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प्रश्न
On dividing 3x3 + x2 + 2x + 5 is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
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उत्तर
By using division rule, we have
Dividend = Quotient × Divisor + Remainder
∴ 3x3 + x2 + 2x + 5 = (3x – 5)g(x) + 9x + 10
⇒ 3x3 + x2 + 2x + 5 – 9x – 10 = (3x – 5)g(x)
⇒ 3x3 + x2 – 7x – 5 = (3x – 5)g(x)
⇒ `g(x) = (3x^3 + x^2 - 7x - 5)/(3x - 5)`
x2 + 2x + 1
`3x - 5")"overline(3x^3 + x^2 - 7x - 5)`
3x3 – 5x2
– +
6x2 – 7x – 5
6x2 – 10x
– +
3x – 5
3x – 5
– +
x
∴ g(x) = x2 + 2x + 1
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