Question

factorise :
2x³-7x²-2x+1

Answer 1

Greetings,
The answer to your question is typed below ^.
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Given:

To factorise: 2x³ - 7x² - 2x + 1

Solution:

We use Trial and error method to determine x. (1, -1, 2, -2 [like so])
After trial and error method we find x = - 1/2.
∴ when x= - 1/2
f (x) = 2(-1/2)³ - 7(-1/2)² - 2(-1/2) + 1
⇒f (x) = 0
∴ x+ 1/ 2 is a factor of 2x³ - 7x² - 2x +1
Then we multiply the factor by 2 to make things easier

2 ( x + 1/2 ) = 2x + 1

we the start factorising by the long division method: 

               x²  - 4 x  + 1
            ______________
2x + 1 ) 2x³ - 7x² - 2x + 1          (Please note that the signs are already
            -2x³ - x²                           changed here, and are marked in bold)
            ________________
                   -8x² -  2x
                  +8x² + 4x
                 _____________
                            2x + 1
                         - 2x   - 1
                       _____________
                             --------------

Therefore we obtain the quadratic equation x² -4x + 1=0

We then factorise the equation;

x² - (√3+2)x - (2-√3)x +1 = 0
x(x-(√3+2))-1(x-(√3+2))+1=0
(x-(√3+2))(x-1)=0

∴ (x-(√3+2)), (x-1) , (x + 1/2) are all factors of 2x³ - 7x² - 2x +1
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PS: Enjoy, ;)