Step 1- Divide the polynomial by x-2 via normal division method. You will get remainder in the form of a and b. ( 2(14+a) + b. Equate it to 2

Step 2- Divide the polynomial by x+2 via normal division method. You will get remainder in the form of a and b. Equate it to -2.

Step 3- Now, you have got 2 equations. Now, since both of these equations are in form of a and b, solve them and you will get the answer for a and b. ( it will be a=-7 and b=-12!)

Hope this helps!

Hello,

Let P(x) = 2x^3+ 3x^2+ ax+ b

Now when the P(x) divides by x-2 then the reminder is b+ 2a+ 28 but according to question reminder should be +2. So the b+ 2a+ 28 = 2

Hence b+ 2a = -26 this is 1 equation

Now when the P(x) divides by x+2 then the reminder is b- 2a- 4 but according to question reminder should be -2 . So the b- 2a- 4= -2

Hence b- 2a = 2 this is 2 equation.

By solving both the equation you may get the values

a = -7

b = -12

Hope this may helps you!