Which is the completely factored form of 12×4 39×3 9×2 – The completely factored form of 12x 439x 39x 2is a mathematical expression that represents the polynomial in its simplest form, where all factors are irreducible. Factoring polynomials involves identifying the greatest common factor (GCF) and factoring it out from each term, followed by factoring the remaining factors into their simplest form.
Understanding the factoring techniques and applying them effectively is essential for solving various algebraic equations and simplifying complex expressions.
Factoring Techniques: Which Is The Completely Factored Form Of 12×4 39×3 9×2
Factoring polynomials involves breaking them down into simpler expressions. By identifying common factors and applying different factoring methods, we can simplify complex polynomials into manageable forms.
Greatest Common Factor (GCF)
To factor out the GCF, we first determine the largest common factor among all the terms. The GCF is then factored out from each term, resulting in a simplified polynomial.
Factoring Methods
- Common Factor Factoring:Identifying and factoring out the common factor from each term.
- Grouping:Grouping terms with common factors and factoring them out as a group.
- Difference of Squares:Factoring polynomials of the form a2– b 2as (a + b)(a- b) .
- Sum and Difference of Cubes:Factoring polynomials of the form a3+ b 3as (a + b)(a2– ab + b 2) and a3– b 3as (a- b)(a 2+ ab + b 2) .
- Quadratic Formula:Using the formula x = (-b ± √(b2– 4ac)) / 2a to factor quadratic polynomials of the form ax2+ bx + c .
Factors of 12x4 39x3 9x2
Greatest Common Factor (GCF)
The GCF of the polynomial is 3x 2. We factor this out from each term:
| Term | GCF | Factored Term |
|---|---|---|
| 12x4 | 3x2 | 3x2(4x2) |
| 39x3 | 3x2 | 3x2(13x) |
| 9x2 | 3x2 | 3x2(3) |
Remaining Factors, Which is the completely factored form of 12×4 39×3 9×2
After factoring out the GCF, we are left with the following polynomial:
3x 2(4x 2+ 13x + 3)
We factor the remaining polynomial as follows:
| Term | Factored Term |
|---|---|
| 4x2 + 13x + 3 | (4x + 1)(x + 3) |
Completely Factored Form
The completely factored form of the polynomial is:
3x 2(4x + 1)(x + 3)
Quick FAQs
What is the greatest common factor (GCF) of 12x439x 39x 2?
The GCF is 3x 2.
How do you factor out the GCF from each term?
Divide each term by the GCF.
What are the remaining factors after removing the GCF?
4x 2, 13x, 3.
