Question

By using factor theorem show that x+2 is a factor of polynomial 3x³-x²-20x-12 hence factorise the given polynomial

Answer 1

By factor theorem if a polynomial p(x) = 0 at x = c then x-c is a factor. So if p(x) = 3x³-x²-20x-12
is zero at x = -2 then x +2 is a factor.
p(-2) = 3(-2)^3 -(-2)^2 -20(-2) -12 = 3(-8)-4+40 -12 = -24-4 +40 -12 = 0
This proves x+2 is a factor.
To get other factors, divide 3x³-x²-20x-12 by x+2.

3x^2-7x-6
------------------------------
x+2 | 3x^3 -x^2 -20x -12
3x^3+6x^2
-------------------
-7x^2 -20x
-7x^2 -14x
---------------------
-6x -12
-6x -12
-----------
-- --
So other factor is 3x^2-7x-6. We can factor this further as (3x + 2 )(x - 3 )
So full factors are: 3x³-x²-20x-12 = (x+2)(3x+2)(x-3) Answer