How do you divide #(5m^3 - 7m^2 + 14) / (m^2 - 2)#?

Question

Julia Adams · Accepted Answer

#Here , quotient" =>(5m- 7) ##"and Remainder" =10m# #(5m^3 - 7m^2 + 14) / (m^2 - 2)# #=>((5m(m^2-2)+10m - 7(m^2-2)-cancel14 +cancel 14) )/ (m^2 - 2)# #=>((5m(m^2-2) - 7(m^2-2)+10m) )/ (m^2 - 2)# #=>((5m(m^2-2))/ (m^2 - 2)- 7(m^2-2)/ (m^2 - 2)+(10m)/(m^2 - 2) )# #=>(5m- 7+(10m)/(m^2 - 2) )#

Abigail Allen · Answer

undefined To divide (5m^3 - 7m^2 + 14) by (m^2 - 2), we can use polynomial long division.

First, divide the highest degree term of the numerator (5m^3) by the highest degree term of the denominator (m^2). This gives us 5m as the first term of the quotient.

Next, multiply the entire denominator (m^2 - 2) by the first term of the quotient (5m). This gives us 5m * (m^2 - 2) = 5m^3 - 10m.

Subtract this result from the numerator (5m^3 - 7m^2 + 14) to get the new numerator: (5m^3 - 7m^2 + 14) - (5m^3 - 10m) = -7m^2 + 10m + 14.

Now, repeat the process with the new numerator (-7m^2 + 10m + 14) and the denominator (m^2 - 2).

Divide the highest degree term of the new numerator (-7m^2) by the highest degree term of the denominator (m^2). This gives us -7 as the next term of the quotient.

Multiply the entire denominator (m^2 - 2) by the new term of the quotient (-7). This gives us -7 * (m^2 - 2) = -7m^2 + 14.

Subtract this result from the new numerator (-7m^2 + 10m + 14) to get the new numerator: (-7m^2 + 10m + 14) - (-7m^2 + 14) = 10m.

Since the degree of the new numerator (10m) is less than the degree of the denominator (m^2 - 2), we have reached the end of the division.

Therefore, the quotient is 5m - 7 and the remainder is 10m.