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प्रश्न
While factorizing a given polynomial, using remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x3 + 7x2 + 2x – 3.
- Is the student's solution correct stating that (2x + 1) is a factor of the given polynomial?
- Give a valid reason for your answer.
Also, factorize the given polynomial completely.
उत्तर
f(x) = 2x3 + 7x2 + 2x – 3
`f(-1/2) = 2(-1/2)^3 + 7(-1/2)^2 + 2(-1/2) - 3 ≠ 0`
∴ (2x + 1) is not a factor of f(x).
`f(1/2) = 2(1/2)^3 + 7(1/2)^2 + 2(1/2) - 3 = 0`
∴ (2x – 1) is a factor of f(x)
x2 + 4x + 3
`2x - 1")"overline(2x^3 + 7x^2 + 2x - 3)`
2x3 – x2
8x2 + 2x
8x2 – 4x
6x – 3
6x – 3
xx
f(x) = (2x – 1)(x2 + 4x + 3)
f(x) = (2x – 1)(x + 3)(x + 1)
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