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प्रश्न
By actual division, show that x2 – 3 is a factor of 2x4 + 3x3 – 2x2 – 9x – 12.
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उत्तर
Let f(x) = 2x4 + 3x3 – 2x2 – 9x – 12 and g(x) as x2 – 3
2x2 + 3x + 4
`x^2 - 3")"overline(2x^4 + 3x^3 - 2x^2 - 9x - 12)`
2x4 – 6x2
– +
3x3 + 4x2 – 9x – 12
3x3 – 9x
– +
4x2 – 12
4x2 – 12
– +
x
Quotient q(x) = 2x2 + 3x + 4
Remainder r(x) = 0
Since, the remainder is 0.
Hence, x2 – 3 is a factor of 2x4 + 3x3 – 2x2 – 9x – 12.
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