To find the Greatest Common Factor (GCF) of the given polynomial terms \(18x^4 - 27x^3 - 36x^2\), let's break down each term and find the GCF of both the coefficients and the variable parts.
**Step 1: Factor the coefficients**
- The coefficients are 18, 27, and 36.
- The prime factors of 18 are \(2 \times 3^2\).
- The prime factors of 27 are \(3^3\).
- The prime factors of 36 are \(2^2 \times 3^2\).
The common prime factor among these coefficients is \(3\), and the highest power of 3 common to all is \(3^2 = 9\).
**Step 2: Factor the variable parts**
- The variable parts are \(x^4, x^3, \) and \(x^2\).
- The GCF of \(x^4, x^3,\) and \(x^2\) is \(x^2\) since \(x^2\) is the highest power of \(x\) that is present in each term.
**Step 3: Combine the GCF of the coefficients and the variable parts**
- The GCF of the coefficients is \(9\).
- The GCF of the variable parts is \(x^2\).
Therefore, the GCF of the terms \(18x^4 - 27x^3 - 36x^2\) is:
\[
9x^2
\]
So, the correct answer is:
\(9x^2\).
16.
Find the GCF of the terms of the polynomial.
18x4 – 27x3– 36x2
8x
18x2
9x
9x2
1 answer