Respuesta :
Note that a prime polynomial cannot be factored into polynomials with lower degrees, with real integer coefficients.
Therefore we can test whether the discriminant of a quadratic polynomial to see if it is a perfect square. If the discriminant is not a perfect square, the polynomial is prime.
Note that for the quadratic polynomial ax² + bx + c, the discriminant is
D = b² - 4ac.
Test x² + 9
D = -4*9 = -36
The polynomial is prime.
Test x² - 9
D = 4*9 = 36 (perfect square)
The polynomial is not prime.
Test x² + 3x + 9
D = 9 - 4*9 = -27
The polynomial is prime.
Test -2x² + 8
D = -4(-2)(8) = 64 (perfect square)
The polynomial is not prime.
Answer:
The prime polynomials are
x² + 9
x² + 3x + 9
Therefore we can test whether the discriminant of a quadratic polynomial to see if it is a perfect square. If the discriminant is not a perfect square, the polynomial is prime.
Note that for the quadratic polynomial ax² + bx + c, the discriminant is
D = b² - 4ac.
Test x² + 9
D = -4*9 = -36
The polynomial is prime.
Test x² - 9
D = 4*9 = 36 (perfect square)
The polynomial is not prime.
Test x² + 3x + 9
D = 9 - 4*9 = -27
The polynomial is prime.
Test -2x² + 8
D = -4(-2)(8) = 64 (perfect square)
The polynomial is not prime.
Answer:
The prime polynomials are
x² + 9
x² + 3x + 9
Polynomials which are prime is 1st and 3rd function and it can be determine by using the discriminent of the quadratic equation.
Given :
1st Function - [tex]x^2+9[/tex]
2nd Function - [tex]x^2-9[/tex]
3rd Function - [tex]x^2-3x+9[/tex]
4th Function - [tex]-2x^2+8[/tex]
To determine which polynomial are prime, discriminent of the quadratic equation [tex](ax^2+bx+c)[/tex] can be use.
D = [tex]b^2-4ac[/tex]
1st Function [tex]=x^2+9[/tex]
D = 0 - 36 = -36
Therefore, this polynomial is a prime.
2nd Function [tex]=x^2-9[/tex]
D = 0 + 36 = 36
Therefore, this polynomial is not prime.
3rd Function [tex]=x^2+3x+9[/tex]
D = 9 - 36 = -27
Therefore, this polynomial is a prime.
4th Function [tex]=-2x^2+8[/tex]
D = 0 + 64 = 64
Therefore, this polynomial is not prime.
For more information, refer the link given below:
https://brainly.com/question/13738061
