Question

Using factor theorem, factorise x^3-8x+x+42

Answer 1

ok ..the first thing u do in ques in which u have x to the power 3 is

step 1 : try to put in some no. like ( -1 ,1 ,0 ,2,-2,-3 ... etc ) so that the equation becomes = 0 , in this que , if u try to put +3 u will see u get zero it becomes

27 - 8(9) +3 +42 = 72 -72 =0

so ur first factor is 3 hence u write it as (x-3)

step 2 : now take the coefficients of the equation ie 1 -8 1 42 factorise it with 3 like this
3( 1 -8 1 42 )
____3_ -15_-42_
1 -5 -14 0

step 3 : take des coefficients 1 ,-5 ,-14 , write the equation as x^2 -5x -14 then factorise it ... u will get the factors (x-7)(x+2)

hence the final answer will be

x^3 - 8x^2 + x +42 = (x-3)(x-7)(x+2)

Answer 2

Here is your answer learner

Step-by-step explanation:

See the photo