k such that 3 is the remainder when f(x)=x to the 4 power minus 4xcube minus 8xsquare minus 7x plus 1. Tapos which of the following binomial factor of 2xcube plus 5xsquared minus 10x plus 16.
Try using math symbols. I believe you meant
f(x) = x^4-4x^3-8x^2-7x+1
No idea what "Tapos" means, but
2x^3+5x^2-10x+16 used as a divisor does not leave a remainder of 3.
Also, what does "k" have to do with any of the other stuff?
Maybe you can fill in the missing information and say just what it is you want to know ...
To find the value of k such that 3 is the remainder when dividing f(x) = x^4 - 4x^3 - 8x^2 - 7x + 1 by x - k, we can use the Remainder Theorem.
According to the Remainder Theorem, if we divide f(x) by x - k, then the remainder will be equal to f(k). In this case, we are given that the remainder is 3 when f(x) is divided by x - k. Thus, we need to find the value of k that satisfies f(k) = 3.
Substituting x = k into f(x), we get:
f(k) = k^4 - 4k^3 - 8k^2 - 7k + 1
We want f(k) = 3, so we set up the equation:
k^4 - 4k^3 - 8k^2 - 7k + 1 = 3
Rearranging the terms and simplifying, we have:
k^4 - 4k^3 - 8k^2 - 7k - 2 = 0
Now, we can use numerical methods such as graphing or numerical approximation techniques like Newton's method or the bisection method to find the values of k that satisfy this equation. These methods can be performed using mathematical software or calculators.
Moving on to the second question, we have to determine which of the following binomials is a factor of 2x^3 + 5x^2 - 10x + 16. However, you did not provide the options for the binomials. Please provide the choices, and I will help you identify the correct binomial factor.