Answer:
f(x) = [tex]x^{4}[/tex] + 8x³ - 51x² - 378x
Step-by-step explanation:
Given the polynomial has zeros x = - 6, x = - 9, x = 0, x = 7, then
The factors are (x + 6), (x + 9), x , (x - 7)
and f(x) is the product of it's factors, that is
f(x) = x(x + 6)(x + 9)(x - 7) ← expand the last pair using FOIL
= x(x + 6)(x² + 2x - 63)
= (x² + 6x)(x² + 2x - 63) ← distribute
= [tex]x^{4}[/tex] + 2x³ - 63x² + 6x³ + 12x² - 378x
= [tex]x^{4}[/tex] + 8x³ - 51x² - 378x
