Help please
(x^3 + 3x^2 - 2x+7)/(x+1)=11
I don't how how to solve this at all-the answer should be 11 but I don't have a clue how to get it-please show me this one so I can hopefully do my homeowrk-we did this in class today but I don't understand it
well, disallowing x = -1 because that would cause division by zero, just solve
x^3 + 3x^2 - 2x + 7 = 11x + 11
x^3 + 3x^2 - 13x - 4 = 0
cubics aren't easy to solve in general, so look first for low-hanging fruit: +/- 1,2,4
Hmm. No joy there. Some iterative method, or wolframalpha will provide the three real roots:
-5.3, -0.3, 2.6
If the answer is 11, there's a typo somewhere in the problem. f(11) = 139.9
To solve the equation:
(x^3 + 3x^2 - 2x + 7)/(x + 1) = 11,
you need to isolate the variable x. Here are the steps to solve this equation:
Step 1: Distribute the denominator (x + 1) to the numerator (x^3 + 3x^2 - 2x + 7).
(x^3 + 3x^2 - 2x + 7)/(x + 1) = 11
(x^3 + 3x^2 - 2x + 7) = 11(x + 1)
Step 2: Expand and rearrange the equation.
x^3 + 3x^2 - 2x + 7 = 11x + 11
Step 3: Move all terms to one side to get a quadratic equation equal to zero.
x^3 + 3x^2 - 2x - 11x - 4 = 0
x^3 + 3x^2 - 13x - 4 = 0
Step 4: If possible, factor the quadratic equation.
One method to factorize the equation is to use synthetic division. However, in this case, the equation does not appear to have any rational roots or factors that can be easily determined. So, factoring might not be an efficient method here.
Step 5: Alternatively, you can use numerical methods like polynomial long division or a graphing calculator to find approximate solutions. Software programs, such as WolframAlpha or graphing calculators, can help you find the solution.
Overall, solving equations involving higher degree polynomials can be complex, and finding exact solutions may require advanced techniques. It's recommended to consult your instructor or use appropriate mathematical software to solve such equations.