting in x + 4 times x + 5.
- For the expression 2x^3 + 8x^2 - 3x - 12, confirm the ability to factor by grouping.
- Extract the GCF for the first two terms (2x^2) and the last two terms (-3), yielding x + 4.
- Factor out x + 4, leaving 2x^2 and -3, resulting in x + 4 times 2x^2 - 3.
- In the expression 10a^2 - 8ab + 15ab - 12b^2, identify the GCF for the first two terms (5a - 4b) and the last two terms (3b).
- Factor out 5a - 4b, leading to 2a + 3b as the answer.
- For 2x^2 - 3x - 9, adjust the polynomial to include four terms by replacing -3x with -6x + 3x.
- Confirm the ability to factor by grouping by checking the ratios (-6/2 = -3, -9/3 = -3), resulting in x - 3.
- Factor out x - 3, leaving 2x + 3 as the final answer.
- To factor 21x^2 - 5x - 6, calculate 21 * -6 = -126 and find two numbers that multiply to -126 but add to -5.
- After determining 9 and -14 as the numbers, convert the three-term polynomial into a four-term one: 21x^2 + 9x - 14x - 6.
- Extract the GCF for the first two terms (3x) and the last two terms (-2), leading to 7x + 3 times 3x - 2 as the answer.
