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 ______.
For the polynomial 2x^2 -- 13x + 21, the GCF is ______.
For the polynomial 2x^2 -- 13x + 21, the GCF is ______.
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.
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.
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).
256x^2 -- 81 is an example of a difference of squares.
256x^2 -- 81 is an example of a difference of squares.
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).
Flashcards
Factor by GCF
Factor by GCF
Find the greatest common factor (GCF) of terms in a polynomial and rewrite the polynomial by factoring out the GCF.
Factoring Polynomials
Factoring Polynomials
Express a polynomial as a product of simpler expressions.
Difference of Squares
Difference of Squares
Factoring expressions in the form a² - b² = (a-b)(a+b)
Trinomial Factoring
Trinomial Factoring
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Greatest Common Factor (GCF)
Greatest Common Factor (GCF)
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GCF of a polynomial
GCF of a polynomial
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Factoring Trinomials
Factoring Trinomials
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Factoring a Quadratic
Factoring a Quadratic
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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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