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Solve by long division method.$15 a^{3}+3 a^{4}+10 a^{2}+5 a+3$ by $3 a^{2}+1$.
Given :
Dividend $= 15a^3+3a^4+10a^2+5a+3 = 3a^4+15a^3+10a^2+5a+3$.
Divisor $= 3a^2+1$.
To do :
We have to divide the given terms by the long division method.
Solution :
$3a^2+1)3a^4+15a^3+10a^2+5a+3 (a^2+5a+3$
$3a^4+a^2$ $\frac{3a^4}{3a^2}=a^2$
-----------------------------------
$15a^3+9a^2+5a+3$ $\frac{15a^3}{3a^2}=5a$
$15a^3+5a$
-----------------------------------
$9a^2+3$ $\frac{9a^2}{3a^2}=3$
$9a^2+3$
--------------------------------
0
The quotient is $a^2+5a+3$.
The remainder is 0.