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Sagot :
The polynomial is given below as
[tex]6v^5-18v^4-168v^3[/tex]Step 1: Factor out the highest common factor which is
[tex]6v^3[/tex][tex]\begin{gathered} 6v^5-18v^4-168v^3=6v^3(\frac{6v^5}{6v^3}-\frac{18v^4}{6v^3}-\frac{168v^3}{6v^3}) \\ 6v^5-18v^4-168v^3=6v^3(v^2-3v-28) \end{gathered}[/tex]Step 2: Factorise the quadratic expression
[tex]v^2-3v-28[/tex]To factorize the quadratic expression, we will have to look for two factors that will multiply each other to give a -28, and then the same two factors will add up together to give -3
By try and error, we will have the two factors to be
[tex]\begin{gathered} -7\times+4=-28 \\ -7+4=-3 \end{gathered}[/tex]By replacing the two factors in the equation above, we will have
[tex]\begin{gathered} v^2-3v-28=v^2-7v+4v-28 \\ \text{group the factors to have} \\ (v^2-7v)+(4v-28)=v(v-7)+4(v-7) \\ v^2-3v-28=(v-7)(v+4) \end{gathered}[/tex]Hence,
[tex]6v^5-18v^4-168v^3=6v^3(v-7)(v+4)[/tex]Therefore,
The final answer is 6v³(v - 7)(v + 4)
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