Question

Find the value of k so that the polynomial x3 − 3² − 4 + is divisible by (x+2). Hence factorise the polynomial.

Answer 1

let p(x) = x^3 - 3^2 - 4 + k

p(x) = x^3 -13 +k -------(1)

let g(x) = x +2

x+ 2 = 0 ,

x= -2

now put value of "x" in (1)

p(-2) = (-2)^3 - 13 +k

= -8 -13 + k

-21 + k =0

k =21

this implies that" K "= 21

put value of "k" in eq.(1)

so the obtained
poliynomial ,

x^3 - 13 +21

= x^3 + 8

= x^3 + 2^3

= ( x + 2) ( x^2 - 2x + 2^2)

= (x+2 ) ( x^2 -2 x + 4 )

hope it helps!
thank you !

=-

Answer 2

Here's your answer for this question