How do you find the quotient #(3y^3+8y^2+y-7)div(y+2)# using long division?

Question

Ethan Adkins · Accepted Answer

#3y^2+2y-3#

Kennedy Adams · Answer

The quotient is #=3y^2+2y-3#

Let's perform the long division

#color(white)(aaaa)##3y^3+8y^2+y-7##color(white)(aaaa)##|##y+2#

#color(white)(aaaa)##3y^3+6y^2##color(white)(aaaaaaaaaaa)##|##3y^2+2y-3#

#color(white)(aaaaa)##0+2y^2+y#

#color(white)(aaaaaaa)##+2y^2+4y#

#color(white)(aaaaaaaa)##+0-3y-7#

#color(white)(aaaaaaaaaaaa)##-3y-6#

#color(white)(aaaaaaaaaaaaa)##-0-1#

The quotient is #=3y^2+2y-3# and the remainder is #=-1#

Eva Adamson · Answer

undefined To find the quotient using long division, follow these steps:

1. Divide the first term of the dividend (3y^3) by the first term of the divisor (y). The result is 3y^2.
2. Multiply the entire divisor (y+2) by the quotient obtained in step 1 (3y^2). The result is 3y^3 + 6y^2.
3. Subtract the product obtained in step 2 from the dividend (3y^3 + 8y^2 + y - 7). The result is 2y^2 + y - 7.
4. Bring down the next term from the dividend (-7).
5. Divide the first term of the new dividend (2y^2) by the first term of the divisor (y). The result is 2y.
6. Multiply the entire divisor (y+2) by the quotient obtained in step 5 (2y). The result is 2y^2 + 4y.
7. Subtract the product obtained in step 6 from the new dividend (2y^2 + y - 7). The result is -3y - 7.
8. Bring down the next term from the dividend (-7).
9. Divide the first term of the new dividend (-3y) by the first term of the divisor (y). The result is -3.
10. Multiply the entire divisor (y+2) by the quotient obtained in step 9 (-3). The result is -3y - 6.
11. Subtract the product obtained in step 10 from the new dividend (-3y - 7). The result is -1.
12. There are no more terms to bring down, so the division is complete.
13. The quotient is 3y^2 + 2y - 3, and the remainder is -1.