Question

using factor theorem , factorize
2x^3-13x^2+26x-15​

Answer 1

Answer:

x(2x^2 -13x+26x)- 15

Does not factorise further

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Answer 2

let x+1=0

thus,

x=-1

f(x)= 2x³- 13x²+26x-15

f(-1)= 2(-1)³ - 13(-1)²+26(-1)-15

=> -2+13-26-15

=>-20

therefore, x+1 is not a factor

let x+2 = 0

thus, x= -2

f(x)= 2x³- 13x²+26x-15

f(-2)= 2(-2)³-13(-2)²+26(-2)-15

=>-16-52-46-15

therefore, x+2 is also not a factor.

let x-2= 0

thus, x=2

f(x)= 2x³- 13x²+26x-15

f(2) = 2(2)³-13(2)²+26(2)-15

=>16-52+46-15

therefore,x-2 is also not a factor.

let x-1=0

thus , x= 1

f(x)= 2x³- 13x²+26x-15

f(1)= 2(1) -13(1)+26(1)-15

=>2-13+26-15

=>28-28 = 0

thus,

x-1 is a factor.

by using synthetic division,

we get ...

1 2 -13 26 -15

2 -11 15 0

thus the remaining polynomial =

(2x²-11x+15)=> (2x²-6x-5x+15)

[2x(x-3)-5(x-3)]

thus,

the other other factors are...

(2x-5)(x-3)(x-1)

therefore,

x= 5/2 , 3 , 1