Question
Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
15y6–30y5+15y4–15y3
15y6–30y5+15y4–15y3
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Answered by
GPT-4o mini
To factor out the greatest common factor (GCF) from the polynomial \(15y^6 - 30y^5 + 15y^4 - 15y^3\), we first need to identify the GCF of the coefficients and the lowest power of \(y\) in each term.
1. **Coefficients**: The coefficients are 15, -30, 15, and -15. The GCF of these numbers is 15.
2. **Powers of \(y\)**: The powers of \(y\) are \(y^6\), \(y^5\), \(y^4\), and \(y^3\). The lowest power is \(y^3\).
Thus, the GCF of the entire polynomial is \(15y^3\).
Now, we can factor out \(15y^3\) from each term:
\[
15y^6 - 30y^5 + 15y^4 - 15y^3 = 15y^3(y^3 - 2y^2 + y - 1)
\]
So, the fully factored form of the polynomial is:
\[
\boxed{15y^3(y^3 - 2y^2 + y - 1)}
\]
1. **Coefficients**: The coefficients are 15, -30, 15, and -15. The GCF of these numbers is 15.
2. **Powers of \(y\)**: The powers of \(y\) are \(y^6\), \(y^5\), \(y^4\), and \(y^3\). The lowest power is \(y^3\).
Thus, the GCF of the entire polynomial is \(15y^3\).
Now, we can factor out \(15y^3\) from each term:
\[
15y^6 - 30y^5 + 15y^4 - 15y^3 = 15y^3(y^3 - 2y^2 + y - 1)
\]
So, the fully factored form of the polynomial is:
\[
\boxed{15y^3(y^3 - 2y^2 + y - 1)}
\]
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