When mn+m^2-30n^2 is divided by m-5n, what is the quotient. Thank you
what is (m-5n)(m+6n)/(m-5n) ?
Don't be put off by the extra variable. You can easily factor
m^2+m-30, right? That's what you have if n=1.
I don't understand. Then what is the final answer
ahem
(m-5n)(m+6n)/(m-5n) = m+6n
!!
There is an interesting video showing how to do long division with two variables at
http://www.mathsisfun.com/algebra/polynomials-division-long.html
Scroll most of the way down the page to where the heading is "More than One Variable".
Follow its method using your problem and it should become clear.
Thanks
To find the quotient, we need to perform polynomial long division. Here's how you can do it step-by-step:
Step 1: Arrange the terms in descending order of degree.
Start by arranging the terms of the dividend, which is mn + m^2 - 30n^2, in descending order of degree:
m^2 + mn - 30n^2.
Step 2: Start the division process.
Divide the first term of the dividend (m^2) by the first term of the divisor (m):
m^2 / (m - 5n) = m.
Step 3: Multiply the divisor by the quotient obtained.
Multiply the divisor (m - 5n) by the quotient obtained (m):
m * (m - 5n) = m^2 - 5mn.
Step 4: Subtract the result from the dividend.
Subtract the result of the multiplication (m^2 - 5mn) from the dividend (m^2 + mn - 30n^2):
(m^2 + mn - 30n^2) - (m^2 - 5mn) = mn + 30n^2.
Step 5: Repeat the division process.
Repeat steps 2-4 with the new dividend (mn + 30n^2) and the same divisor (m - 5n).
Step 6: Divide the first term of the new dividend by the first term of the divisor.
Divide the first term of the new dividend (mn) by the first term of the divisor (m):
mn / (m - 5n) = n.
Step 7: Multiply the divisor by the new quotient.
Multiply the divisor (m - 5n) by the new quotient (n):
n * (m - 5n) = mn - 5n^2.
Step 8: Subtract the result from the new dividend.
Subtract the result of the multiplication (mn - 5n^2) from the new dividend (mn + 30n^2):
(mn + 30n^2) - (mn - 5n^2) = 35n^2.
Step 9: Check if there is any remainder.
Since we cannot further divide 35n^2 by m - 5n without a remainder, we have completed the division process.
Step 10: Write the final quotient.
The final quotient is obtained by combining the quotients obtained in steps 2 and 6:
m + n.
So, when mn + m^2 - 30n^2 is divided by m - 5n, the quotient is m + n.