Question

Factorise: 2x^3-9x^2+x+12 r n rn

Answer 1

Using hit and trial method put x = -1, therefore the expression becomes 0. Hence (x+1) is a factor of the polynomial expression P(x). Divide P(x) by x-1 to obtain G(x) as 2x²-11x+12.

Now apply factorisation by Splitting the middle terms method to obtain the following factors.
(2x-3)(x-4)

Hence, there are three factors in totality. (x+1)(x-4)(2x-3).

Hope, that helps! :)

Answer 2

let  P(x) /2  =   x³ - 4.5 x² + 0.50 x + 6  = 0

let x = y + 1.5

P(x)/2 = y³ + 4.5 y² + 6.75 y + 3.375 - 4.5 y² - 4.5*2.25 -13.5y+0.5y+0.75+6=0
 =>   y³ - 6.25 y = 0
=>    y = 0  or    y² - 6.25 = 0
=>     y = 0 or  2.5  or  -2.5
=>    x =  1.5  or  4   or    -1

so  P(x) /2 = (x - 1.5) (x - 4) (x + 1)

P(x) = 2 (x - 3/2) (x - 4) (x + 1)