Help me
Solve
1. (2p2 + 7p - 39) ÷(2p-7)
2 (n3 + 7n2 + 14n + 3) ÷ (n +2)
3. (p3-10p2 + 20p + 26) ÷ (p-5)
4. (v3- 2v2 -14v - 5) ÷ (v + 3)
5 ( x3 - 13x2 + 40x + 18) ÷ (x -7)
You will need to know "algebraic long division"
It is very difficult to show it on this text format, but this webpage has a couple of good examples
http://www.sosmath.com/algebra/factor/fac01/fac01.html
Try your questions by following the above method
If the coefficient of the variable in your divisor is 1 , like in your last 4 problems, "synthetic division" can be used.
Khan has an excellent video showing the steps of synthetic division
http://www.sosmath.com/algebra/factor/fac01/fac01.html
I suggest doing the last 4 using this method and seeing how much faster the method is.
You should of course get the same answers
Sorry, gave you the same link twice
should have been this for synthetic division
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/synthetic-division/v/synthetic-division
To solve these polynomial division problems, we will use long division. Here are the step-by-step explanations for each problem:
1. (2p^2 + 7p - 39) ÷ (2p - 7)
Step 1: Divide the first term of the numerator (2p^2) by the first term of the denominator (2p). The result is p.
Step 2: Multiply the entire denominator (2p - 7) by the quotient from Step 1. The result is (2p - 7) * p = 2p^2 - 7p.
Step 3: Subtract the result from Step 2 from the numerator (2p^2 + 7p - 39) to get the new numerator: 2p^2 + 7p - 39 - (2p^2 - 7p) = 14p - 39.
Step 4: Repeat Steps 1-3 with the new numerator (14p - 39) until the degree of the new numerator is less than the degree of the denominator. In this case, the new numerator is a linear expression (degree 1), so we can proceed.
Step 5: Divide the first term of the new numerator (14p) by the first term of the denominator (2p). The result is 7.
Step 6: Multiply the entire denominator (2p - 7) by the quotient from Step 5. The result is (2p - 7) * 7 = 14p - 49.
Step 7: Subtract the result from Step 6 from the new numerator (14p - 39) to get the final remainder: (14p - 39) - (14p - 49) = 10.
Step 8: The final answer is the quotient obtained so far (p + 7) plus the remainder (10) divided by the denominator. Therefore, the solution is: p + 7 + (10 / (2p - 7)).
2. (n^3 + 7n^2 + 14n + 3) ÷ (n + 2)
The steps for solving this problem are similar to the previous example. You can follow the same process to find the solution.
3. (p^3 - 10p^2 + 20p + 26) ÷ (p - 5)
Again, use long division to solve this problem. The steps are similar to problem 1, but the specific values will be different.
4. (v^3 - 2v^2 - 14v - 5) ÷ (v + 3)
Apply the same long division process as before to solve this problem.
5. (x^3 - 13x^2 + 40x + 18) ÷ (x - 7)
Use long division as in the previous examples to solve this problem. The steps will be similar, but the specific values will be different.
Remember to be diligent with your calculations and double-check your work to ensure accuracy.