ax^3 + bx^2 +cx + d
P(0) = -3 indicates that d = - 3
And
a + b + c - 3 = 4
a + b + c = 7
ax + (b - a)
x^2 + x + 1 [ ax^3 + bx^2 + cx - 3 ]
ax^3 +ax^2 + ax
____________________________
(b - a) x^2 + ( c - a)x - 3
(b - a)x^2 + (b - a)x + ( b - a)
___________________________
( - b + c))x + ( a - b - 3) = 2x - 1
Then...we have this system
- b + c = 2 c = 2 + b (1)
a - b - 3 = -1 ⇒ a - b = 2 ⇒ a = b + 2 (2)
a + b + c = 7 (3)
Sub (1) and (2) into (3)
(b + 2) + b + ( b + 2) = 7
3b = 3
b = 1
a = 3
c = 3
So
ax + ( b - a) =
3x + ( 1 - 3) =
3x - 2 = the quotient