Answer :
Sure! Let's solve the problem step by step.
We need to find the quotient when the polynomial [tex]\((-12x^9 + 3x^7 + 24x^6)\)[/tex] is divided by [tex]\(6x\)[/tex].
To do this, we'll divide each term of the polynomial by [tex]\(6x\)[/tex].
1. First Term: [tex]\(-12x^9 \div 6x\)[/tex]
[tex]\[
\frac{-12x^9}{6x} = -2x^{9-1} = -2x^8
\][/tex]
2. Second Term: [tex]\(3x^7 \div 6x\)[/tex]
[tex]\[
\frac{3x^7}{6x} = \frac{3}{6}x^{7-1} = \frac{1}{2}x^6
\][/tex]
3. Third Term: [tex]\(24x^6 \div 6x\)[/tex]
[tex]\[
\frac{24x^6}{6x} = 4x^{6-1} = 4x^5
\][/tex]
Now, let's write the quotient from the simplified terms:
[tex]\[
-2x^8 + \frac{1}{2}x^6 + 4x^5
\][/tex]
The correct answer is option B: [tex]\(-2x^8 + \frac{1}{2}x^6 + 4x^5\)[/tex].
We need to find the quotient when the polynomial [tex]\((-12x^9 + 3x^7 + 24x^6)\)[/tex] is divided by [tex]\(6x\)[/tex].
To do this, we'll divide each term of the polynomial by [tex]\(6x\)[/tex].
1. First Term: [tex]\(-12x^9 \div 6x\)[/tex]
[tex]\[
\frac{-12x^9}{6x} = -2x^{9-1} = -2x^8
\][/tex]
2. Second Term: [tex]\(3x^7 \div 6x\)[/tex]
[tex]\[
\frac{3x^7}{6x} = \frac{3}{6}x^{7-1} = \frac{1}{2}x^6
\][/tex]
3. Third Term: [tex]\(24x^6 \div 6x\)[/tex]
[tex]\[
\frac{24x^6}{6x} = 4x^{6-1} = 4x^5
\][/tex]
Now, let's write the quotient from the simplified terms:
[tex]\[
-2x^8 + \frac{1}{2}x^6 + 4x^5
\][/tex]
The correct answer is option B: [tex]\(-2x^8 + \frac{1}{2}x^6 + 4x^5\)[/tex].
