Question

Find all the zeros of the function. f(x) = x^4 + 25x^2 + 144... Then, Write the polynomial as a product of linear factors.

A. x = 3, x = -3, x = 4, x = -4
B. x = 5, x = -5, x = 6, x = -6
C. x = 2, x = -2, x = 7, x = -7
D. x = 1, x = -1, x = 8, x = -8

Answer 1

A. x = 3, x = -3, x = 4, x = -4 is the polynomial as a product of linear factors. (option a)

Step-by-step explanation:

To find the zeros of the function f(x) = x^4 + 25x^2 + 144, set f(x) equal to zero and solve for x. You can use a substitution method to represent the equation as a quadratic equation in terms of x^2. Then, solve for x^2 using the quadratic formula or factorization methods. After obtaining x^2, take the square root to find x. Upon solving, the zeros of the function are x = 3, x = -3, x = 4, and x = -4. (option a)

Factoring a polynomial into linear factors involves expressing the polynomial as a product of factors, each being a linear term (x - a). By using the roots or zeros of the polynomial obtained earlier (x = 3, x = -3, x = 4, x = -4), write the polynomial as a product of linear factors, which would be (x - 3)(x + 3)(x - 4)(x + 4).

Understanding how to find zeros of a polynomial function and factorize it into linear factors is essential in algebra and calculus. This process is crucial in solving polynomial equations and understanding the behavior of polynomial functions.