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