The polynomial function over the complex numbers is,
(x + 1i) ( x - 1i) (x+ 7) ( x + 2).
What is factoring a polynomial?
Factorization of polynomials, also known as polynomial factorization, is a mathematical and computer algebraic technique that combines irreducible factors with coefficients in the same domain to produce a polynomial with coefficients in a given field or in integers.
Consider, the given polynomial
f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14
We can use a factoring "trick" here....write this as
x^4 + 9x^3 + 14x^2 + x^2 + 9x + 14 = 0 factor by grouping
x^2 ( x^2 + 9x + 14) + 1 ( x^2 + 9x + 14) = 0
(x^2 + 1) (x^2 + 9x + 14) = 0
(x^2 + 1) (x^2 + 9x + 14) = 0
⇒ (x^2 + 1) = 0, (x^2 + 9x + 14) = 0
x^2 = -1, x^2 + 7x + 2x + 14 = 0
x = ±i , x(x + 7) + 2(x + 7) = 0
x = ±i , (x + 7)(x + 2) = 0
⇒ (x + i)(x - i)(x + 7)(x - 7) = 0
(x + 1i) ( x - 1i) (x+ 7) ( x + 2) = 0
Hence, the polynomial function over the complex numbers is,
(x + 1i) ( x - 1i) (x+ 7) ( x + 2).
To know more about factoring a polynomial, click on the link
https://brainly.com/question/24351176
#SPJ4
