Questions and Answers
Which polynomial is factored completely?
2g² + 5g + 4
The expression 3(x² - 4) is completely factored.
False
What factoring method can be considered for the polynomial 3x³ + 5x + 6x² + 10?
Factor by grouping
What is the completely factored form of xy³ - x³y?
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Which expression represents the factored form of 6x² - 13x - 5?
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What is the factored form of 2x³ + 4x² - x?
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What factoring method can be considered for the polynomial x² + 12x + 36?
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What is the factored form of a² - 121?
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Which polynomial is factored completely?
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Which value of a would make the expression x² - a completely factored?
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Study Notes
Factoring Polynomials Overview
- 2g² + 5g + 4 is provided as an example of a polynomial that is not completely factored.
Equivalent Expressions
- A student factors 3x² - 12 as 3(x² - 4); this transformation maintains equivalence but is not fully factored.
Methods of Factoring
- For the polynomial 3x³ + 5x + 6x² + 10, the appropriate method is factoring by grouping due to its four terms.
- x² + 12x + 36 is identified as a perfect-square trinomial, indicating a specific factoring approach for three-term polynomials.
Completely Factored Forms
- xy³ - x³y factors to xy(y + x)(y - x), showcasing how variables and polynomial terms can be manipulated.
- The completely factored form of 6x² - 13x - 5 is (2x - 5)(3x + 1), demonstrating the factors of a quadratic expression.
- The expression 2x³ + 4x² - x can be factored as x(2x² + 4x - 1), emphasizing the extraction of common factors.
Special Cases in Factoring
- For the difference of squares, a² - 121 can be factored as (a - 11)(a + 11).
Complete Factor Status
- 3x(9x² + 1) is mentioned as a polynomial that is factored completely, highlighting the end goal of factoring processes.
Completing the Factor
- To make x² - a completely factored, the value of a would be 12, demonstrating how specific values can influence the factorization process.
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Description
Test your understanding of factoring polynomials with this quiz based on Unit 3. Each question challenges you to identify completely factored polynomials and the correct factoring methods. Perfect for reinforcing your algebra skills!
