Question

Check whether (2 + x) is a factor of 3$x^3$ + 7x +19.

Answer 1

Zero of 2 + x is:

2+ x = 0

⇒ x = -2

If p(x) = 3${-2}^3$ + 7x + 19 is divisible by (2 + x) then its remainder is zero i.e. ⇔ p(-2) = 0

p(-2) = 3${(-2)}^3$+ 7(-2) + 19 = 3(-8) +7(-2) + 19

= -24 -14 +19 = -19 ≠ 0

⇒ 2 + x is not a factor of 3$x^3$ + 7x + 19