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Question
If x – 2 is a factor of 2x3 - x2 - px - 2.
with the value of p, factorize the above expression completely.
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Solution
Given expression is 2x3 - x2 - px - 2 and x - 2 is the factor.
Putting the value of P
(2x2 + 3x + 1)
`x - 2)overline(2x3 - x2 - 5x - 2)(`
2x3 - 4x2
- +______
3x2 - 5x
3x2 - 6x
- +_______
x - 2
x - 2
- +_____
. x
∴ 2x3 - x2 - 5x - 2 = (x - 2) (2x2 + 3x + 1)
The expression can be the written as
(2x2 + 3x + 1) (x - 2) or (2x + 1) (x + 1) (x -2).
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