When we divide 3t4+5t3−7t2+2t+2 by t2+3t+1, we

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Question

When we divide $3 t^{4} + 5 t^{3} - 7 t^{2} + 2 t + 2$ by $t^{2} + 3 t + 1$ , we get $3 t^{2} - 4 t + 2$ as quotient.

Options:

A . True

B . False

C .

6 x^{2} + 3 x + 9

D .

2 x^{2} + 3 x + 1

Answer: Option A
:
A

Lets divide $3 t^{4} + 5 t^{3} - 7 t^{2} + 2 t + 2 by t^{2} + 3 t + 1$ ,
$3 t^{2} - 4 t + 2 t^{2} + 3 t + 1) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 3 t^{4} + 5 t^{3} - 7 t^{2} + 2 t + 2_{-} 3 t^{4} \pm 9 t^{3} \pm 3 t^{2} - --------------- - - 4 t^{3} - 10 t^{2} + 2 t \mp 4 t^{3} \mp 12 t^{2} \mp 4 t - ----------------- - 2 t^{2} + 6 t + 2_{-} 2 t^{2} \pm 6 t \pm 2 - ------------ - 00$
Thus, the given statement is true.

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