With the polynomial: f(x) = 5x^3 + 8x^2 -4x + 3
a. The Fundamental Theorem of Algebra states that this polynomial has ______ roots.
b. Find f(-x).
Carefully and patiently watch and listen to Saul explaining this concept.
https://www.khanacademy.org/math/algebra2/polynomial-functions/fundamental-theorem-of-algebra/v/possible-real-roots
a. The Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n roots, counting multiplicity. In this case, the polynomial f(x) = 5x^3 + 8x^2 - 4x + 3 is of degree 3, so it will have 3 roots.
To find the roots of the polynomial, you can use various techniques such as factoring, synthetic division, or numerical methods like the Newton-Raphson method.
b. To find f(-x), simply replace every occurrence of x in the polynomial with -x. So we have:
f(-x) = 5(-x)^3 + 8(-x)^2 - 4(-x) + 3
Simplifying this expression gives:
f(-x) = -5x^3 + 8x^2 + 4x + 3