Answer:
P(x) = [tex]x^{4}[/tex] - 7x² + 12
Step-by-step explanation:
Given zeros x = 2, x = - 2, x = [tex]\sqrt{3}[/tex], x = - [tex]\sqrt{3}[/tex]
Then the factors are (x - 2), (x + 2), (x - [tex]\sqrt{3}[/tex] ), (x + [tex]\sqrt{3}[/tex] )
and the polynomial is the product of the factors, that is
P(x) = (x - 2)(x + 2)(x - [tex]\sqrt{3}[/tex] )(x + [tex]\sqrt{3}[/tex] ) ← expand in pairs using FOIL
= (x² - 4)(x² - 3) ← distribute
= [tex]x^{4}[/tex] - 3x² - 4x² + 12 ← collect like terms
= [tex]x^{4}[/tex] - 7x² + 12
