Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms? A. 3 + 5x − 4x2 b. 8x + x + 5 + x3 A. a. 3 + 5x − 4x2, quadratic trinomial b. 5 + 9x + x3, quadratic trinomial B. a. −4x2 + 5x + 3, quadratic trinomial b. X3 + 9x + 5, cubic trinomial C. a. 3 + 5x − 4x2, cubic trinomial b. 5 + 9x + x3, cubic trinomial D. a. −4x2 + 5x + 3, cubic trinomial b. X3 + 9x + 5, quadratic trinomial

Step-by-step explanation:

By the Fundamental Theorem of Algebra (in a nutshell), the number of solutions that a quadratic has is equal to its highest exponent which is also the same as the degree of the polynomial. Since our polynomial is a quadratic, is an x-squared polynomial. Therefore, it has 2 solutions. Whether they are real or complex remains to be seen. We have to factor it to find the solutions.

Throw this into the quadratic formula to solve:

x = (8 ± √64 - 4(1)(-4))/2 and

x = (8 ± √72)/2 which simplifies to

x = (8 ± 6√2)/2 which simplifies, finally, to

x = 4 ± 3√2