If P(x) = x + ax + 3x – 5 has a remainder of –3 when divided by x – 2 find the value of a.

P(x) = x + ax + 3x – 5

given

P(x) = -3
x-2 = > x=2

-3 = 2 + 2a + 3(2) - 5
-3 = 2 + 2a + 6 - 5
-3 = 3 + 2a
-3 -3 = 2a
-6 = 2a
a= -3 answer//

therefore:

P(x) = x -3x +3x - 5 answer//

P(2) = 2 + 2a + 6 – 5 = -3
=> 2a + 5 = -3
=> a = -4. ///

-3

x=2
P(2)=2+2a+6-5=-3
2a+3=-3
2a=-6
a=-3
God bless you.