[tex]-7x^6(6x+1)[/tex]
Explanation
Step 1
Find the GCF of all the terms in the polynomial.
[tex]\begin{gathered} -42x^7-7x^6 \\ \end{gathered}[/tex][tex]\begin{gathered} -42x^7=-1\cdot2\cdot3\cdot7\cdot x^{}\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x \\ -7x^6=-1\cdot7\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x \end{gathered}[/tex]
so ,
[tex]\begin{gathered} \text{the GCF of }-42x^7-7x^6\text{ is} \\ -7x^6 \end{gathered}[/tex]
Step 2
Express each term as a product of the GCF and another factor.
[tex]-42x^7-7x^6=(6x\cdot-7x^6)+(1\cdot-7x^6)[/tex]
Step 3
Use the distributive property to factor out the GCF.
[tex]\begin{gathered} (6x\cdot-7x^6)+(1\cdot-7x^6)=-7x^6(6x+1) \\ \end{gathered}[/tex]
so, the answer is
[tex]-7x^6(6x+1)[/tex]
I hope this helps you
