Question

please tell me answer​

Answer 1

Solution:

m4-3m2-8/m+2

using synthetic division

To determine root divisor, we have to solve divisor equation m+2=0

Our root becomes x=-2

Write coefficients of the dividend m4+0m3-3m2+0m-8 to the right and our root -2 to the left

-2 |1 0 -3 0 -8


Step-1 : Write down the first coefficient 1

-2 |1 0 -3 0 -8
1


Step-2 : Multiply our root -2 by our last result 1 to get -2 [ (-2) × 1=-2 ]

-2 |1 0 -3 0 -8
-2
1


Step-3 : Add new result -2 to the next coefficient of the dividend 0, and write down the sum -2, [ 0 + (-2)=-2 ]

-2 |1 0 -3 0 -8
-2
1 -2


Step-4 : Multiply our root -2 by our last result -2 to get 4 [ (-2) × (-2)=4 ]

-2 |1 0 -3 0 -8
-2 4
1 -2


Step-5 : Add new result 4 to the next coefficient of the dividend -3, and write down the sum 1, [ (-3) + 4=1 ]

-2 |1 0 -3 0 -8
-2 4
1 -2 1


Step-6 : Multiply our root -2 by our last result 1 to get -2 [ (-2) × 1=-2 ]

-2 |1 0 -3 0 -8
-2 4 -2
1 -2 1


Step-7 : Add new result -2 to the next coefficient of the dividend 0, and write down the sum -2, [ 0 + (-2)=-2 ]

-2 |1 0 -3 0 -8
-2 4 -2
1 -2 1 -2


Step-8 : Multiply our root -2 by our last result -2 to get 4 [ (-2) × (-2)=4 ]

-2 |1 0 -3 0 -8
-2 4 -2 4
1 -2 1 -2


Step-9 : Add new result 4 to the next coefficient of the dividend -8, and write down the sum -4, [ (-8) + 4=-4 ]

-2 |1 0 -3 0 -8
-2 4 -2 4
1 -2 1 -2 -4


We have completed the table and have obtained the following coefficients
1,-2,1,-2,-4

All coefficients, except last one, are coefficients of quotient, last coefficient is remainder.
Thus quotient is m3-2m2+m-2 and remainder is -4

m4+3m2-8=(m3-2m2+m-2)(m+2)+(-4)

Hope this will help.