Divide:
(y^2-y+4) divide by (y+3)
I worked it out, but don't know how to put my answer can you please do it too and show me what the answer is. I used long division.
>>>>>>> y - 4
---------------------
(y+3) | y^2 - y + 4
>>>>>>> y^2 +3y
--------------------
>>>>>>>>>>>> -4y + 4
>>>>>>>>>>>> -4y -12
--------------------
>>>>>>>>>>>> Remainder = -16
by the way
(y^2 - y + 4) does not factor
So like this?
y^2-y+4-16/y+3
???
Certainly! I will guide you through the long division process.
To divide (y^2 - y + 4) by (y + 3), we first set up the division in the long division format:
________________
y + 3 | y^2 - y + 4
1. Start by dividing the leading term of the numerator, y^2, by the leading term of the denominator, y. The result is y, which we write above the division line.
y
________________
y + 3 | y^2 - y + 4
2. Multiply the denominator (y + 3) by the quotient (y): (y) * (y + 3) = y^2 + 3y. Write this below the numerator.
y
________________
y + 3 | y^2 - y + 4
- (y^2 + 3y)
Subtract the numerator from the result of the multiplication:
y
________________
y + 3 | y^2 - y + 4
- (y^2 + 3y)
________________
-4y + 4
3. Bring down the next term from the numerator, which is -4y.
y - 4
________________
y + 3 | y^2 - y + 4
- (y^2 + 3y)
________________
-4y + 4
4. Divide the term -4y by the leading term y. The result is -4, which we write above the division line.
y - 4
________________
y + 3 | y^2 - y + 4
- (y^2 + 3y)
________________
-4y + 4
- (-4y - 12)
Subtract the numerator from the result of the multiplication:
y - 4
________________
y + 3 | y^2 - y + 4
- (y^2 + 3y)
________________
-4y + 4
- (-4y - 12)
_________________
16
5. Since there are no more terms to bring down, we have finished the division. The remainder is 16, which we can write as (16/(y + 3)).
Therefore, the division of (y^2 - y + 4) by (y + 3) gives the result: y - 4 + 16/(y + 3).