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Write in the factored form by factoring out the greatest common factor (or negative common factor if the coefficient of the term of greatest degree is negative)

Write In The Factored Form By Factoring Out The Greatest Common Factor Or Negative Common Factor If The Coefficient Of The Term Of Greatest Degree Is Negative class=

Sagot :

[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

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