Here are some examples of factoring trinomials with GCF:
- Factor out the GCF
- 10x + 30 = 10(x + 3)
- 20y² + 15 = 5(4y² + 3)
- 8x4 - 4x² = 4x²(2x² - 1)
- 32x + 2x³ + 8x² = 2x²(16x² + x + 4)
- 27x³y²³ - 18xy² + 45x²y = 9xy(3xy² - 2y + 5x)
- Factor each trinomial
- x² + 11x + 10
- y² - 16y + 48
- x² + 7xy + 6y²
- 3x² - 33x + 54
Always remember that when there's a GCF, you should factor it out first!
Leading Coefficient #1
Example:
Box method:
Two methods:
- Multiply to 6, add to 5
- 3x² - 25x - 287
- (-28) + (-84) = -25
- (-28) x (-84) = 3x²
- Factor it out first
- 4x² - 18x - 10
- 2(2x² - 9x - 5)
In every case, it's important to factor out the GCF first before proceeding with the rest of the factoring.
3 divide out GCF
- 2(2x - 10)(2x + 1)
- 2(x - 5)(2x + 1)
- (3x + 3)(3x - 28)
These are essential methods for factoring trinomials and should be understood thoroughly in order to solve various types of factoring problems effectively.
Frequently asked questions on the topic of Algebra 2
Q: What is the first step when factoring trinomials with GCF?
A: The first step is to factor out the greatest common factor (GCF) from the trinomial.
Q: What is the box method used for in factoring trinomials?
A: The box method is used to help factor trinomials by breaking them down into two binomials.
Q: What are the two methods for factoring trinomials with leading coefficients?
A: The two methods are to multiply to get the constant term and add to get the coefficient of the middle term, or to factor out the GCF first before proceeding.
Q: Why is it important to factor out the GCF first when factoring trinomials?
A: Factoring out the GCF first simplifies the trinomial and makes it easier to factor the remaining terms.
Q: How can you factor trinomials with GCF using the x method?
A: The x method involves splitting the middle term of the trinomial and using the product-sum method to factor it into two binomials.
