Question

Divide using the division algorithm. Write your answer in the form ( + 7 Where the degree of Ris less than the degree of D.2-16y+4Keypad

Answer 1

The given division is

`(y^2-16)/(y+4)`

At first, we will put zero in the place of the missing term y, then it should be

`(y^2+0y-16)/(y+4)`

Now, divide y^2 by y

`(y^2)/(y)=y`

Multiply the answer by (y + 4)

`y(y+4)=y^2+4y`

Subtract it from (y^2 + 0y - 16)

`\begin{gathered} y^2+0y-16-(y^2+4y)= \\ (y^2-y^2)+(0y+-4y)-16= \\ 0-4y-16= \\ -4y-16 \\ (y^2+0y-16)/(y+4)=y+(-4y-16)/(y+4) \end{gathered}`

Divide -4y by y

`(-4y)/(y)=-4`

Multiply the answer by (y + 4)

`-4(y+4)=-4y-16`

Subtract it from the numerator of the fraction

`\begin{gathered} -4y-16-(-4y-16= \\ -4y-16+4y+16= \\ (-4y+4y)+(-16+16)= \\ 0+0=0 \\ (y^2-16)/(y+4)=(y-4)+(0)/(y+4) \end{gathered}`

The answer to the division is

`(y-4)+(0)/(y+4)`

Q = (y - 4)

R = 0

D = y + 4