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Questions and Answers
What is the factored form of the expression $3x^4(5x^2 + y - 1)$?
What is the factored form of the expression $3x^4(5x^2 + y - 1)$?
- $3x^4(5x^2 + y - 1)$ (correct)
- $3x^4(5x^2 - y - 1)$
- $3x^4(5x^2 - y + 1)$
- $3x^4(5x^2 + y + 1)$
Which of the following represents the factored form of the quadratic expression $n^2 - 9n + 18$?
Which of the following represents the factored form of the quadratic expression $n^2 - 9n + 18$?
- (n + 3)(n - 6)
- (n - 6)(n + 3)
- (n - 3)(n - 6) (correct)
- (n - 3)(n - 2)
What is the factored form of the expression $-8m(8mn + 7)$?
What is the factored form of the expression $-8m(8mn + 7)$?
- $-8m(8mn + 7)$ (correct)
- $-8m(8mn - 7)$
- 8m(-8mn + 7)
- $-8m(7 + 8mn)$
Identify the correctly factored expression among the following options: $v^2 - 81$.
Identify the correctly factored expression among the following options: $v^2 - 81$.
What is the factored form of the expression $10u(uv^2 - 5)$?
What is the factored form of the expression $10u(uv^2 - 5)$?
What is the completely factored form of the expression $-ba + 2b^2 - 2b$?
What is the completely factored form of the expression $-ba + 2b^2 - 2b$?
What is the result of factoring $15x^6 + 3x^4y - 3x^4$?
What is the result of factoring $15x^6 + 3x^4y - 3x^4$?
What is the factored form of the quadratic $v^2 - 6v - 27$?
What is the factored form of the quadratic $v^2 - 6v - 27$?
How can the expression $n^2 - 9n + 18$ be factored?
How can the expression $n^2 - 9n + 18$ be factored?
What is the completely factored form of the expression $1 - k^2$?
What is the completely factored form of the expression $1 - k^2$?
How can the expression $81m^2 - 36$ be factored completely?
How can the expression $81m^2 - 36$ be factored completely?
Which expression represents the factored form of $8x^3 - 7x^2 - 64x + 56$?
Which expression represents the factored form of $8x^3 - 7x^2 - 64x + 56$?
What is the completely factored form of $21x^3 + 3x^2 - 35x - 5$?
What is the completely factored form of $21x^3 + 3x^2 - 35x - 5$?
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Study Notes
Factoring Techniques
- Methods of Factoring: Utilize various methods including GCF (Greatest Common Factor), Magic X, Grouping, and Difference of Squares.
Examples of Factoring
- Factor expressions completely for practice, ensuring to explore different methods for each.
Sample Expressions
- Expression Factors:
- 1) Factored: ( b(-a + 2b - 2) )
- 2) Factored: ( 3x^4(5x^2 + y - 1) )
- 3) Quadratic Factors: ( (v + 3)(v - 9) )
- 4) Quadratic Factors: ( (n - 3)(n - 6) )
- 5) Factored as ( (7x + 2)^2 )
- 6) Difference of Squares: ( (1 + k)(1 - k) )
- 7) Perfect Square Difference: ( 9(3m + 2)(3m - 2) )
- 8) Grouping gives ( (x^2 - 8)(8x - 7) )
Additional Factored Forms
- 9) Factored: ( (3x^2 - 5)(7x + 1) )
- 10) Factored: ( -8m(8mn + 7) )
- 11) Factored out ( 10u ) resulting in ( 10u(uv^2 - 5) )
- 12) Factored as: ( (4b - 1)^2 )
- 13) Quadratic Factors: ( (2n - 3)^2 )
- 14) Quadratic Factors: ( (5n + 2)^2 )
- 15) Factored: ( (7n + 8)(n + 6) )
- 16) Quadratic Factors: ( (7x - 2)(x - 10) )
Focus Areas for Study
- Understand how to identify the appropriate factoring technique based on the structure of the expression.
- Practice factoring using different methods to increase versatility in solving algebraic expressions.
- Review perfect squares and common factor extraction, ensuring clarity on each method's applicability.
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