If x³ − 3x² + 3x + 7 = (x + 1)(ax² + bx + c), Find a + b + c
If \[ x^3-3x^2+3x+7=(x+1)(ax^2+bx+c), \] then \[ a+b+c= \]
(a) \(4\)
(b) \(12\)
(c) \(-10\)
(d) \(3\)
Solution
Put \[ x=1 \]
\[ 1-3+3+7=(1+1)(a+b+c) \]
\[ 8=2(a+b+c) \]
\[ a+b+c=4 \]
Therefore,
\[ \boxed{(a)\ 4} \]