2 x ^ 3 - 3 x ^ 2 - 2 x + 3 = 0
( 2 x ^ 3 - 2 x ) - 3 x ^ 2 + 3 = 0
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Remark :
- 3 x ^ 2 + 3 = - ( 3 x ^ 2 - 3 )
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( 2 x ^ 3 - 2 x ) - ( 3 x ^ 2 - 3 ) = 0
2 x ( x ^ 2 - 1 ) - 3 ( x ^ 2 - 1 ) = 0
( x ^ 2 - 1 ) ( 2 x - 3 ) = 0
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Remark :
( x ^ 2 - 1 ) = ( x + 1 ) ( x - 1 )
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( x + 1 ) ( x - 1 ) ( 2 x - 3 ) = 0
2 x ^ 3 - 3 x ^ 2 - 2 x + 3 = ( x + 1 ) ( x - 1 ) ( 2 x - 3 ) = 0
x + 1 = 0
x = - 1
x - 1 = 0
x = 1
2 x - 3 = 0
2 x = 3
x = 3 / 2
The solutions are :
x = - 1
x = 1
and
x = 3 / 2
Find all rational zeros of the polynomial, and write the polynomial in factored form?
P(x)= 2x^3-3x^2-2x+3
1 answer