Question

factories x3+6x2+11x+6

Answer 1

=>question is,
x³+6x²+11x+6
x³+x²+5x²+5x+6x+6
x²(x+1)+5x(x+1)+6(x+1)
(x+1)(x²+5x+6)
(x+1)(x²+3x+2x+6)
(x+1){x(x+3)+2(x+3)}
(x+1)(x+3)(x+2)

Answer 2

$\textbf{ Hello Mate! }$

$p(x) = x^3 + 6x^2 + 11x + 6 \\ Keeping\: value\: of\: x\:as\:-1 we\:get \\ p(-1) = -1^3 + 6(-1^2) + 11(-1) + 6 \\ p(-1) = - 1 + 6 - 11 + 6 \\ = 0$

Hence, factor of p(x) is ( x + 1 ). On doing actual division we get,

 $\frac{ x^3 + 6x^2 + 11x + 6 }{ x + 1 } \\ => x^2 + 5x + 6$

Dividend = divisior × questiont

$p(x) = ( x + 1 )( x^2 + 5x + 6 ) \\ = ( x + 1 )[ x^2 + 2x + 3x + 6 ] \\ = ( x + 1 )[x(x + 2) + 3(x + 2) ] \\ = (x+1)(x+2)(x+3)$

$\boxed{ \textsf{ \red{ Factors\:are\:(x+1)(x+2)(x+3) }}}$

Have great future ahead!