divide:
(39w+ 14 + 10w squared) / 72+ w
=]
To divide the expression (39w + 14 + 10w^2) by (72 + w), you can use long division. Here's how you can proceed:
1. Start by dividing the highest degree term in the numerator by the highest degree term in the denominator in terms of the variable "w". In this case, divide 10w^2 by 1w, which gives you 10w. Write this as the first term in your quotient.
10w
_______
72 + w | 39w + 14 + 10w^2
2. Multiply the entire denominator (72 + w) by the first term in your quotient (10w) and subtract the result from the numerator (39w + 14 + 10w^2) to obtain the remainder.
10w * (72 + w) = 720w + 10w^2
Subtracting this from the numerator gives:
(39w + 14 + 10w^2) - (720w + 10w^2) = (39w - 720w) + (14) = -681w + 14
3. Bring down the next term from the numerator and repeat the process. Bring down the term -681w from the remainder obtained.
10w - 681
_______
72 + w | 39w + 14 + 10w^2 - 681w
4. Divide the highest degree term in the new numerator (-681w) by the highest degree term in the denominator (1w). The quotient will be -681.
10w - 681
_______
72 + w | 39w + 14 + 10w^2 - 681w
5. Multiply the entire denominator (72 + w) by the second term in your quotient (-681) and subtract the result from the new numerator (-681w) to obtain the remainder.
-681 * (72 + w) = -48912 - 681w
Subtracting this from -681w gives: -681w - (-48912 - 681w) = 48912
6. At this point, you have obtained your quotient and remainder:
Quotient: 10w - 681
Remainder: 48912
Therefore, the final division expression would be:
(39w + 14 + 10w^2) / (72 + w) = 10w - 681 + (48912 / (72 + w))