Questions and Answers
What is the factored form of 15x^2 + 4x - 32?
What is the factored form of 4x^2 - 13x + 10?
What is the factored form of 9x^2 - 4?
What is the factored form of 64x^2 - 16?
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What is the factored form of -6x^2 - 6x + 36?
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What is the factored form of 56p^3 - 72p?
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What is the factored form of 3x^2 + 6x - 144?
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What is the factored form of 108s^2 + 54?
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What is the factored form of 16x^2 - 36?
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What is the factored form of -x^2 - 10x - 24?
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What is the factored form of 81y^2 - 49/144?
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What is the factored form of d^2 - 6d + 9?
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What is the factored form of -12x^2 - 26x - 12?
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What is the factored form of 6a^2 - 12a - 48?
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What is the factored form of 9x^2 + 49?
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What is the factored form of 25/49a^2 - b^2?
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What is the factored form of 40x^2 + 150x + 135?
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What is the factored form of 3a^2 + 24a + 48?
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What is the factored form of 24x^3 - 26x^2 + 6x?
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What is the factored form of x^2 - 11x + 18?
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Study Notes
Factoring Algebraic Expressions
- Factoring is the process of breaking down an expression into simpler components, known as factors.
- Key strategies include finding common factors, using special products, and applying the quadratic formula when necessary.
Specific Factored Expressions
- 15x² + 4x - 32 factors into (5x + 8)(3x - 4).
- 4x² - 13x + 10 simplifies to (4x - 5)(x - 2).
- 9x² - 4 is factored as (3x - 2)(3x + 2), representing a difference of squares.
- 64x² - 16 can be broken down to (8x - 4)(8x + 4).
- Expression -6x² - 6x + 36 simplifies to -6(x + 3)(x - 2).
- For 56p³ - 72p, the greatest common factor (GCF) is 8p(7p² - 9).
GCF and Special Cases
- 3x² + 6x - 144 factors to 3(x + 8)(x - 6).
- 108s² + 54 can be factored to 54(2s² + 1).
- 16x² - 36 simplifies to (4x - 6)(4x + 6).
- Expression -x² - 10x - 24 factors as -(x + 6)(x + 4).
Perfect Squares and Parabolic Functions
- d² - 6d + 9 can be written as (d - 3)², indicating a perfect square trinomial.
- -12x² - 26x - 12 can be factored into -2(3x + 2)(2x + 3).
More Complex Factoring
- The expression 6a² - 12a - 48 breaks down to 6(a - 4)(a + 2).
- 9x² + 49 is classified as prime, meaning it cannot be factored further over the integers.
- For the expression 25/49a² - b², it factors as (5/7a - b)(5/7a + b), indicating a difference of squares.
- 40x² + 150x + 135 simplifies to 5(4x + 9)(2x + 3).
- 3a² + 24a + 48 can be factored as 3(a + 4)², indicating a repeated root.
- Finally, 24x³ - 26x² + 6x factors to 2x(4x - 3)(3x - 1), showcasing the procedure for cubic expressions.
- The quadratic equation x² - 11x + 18 factors as (x - 9)(x - 2).
Conclusion
- Understanding these factoring techniques is vital for solving quadratic equations and simplifying polynomial expressions effectively.
Studying That Suits You
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Description
Test your skills in factoring algebraic expressions with these flashcards. Each card presents a polynomial to factor along with its solution. Perfect for students looking to reinforce their understanding of algebraic concepts.
