Divide $10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3$ by $2 x^{2} + 7 x - 1$
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Solution

Concept: 1 Mark
Application: 3 Marks

On dividing, we get

$\begin{matrix} 5 x^{2} - 9 x + 3 2 x^{2} + 7 x - 1 & 10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3 10 x^{4} + 35 x^{3} - 5 x^{2} - - + - 18 x^{3} - 57 x^{2} + 30 x - 3 - 18 x^{3} - 63 x^{2} + 9 x + + - 6 x^{2} + 21 x - 3 6 x^{2} + 21 x - 3 - - + 0 \end{matrix}$

$∴ 10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3 = (2 x^{2} + 7 x - 1) (5 x^{2} - 9 x + 3)$
$∴ \frac{10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3}{(2 x^{2} + 7 x - 1)} = 5 x^{2} - 9 x + 3$

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$2 x^{2} + 7 x - 1$ completely divides $10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3$ .

(10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3)

(2 x^{2} + 7 x - 1)

f (x) = 10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3

g (x) = 2 x^{2} - x + 1

(5 x^{2} - 9 x + 3), (10 x^{4} + 17 x^{3} - 62 x^{2} + 30 x - 3)

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