Answer :

Final answer:

To find the remaining linear factors of the polynomial 2x⁴ + 23x³ + 58x² - 35x, divide the polynomial by the known factor (x-5) and then use methods like the Rational Root Theorem or the quadratic formula to find the remaining roots which will give the linear factors.

Explanation:

The student is asking to find the remaining linear factors of a polynomial given that (x-5) is one of its factors. Given the polynomial is 2x⁴ + 23x³ + 58x² - 35x, we know that this can be factored further.

We start by performing polynomial division or using synthetic division to divide the polynomial by (x-5), which will result in a cubic polynomial. Next, we seek to factorize the resulting cubic polynomial. A possible method is to find the roots by trial and error, graphing, or using the Rational Root Theorem to test possible factors of the constant term divided by factors of the leading coefficient.

Once a root is found, we can factor it out, potentially reducing the cubic polynomial to a quadratic from which the remaining linear factors can be determined. If the quadratic is in the form ax² + bx + c = 0, we can use the quadratic formula, rearrange the equation accordingly, and solve for x to get the remaining linear factors.

Thanks for taking the time to read Given that x 5 is a factor of 2x 4 23x 3 58x 2 35x find the other linear factors. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada