Question

plzz with steps
factorize
$x {}^{3} + 13x {}^{2} + 31x - 45$
given that (x+9) is a factor

Answer 1

P(X) => X³+13X²+31X-45


G(X) => X+9


On dividing P(X) by G(X) we get,

Remainder = 0


And,


Quotient = X2+4X-5


Now,


Factories the Quotient X²+4X-5


=> X²+4X-5


=> X²+5X-X-5


=> X(X+5) -1(X+5)


=> (X+5) (X-1)


=> (X+5) = 0 OR (X-1) = 0


=> X = -5 OR X = 1