Question

If (x-2) is a factor of the expression 2xcube+axsquare+bx-14 and when the expression is divided by (x-3), it leaves a remainder 52, find the values a and b.

Answer 1

hello...

p(x)= 2x³+ax²+bx-14
put (x-2) factor of p(x)
x-2=0
x=2
put x=2
2(2)³+a(2)²+b(2)-14=0
16+2a+2b-14=0
8+2a+2b-14=0
2a+b+1=0... eq 1

Now divide p(x) by x-3
(x-3)=0
x=3

Now put x=3
2(3)³+a(3)²+b(3)-14=52
2(27)+a(9)+b(3)-14=52
54+9a+3b-14=52
54+9a+3b-14-52=0
9a+3b-12=0
3a+b-4=0 .... eq 2

If you​ will subtract eq2 - eq1 You will get value of a that will be a-5
when u will have zero...
a-5=0
a=5

now you have to take a=5
2(5)+b(1)=0 
10+b=0
b= -10