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Answer :
To factor the polynomial
[tex]$$3x^7 + 2x^6 + 7x^5,$$[/tex]
follow these steps:
1. Identify the common factor:
All terms in the polynomial have a factor of [tex]$x^5$[/tex].
2. Factor out [tex]$x^5$[/tex]:
Divide each term by [tex]$x^5$[/tex]:
[tex]\[
\begin{aligned}
3x^7 & = x^5 \cdot 3x^2, \\
2x^6 & = x^5 \cdot 2x, \\
7x^5 & = x^5 \cdot 7.
\end{aligned}
\][/tex]
Thus, the polynomial can be written as:
[tex]\[
3x^7 + 2x^6 + 7x^5 = x^5(3x^2 + 2x + 7).
\][/tex]
3. Final factored form:
The polynomial is completely factored as:
[tex]\[
x^5(3x^2 + 2x + 7).
\][/tex]
This is the final answer.
[tex]$$3x^7 + 2x^6 + 7x^5,$$[/tex]
follow these steps:
1. Identify the common factor:
All terms in the polynomial have a factor of [tex]$x^5$[/tex].
2. Factor out [tex]$x^5$[/tex]:
Divide each term by [tex]$x^5$[/tex]:
[tex]\[
\begin{aligned}
3x^7 & = x^5 \cdot 3x^2, \\
2x^6 & = x^5 \cdot 2x, \\
7x^5 & = x^5 \cdot 7.
\end{aligned}
\][/tex]
Thus, the polynomial can be written as:
[tex]\[
3x^7 + 2x^6 + 7x^5 = x^5(3x^2 + 2x + 7).
\][/tex]
3. Final factored form:
The polynomial is completely factored as:
[tex]\[
x^5(3x^2 + 2x + 7).
\][/tex]
This is the final answer.
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