Question

Prove that x+2 is a factor of 6x^3+19x^2+16x+4 by using factor theorem and also factorise 6x^3+19x^2+4​

Answer 1

let p(x) = 6x^3 +19x^2 +16x +4

g(x) = x +2

here x = -2

by factor theorem if p(-2) is equal to 0 then g(x) is the factor of p(-2)

p(-2) = 6(-2)^3 +19(-2)^2 +16(-2) +4

p(-2) = 6(-8) +19(4) +16(-2)+4

p(-2) = -48 +76 -32 +4

p(-2) = -80 +80

p(-2) = 0

so g(x) = x+2 is the factor of p(-2)