Question

If ( x + 1 ) is a factor of x^3 + ax^2 + 11x + 6 then find ( a + 2 ).​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

( x + 1 ) is a factor of the polynomial

$x^3 + ax^2 + 11x + 6$

TO DETERMINE

The value of ( a + 2)

CALCULATION

The zero of the polynomial x +1 is given by

$x + 1 = 0$

$\implies\displaystyle \: x = - 1$

$Let \: \: f(x) = x^3 + ax^2 + 11x + 6$

Now by the Remainder Theorem the required Remainder is

$f( - 1) = ( - 1)^3 + a \times ( - 1)^2 + 11 \times ( - 1) + 6$

$\implies \: f( - 1) = - 1 + a - 11 + 6 = a - 6$

Since ( x + 1 ) is a factor of the polynomial

So

$a - 6 = 0$

$\implies \: a = 6$

$\therefore \: a + 2 = 6 + 2 = 8$

RESULT

$\red{ \fbox{SO THE REQUIRED ANSWER IS 8}}$