Question

(y⁴ + 24y - 10y²) ÷ (y + 4). What is the quotient and remainder?

Answer 1

Answer:

Quotient =  y³  - 4y² + 6y

remainder = 0

Step-by-step explanation:

                    y³  - 4y² + 6y

                     ____________

 (y + 4)         (y⁴  - 10y² + 24y )

                     y⁴  + 4y³

                    __________

                             -4y³  - 10y² + 24y

                             -4y³ - 16y²

                         ________________

                                        6y²  + 24y

                                        6y²   + 24y

                                        __________

                                                  0

                                        ____________

Answer 2

Answer:

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

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,

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

Therefore, the Quotient is given by,

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

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