Question

If x3 + ax2 + bx + 6 has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3)

Answer 1

Answer:

a=-3,b=-1

Step-by-step explanation

X^3+ax^2+bx+6

x-2 is factor

x-2=0

x=2

2^3+a2^2+2b+6=0

8+4a+2b+6=0

4a+2b=-14

2a+b=-7-eqn-1

x^3+ax^2+bx+6 is dived by x-3

so x-3=0

x=3

3^3+9a+3b+6=3

9a+3b=-30

3a+b=-10-eqn-2

from eqn-1&2

a=-3&b=-1