Question

y⁶+1000= ( ) (y⁴-10y²+100)

Answer 1

Step-by-step explanation:

$Quotient : y^{3}-4y^{2}+6yy$

Remainder : 0

Step-by-step explanation:

In the question,

We have the Divisor as,

D = (y + 4)

And,

Dividend is given by,

DD = (y⁴ - 10y² + 24y)

Now on dividing the Dividend with the Divisor we get,

$\begin{gathered}(y+4)\ |\ y^{4}-10y^{2}+24y\ |\ y^{3}-4y^{2}+6y\\.\ \ \ \ \ \ \ \ \ \ \ y^{4}+4y^{3}\\\\.\ \ \ \ \ \ -4y^{3}-10y^{2}+24y\\.\ \ \ \ \ \ -4y^{3}-16y^{2}\\\\.\ \ \ \ \ \ \ \ \ \ 6y^{2}+24y\\.\ \ \ \ \ \ \ \ \ \ 6y^{2}+24y\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\end{gathered}$

Therefore, the Quotient is given by,

$y^{3}-4y^{2}+6yy$

Also, the Remainder is taken out as 0 as all the terms in the end get cancelled out.

Answer 2

Step-by-step explanation:

Quotient : y^{3}-4y^{2}+6yyQuotient:y3−4y2+6yy

Remainder : 0

Step-by-step explanation:

In the question,

We have the Divisor as,

D = (y + 4)

And,

Dividend is given by,

DD = (y⁴ - 10y² + 24y)

Now on dividing the Dividend with the Divisor we get,

\begin{gathered}\begin{gathered}(y+4)\ |\ y^{4}-10y^{2}+24y\ |\ y^{3}-4y^{2}+6y\\.\ \ \ \ \ \ \ \ \ \ \ y^{4}+4y^{3}\\\\.\ \ \ \ \ \ -4y^{3}-10y^{2}+24y\\.\ \ \ \ \ \ -4y^{3}-16y^{2}\\\\.\ \ \ \ \ \ \ \ \ \ 6y^{2}+24y\\.\ \ \ \ \ \ \ \ \ \ 6y^{2}+24y\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\end{gathered} < /p > < p > \end{gathered}(y+4) ∣ y4−10y2+24y ∣ y3−4y2+6y.           y4+4y3.      −4y3−10y2+24y.      −4y3−16y2.          6y2+24y.          6y2+24y.               0</p><p>

Therefore, the Quotient is given by,

< /p > < p > y^{3}-4y^{2}+6yy</p><p>y3−4y2+6yy

Also, the Remainder is taken out as 0 as all the terms in the end get cancelled out.