College

We appreciate your visit to What is the quotient when tex left 12x 9 3x 7 24x 6 right tex is divided by tex 6x tex A tex 2x 9. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

What is the quotient when [tex]\left(-12x^9 + 3x^7 + 24x^6\right)[/tex] is divided by [tex]6x[/tex]?

A. [tex]2x^9 + 2x^7 + 4x^6[/tex]

B. [tex]-2x^8 + 2x^6 + 4x^5[/tex]

C. [tex]-2x^8 + \frac{1}{2}x^6 + 4x^5[/tex]

D. [tex]2x^8 + \frac{1}{2}x^6 + 4x^5[/tex]

Answer :

To divide the polynomial [tex]\((-12x^9 + 3x^7 + 24x^6)\)[/tex] by [tex]\(6x\)[/tex], we need to divide each term of the polynomial by [tex]\(6x\)[/tex].

1. Divide [tex]\(-12x^9\)[/tex] by [tex]\(6x\)[/tex]:

[tex]\[ \frac{-12x^9}{6x} = -2x^{9-1} = -2x^8 \][/tex]

2. Divide [tex]\(3x^7\)[/tex] by [tex]\(6x\)[/tex]:

[tex]\[ \frac{3x^7}{6x} = \frac{3}{6}x^{7-1} = \frac{1}{2}x^6 \][/tex]

3. Divide [tex]\(24x^6\)[/tex] by [tex]\(6x\)[/tex]:

[tex]\[ \frac{24x^6}{6x} = 4x^{6-1} = 4x^5 \][/tex]

Putting it all together, the quotient is:

[tex]\[ -2x^8 + \frac{1}{2}x^6 + 4x^5 \][/tex]

The correct option that matches this result is:

C. [tex]\(-2x^8 + \frac{1}{2}x^6 + 4x^5\)[/tex]

Thanks for taking the time to read What is the quotient when tex left 12x 9 3x 7 24x 6 right tex is divided by tex 6x tex A tex 2x 9. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada