Answer
Verified
418.2k+ views
Hint: In this question we have to divide the $\left( 6{{\omega }^{5}}-18{{\omega }^{2}}-120 \right)$ by $\left( \omega -2 \right)$. To solve the question we will use the long division method. For this first we will write the all terms in decreasing power of the variable order including the missing terms. Then we start dividing the terms by following the step by step procedure.
Complete step by step answer:
We have been given that $\left( 6{{\omega }^{5}}-18{{\omega }^{2}}-120 \right)\div \left( \omega -2 \right)$.
We have to perform division.
We know that the dividend is divided by divisor to get the quotient.
Here we have dividend $=\left( 6{{\omega }^{5}}-18{{\omega }^{2}}-120 \right)$, divisor $=\left( \omega -2 \right)$.
To solve the given equation we will use the long division method.
For this first we need to arrange the terms in decreasing power of the variable including the missing terms. Missing terms will be written with the coefficient zero so that the meaning of the given expression cannot be changed. Then we will get
$\Rightarrow \left( 6{{\omega }^{5}}+0{{\omega }^{4}}+0{{\omega }^{3}}-18{{\omega }^{2}}+0\omega -120 \right)$
Now, let us start dividing the terms by long division method. Then we will get
\[\omega -2\overset{6{{\omega }^{4}}+12{{\omega }^{3}}+24{{\omega }^{2}}+30\omega +60}{\overline{\left){\begin{align}
& 6{{\omega }^{5}}+0{{\omega }^{4}}+0{{\omega }^{3}}-18{{\omega }^{2}}+0\omega -120 \\
& \underline{6{{\omega }^{5}}-12{{\omega }^{4}}} \\
& 12{{\omega }^{4}} \\
& 12{{\omega }^{4}}-24{{\omega }^{3}} \\
& \underline{\overline{\begin{align}
& 24{{\omega }^{3}}-18{{\omega }^{2}} \\
& 24{{\omega }^{3}}-48{{\omega }^{2}} \\
\end{align}}} \\
& 30{{\omega }^{2}} \\
& \underline{30{{\omega }^{2}}-60\omega } \\
& 60\omega -120 \\
& \underline{60\omega -120} \\
& 0 \\
\end{align}}\right.}}\]
So on dividing the given expression $\left( 6{{\omega }^{5}}-18{{\omega }^{2}}-120 \right)\div \left( \omega -2 \right)$ we get the quotient as \[6{{\omega }^{4}}+12{{\omega }^{3}}+24{{\omega }^{2}}+30\omega +60\].
Note:
In algebraic long division methods we need to follow the same steps as we follow in the arithmetic. We need to perform division until no term is left in the divisor. We can also check our answer by using the formula that $\text{Dividend=quotient}\times \text{divisor+remainder}\text{.}$. So by substituting the values we can verify the answer.
Complete step by step answer:
We have been given that $\left( 6{{\omega }^{5}}-18{{\omega }^{2}}-120 \right)\div \left( \omega -2 \right)$.
We have to perform division.
We know that the dividend is divided by divisor to get the quotient.
Here we have dividend $=\left( 6{{\omega }^{5}}-18{{\omega }^{2}}-120 \right)$, divisor $=\left( \omega -2 \right)$.
To solve the given equation we will use the long division method.
For this first we need to arrange the terms in decreasing power of the variable including the missing terms. Missing terms will be written with the coefficient zero so that the meaning of the given expression cannot be changed. Then we will get
$\Rightarrow \left( 6{{\omega }^{5}}+0{{\omega }^{4}}+0{{\omega }^{3}}-18{{\omega }^{2}}+0\omega -120 \right)$
Now, let us start dividing the terms by long division method. Then we will get
\[\omega -2\overset{6{{\omega }^{4}}+12{{\omega }^{3}}+24{{\omega }^{2}}+30\omega +60}{\overline{\left){\begin{align}
& 6{{\omega }^{5}}+0{{\omega }^{4}}+0{{\omega }^{3}}-18{{\omega }^{2}}+0\omega -120 \\
& \underline{6{{\omega }^{5}}-12{{\omega }^{4}}} \\
& 12{{\omega }^{4}} \\
& 12{{\omega }^{4}}-24{{\omega }^{3}} \\
& \underline{\overline{\begin{align}
& 24{{\omega }^{3}}-18{{\omega }^{2}} \\
& 24{{\omega }^{3}}-48{{\omega }^{2}} \\
\end{align}}} \\
& 30{{\omega }^{2}} \\
& \underline{30{{\omega }^{2}}-60\omega } \\
& 60\omega -120 \\
& \underline{60\omega -120} \\
& 0 \\
\end{align}}\right.}}\]
So on dividing the given expression $\left( 6{{\omega }^{5}}-18{{\omega }^{2}}-120 \right)\div \left( \omega -2 \right)$ we get the quotient as \[6{{\omega }^{4}}+12{{\omega }^{3}}+24{{\omega }^{2}}+30\omega +60\].
Note:
In algebraic long division methods we need to follow the same steps as we follow in the arithmetic. We need to perform division until no term is left in the divisor. We can also check our answer by using the formula that $\text{Dividend=quotient}\times \text{divisor+remainder}\text{.}$. So by substituting the values we can verify the answer.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which places in India experience sunrise first and class 9 social science CBSE
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE