A real world problem would be using division of polynomials if the area of a rectangle is given for example: x^2+7x+12 and the length is given as (x+3), you want to find the width in terms of x you divide x^2 +7x+12 by x + 3 and you get x+4 as an answer by using the steps in division.
Is this answer right and how, please help thanks..
************ x
****________________
x+3 | x^2 + 7 x + 12
***** x^2 + 3 x
******----------
******* 0 + 4 x
then
************ x + 4
****________________
x+3 | x^2 + 7 x + 12
***** x^2 + 3 x
******----------
******* 0 + 4 x + 12 (bringing down the 12)
************4 x + 12
***********---------
************** R = 0
thank you, now I have a better understanding
Yes, your answer is correct. When faced with the problem of finding the width of a rectangle given the area polynomial and the length polynomial, we can use polynomial division to obtain the answer.
To begin, let's review the steps for polynomial division:
1. Arrange the polynomials in descending order of degree, with any missing terms filled in with zeros. In this case, we have x^2 + 7x + 12 as the dividend (area polynomial) and x + 3 as the divisor (length polynomial).
2. Divide the first term of the dividend by the first term of the divisor. In this case, x^2 ÷ x gives us x.
3. Multiply the divisor by the result from step 2. x * (x + 3) gives us x^2 + 3x.
4. Subtract the product obtained in step 3 from the dividend. (x^2 + 7x + 12) - (x^2 + 3x) gives us 4x + 12.
5. Bring down the next term from the dividend, which is 4x in this case.
6. Repeat steps 2-5 until there are no more terms in the dividend.
7. The final quotient obtained from the division will be the width of the rectangle.
In this case, after completing the division, we obtain a quotient of x + 4. Therefore, the width of the rectangle in terms of x is x + 4.
By following these steps, we can find the answer using polynomial division.