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Standard X

Mathematics

Polynomial

On dividing 3...

Question

On dividing $3 x^{3} + x^{2} + 2 x + 5$ by a polynomial g(x), the quotient and remainder are (3x-5) and (9x+10) respectively. Find g(x).
[3 marks]

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Solution

Given quotient = (3x-5)
remainder = (9x+10)
divident = $3 x^{3} + x^{2} + 2 x + 5$

By division algorithm $d i v i d e n t = d i v i s o r \times q u o t i a n t + r e m i n d e r$

$3 x^{3} + x^{2} + 2 x + 5 = g (x) \times (3 x - 5) + (9 x + 10)$
[1 mark]

$3 x^{3} + x^{2} + 2 x + 5 - (9 x + 10) = g (x) \times (3 x - 5)$

$3 x^{3} + x^{2} - 7 x - 5 = g (x) \times (3 x - 5)$

$g (x) = \frac{3 x^{3} + x^{2} - 7 x - 5}{3 x - 5}$
[1 mark]
$g (x) = x^{2} + 2 x + 1$

[1 mark]

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