Respuesta :
If the polynomial is factorized, then the value of [tex]b^2-4ac[/tex] should be a perfect square. The given polynomial is prime. The option 4 is the correct option.
How to find the factors of polynomial?
Factors of the polynomial which are multiplied to produce the original polynomial. The polynomial which can not be factored is known as prime polynomial.
The standard form of the polynomial with highest power of 2 can be given as,
[tex]ax^2+bx+c[/tex]
Given information-
The given polynomial is,
[tex]x^2+8x-6[/tex]
Compare the above polynomial with standard form, we get,
[tex]a=1\\b=8\\c=-6[/tex]
If the polynomial is factorized, then the value of [tex]b^2-4ac[/tex] should be a perfect square. Let check,
[tex]b^2-4ac=8^2-[4\times1\times(-6)]\\b^2-4ac=64+24\\b^2-4ac=88[/tex]
Thus the result is not perfect square.
Hence the given polynomial is prime. The option 4 is the correct option.
learn more about the factors of polynomial here;
https://brainly.com/question/24380382
