Question
Factor out the greatest common factor from the terms of the polynomial 6x3−12x2+18x
6
𝑥
3
−
12
𝑥
2
+
18
𝑥
How to find Greatest Common Factor in polynomials.
(1 point)
The GCF of the polynomial given is: BLANK
6
𝑥
3
−
12
𝑥
2
+
18
𝑥
How to find Greatest Common Factor in polynomials.
(1 point)
The GCF of the polynomial given is: BLANK
Answers
GPT-4o mini
To find the Greatest Common Factor (GCF) of the polynomial \(6x^3 - 12x^2 + 18x\), follow these steps:
1. **Identify the coefficients**: The coefficients are 6, -12, and 18.
- The GCF of these numbers is 6.
2. **Identify the variable part**: The variable terms are \(x^3\), \(x^2\), and \(x\).
- The GCF of the powers of \(x\) is \(x\) (the lowest power).
3. **Combine the GCF of the coefficients and the variable part**:
- The GCF of the entire polynomial is \(6x\).
Now, let's write the polynomial factored by the GCF:
\[
6x^3 - 12x^2 + 18x = 6x(x^2 - 2x + 3)
\]
Thus, the GCF of the polynomial \(6x^3 - 12x^2 + 18x\) is **6x**.
1. **Identify the coefficients**: The coefficients are 6, -12, and 18.
- The GCF of these numbers is 6.
2. **Identify the variable part**: The variable terms are \(x^3\), \(x^2\), and \(x\).
- The GCF of the powers of \(x\) is \(x\) (the lowest power).
3. **Combine the GCF of the coefficients and the variable part**:
- The GCF of the entire polynomial is \(6x\).
Now, let's write the polynomial factored by the GCF:
\[
6x^3 - 12x^2 + 18x = 6x(x^2 - 2x + 3)
\]
Thus, the GCF of the polynomial \(6x^3 - 12x^2 + 18x\) is **6x**.