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Answer :
To factor the polynomial [tex]\(-80x^5 + 90x + 60\)[/tex], we need to first identify the greatest common factor (GCF) of the terms in the polynomial.
### Step-by-Step Solution:
1. Identify the terms:
- The polynomial given is [tex]\(-80x^5 + 90x + 60\)[/tex].
2. Find the GCF of the coefficients:
- We look at the coefficients: [tex]\(-80\)[/tex], [tex]\(90\)[/tex], and [tex]\(60\)[/tex].
- The GCF of these numbers is [tex]\(10\)[/tex].
3. Factor out the GCF:
- We factor out [tex]\(10\)[/tex] from each term in the polynomial:
[tex]\[
\begin{align*}
&-80x^5 \,(\text{divided by } 10) = -8x^5, \\
&90x \,(\text{divided by } 10) = 9x, \\
&60 \,(\text{divided by } 10) = 6.
\end{align*}
\][/tex]
4. Rewrite the polynomial:
- After factoring out the GCF, the polynomial becomes:
[tex]\[
10(-8x^5 + 9x + 6)
\][/tex]
Thus, the polynomial [tex]\(-80x^5 + 90x + 60\)[/tex] can be factored as [tex]\(10(-8x^5 + 9x + 6)\)[/tex].
### Step-by-Step Solution:
1. Identify the terms:
- The polynomial given is [tex]\(-80x^5 + 90x + 60\)[/tex].
2. Find the GCF of the coefficients:
- We look at the coefficients: [tex]\(-80\)[/tex], [tex]\(90\)[/tex], and [tex]\(60\)[/tex].
- The GCF of these numbers is [tex]\(10\)[/tex].
3. Factor out the GCF:
- We factor out [tex]\(10\)[/tex] from each term in the polynomial:
[tex]\[
\begin{align*}
&-80x^5 \,(\text{divided by } 10) = -8x^5, \\
&90x \,(\text{divided by } 10) = 9x, \\
&60 \,(\text{divided by } 10) = 6.
\end{align*}
\][/tex]
4. Rewrite the polynomial:
- After factoring out the GCF, the polynomial becomes:
[tex]\[
10(-8x^5 + 9x + 6)
\][/tex]
Thus, the polynomial [tex]\(-80x^5 + 90x + 60\)[/tex] can be factored as [tex]\(10(-8x^5 + 9x + 6)\)[/tex].
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