Question

factorise x 3 + 6 x 2 + 11 x + 6​

Answer 1

QUESTION :

factorise x 3 + 6 x 2 + 11 x + 6

CORRECTION IN QUESTION :

Factorise x³+6x²+11x+6

ANSWER :

let p(X) = x³+6x²+11x+6

now by trial an error method

let us find the value of x for which p(X) will be equal to zero

now p(X)= x³+6x²+11x+6

let x=(-1)

so p(-1) = (-1)³+6(-1)²+11(-1)+6

=-1+6-11+6

=-12+12

=0

so for X=(-1)

p(X)=0

so (x+1) =0

i.e (X+1) is a factor of p(X)

now

by long division method (refer attachment)

dividing p(X) by (X+1)

we get

(X+1)(x²+5x+6)

now by splitting the middle term method

(X+1)(x²+2x+3x+6)

(X+1)(X(X+2)+3(X+2))

(X+1)(X+2)(X+3)

so the factors of p(X)=x³+6x²+11x+6

are (X+1)(X+2)(X+3)

and the zeroes of p(X) = x³+6x²+11x+6

are x={-1,-2,-3}