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Questions and Answers
What is the greatest common factor of the expression $12k - 18$?
What is the greatest common factor of the expression $12k - 18$?
- 4(3k - 4.5)
- 3(4k - 6)
- 6(2k - 3) (correct)
- 2(6k - 9)
What is the greatest common factor of the expression $3ab^2 - 5a^2b + 8ab$?
What is the greatest common factor of the expression $3ab^2 - 5a^2b + 8ab$?
- a(3b^2 - 5a + 8b)
- b(3a - 5a^2 + 8)
- ab(3b - 5a + 8) (correct)
- 3b(1 - rac{5a}{3} + rac{8}{3b})
What is the first thing you look for when factoring?
What is the first thing you look for when factoring?
Greatest common factor
For the trinomial $ax^2 + bx + cx^2 + 14x + 45$ with $x = 1$, what are the values of $x$?
For the trinomial $ax^2 + bx + cx^2 + 14x + 45$ with $x = 1$, what are the values of $x$?
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For the trinomial $ax^2 + bx + cx^2 + 14x + 45$ with $x > 1$, what are the values of $x$?
For the trinomial $ax^2 + bx + cx^2 + 14x + 45$ with $x > 1$, what are the values of $x$?
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What are the solutions for the equation $x^2 - 4 = 0$?
What are the solutions for the equation $x^2 - 4 = 0$?
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What are the factors of the expression $9x^2 - 25y^4 = 0$?
What are the factors of the expression $9x^2 - 25y^4 = 0$?
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Study Notes
Factoring Basics
- Greatest common factor (GCF) is the largest factor that divides all terms in an expression.
- Example: For the expression 12k - 18, the GCF is 6. Thus, it can be factored as 6(2k - 3).
Factoring Trinomials
- Factoring trinomials involves finding values of x that satisfy the equation.
- Example: For the trinomial ax² + 14x + 45, when x = 1, the solutions are x = -9 and x = -5.
- If the leading coefficient (a) is less than 1, different values emerge, such as x = 3/2 and x = 6 when x > 1.
Difference of Squares
- A difference of squares takes the form a² - b² and can be factored into (a + b)(a - b).
- For the equation x² - 4 = 0, the solutions are x = 2 and x = -2.
- For the expression 9x² - 25y⁴ = 0, it can be factored into (3x + 5y²)(3x - 5y²).
General Factoring Strategies
- When factoring polynomials, the first step is always to look for the greatest common factor (GCF) to simplify before proceeding with other methods.
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