Question
Find the greatest common factor of the terms of the polynomial. \[ 18 u^{4}-17 u+8 \]
Ask by Lindsey Ortiz. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The greatest common factor of the terms in the polynomial \(18u^{4} - 17u + 8\) is 1.
Solution
1. Write the polynomial:
\[
18u^4 - 17u + 8
\]
2. Identify the coefficients of each term:
\[
18, \quad -17, \quad 8
\]
3. Find the greatest common divisor (GCD) of the coefficients.
The GCD of \(18\), \(17\) (which is prime), and \(8\) is 1 because \(17\) does not share any factors with \(18\) or \(8\) other than 1.
4. Check for any common variable factors.
The terms have the variables: \(u^4\), \(u\), and no variable in \(8\). Since not all terms contain the variable \(u\), there is no common variable factor.
5. Conclude that the greatest common factor (GCF) of the terms of the polynomial is:
\[
1
\]
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Simplify this solution Mind Expander
To find the greatest common factor (GCF) of the terms in the polynomial \( 18 u^{4} - 17 u + 8 \), we can look at the coefficients of each term: 18, -17, and 8. The factors of 18 are \(1, 2, 3, 6, 9, 18\), the factors of -17 are \(1, 17\) (considering only the positive factor since GCF is positive), and the factors of 8 are \(1, 2, 4, 8\). The only common factor among them is 1. Thus, the GCF of the polynomial \( 18 u^{4} - 17 u + 8 \) is \(1\). Therefore, there is no common factor among the terms other than 1.
