Podcast
Questions and Answers
The GCF of 56x^8, 24x^6, and 8x^2 is ______.
The GCF of 56x^8, 24x^6, and 8x^2 is ______.
8x^2
For the polynomial 27x^4 -- 33x^5 -- 96x^6 -- 60x^7, the GCF is ______.
For the polynomial 27x^4 -- 33x^5 -- 96x^6 -- 60x^7, the GCF is ______.
3x^4
When factoring 9x^2 + 14x + 24, the factored form includes ______.
When factoring 9x^2 + 14x + 24, the factored form includes ______.
(3x + 4)(3x + 6)
The expression 256x^2 -- 81 can be factored as ______.
The expression 256x^2 -- 81 can be factored as ______.
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For the polynomial 2x^2 -- 13x + 21, the GCF is ______.
For the polynomial 2x^2 -- 13x + 21, the GCF is ______.
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The greatest common factor (GCF) of 56x^8, 24x^6, and 8x^2 is 8x^2.
The greatest common factor (GCF) of 56x^8, 24x^6, and 8x^2 is 8x^2.
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The polynomial 27x^4 -- 33x^5 -- 96x^6 -- 60x^7 can be factored using the GCF of 3x^4.
The polynomial 27x^4 -- 33x^5 -- 96x^6 -- 60x^7 can be factored using the GCF of 3x^4.
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The expression 9x^2 + 14x + 24 can be factored into (3x + 4)(3x + 6).
The expression 9x^2 + 14x + 24 can be factored into (3x + 4)(3x + 6).
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256x^2 -- 81 is an example of a difference of squares.
256x^2 -- 81 is an example of a difference of squares.
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The polynomial x^2 -- 6x -- 16 can be factored as (x -- 8)(x + 2).
The polynomial x^2 -- 6x -- 16 can be factored as (x -- 8)(x + 2).
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Study Notes
Factoring Polynomials
- GCF (Greatest Common Factor): Find the largest factor that divides all terms in the polynomial.
- Example 1: 56x³ + 24x² + 8x² has a GCF of 4x².
- Example 2: 27x4 - 33x5 - 96x6 - 60x7 has a GCF of 3x4.
Factoring Trinomials
- Example 1: x² + 14x + 24 Factors to (x + 2)(x + 12).
- Example 2: 256x² - 81 Factors to (16x + 9)(16x - 9) (Difference of Squares)
- Example 3: 16x² + 9 is a sum of squares and does not factor using real numbers.
- Example 4: 2x² - 13x + 21 Factors to (2x – 3)(x – 7).
Factoring Other Expressions
- Example 1: 49x² – 1 Factors to (7x + 1)(7x - 1).
- Example 2: x² - 6x – 16 factors to (x - 8)(x + 2)
- Example 3: 3x² + 11x + 10 factors to (3x + 5)(x + 2)
- Example 4: x² – 289 is a difference of squares, factoring to (x + 17)(x – 17)
- Example 5: 2x² - x - 10 factors to (2x - 5)(x + 2)
- Example 6: x² + 7x - 60 Factors to (x + 12)(x - 5).
Important Considerations
- Show your work: Steps should be clear to reach the solutions.
- Check your work: Verify results are correct.
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Description
This quiz covers the techniques for factoring polynomials, including finding the Greatest Common Factor (GCF) and factoring trinomials. Test your understanding with various example problems that illustrate different factoring methods, such as difference of squares and sum of squares.
