Answer:
The polynomial function in the factored form is P(x) = -5 ( x - 5) (x - [tex]\frac{5}{3}[/tex] ) ( x - [tex]\frac{2}{5}[/tex] ) (x - 7)
Step-by-step explanation:
Let P(x) be a polynomial
As given, zeroes of the polynomial are at x = 5 ,x = [tex]\frac{5}{3}[/tex], x = [tex]\frac{2}{5}[/tex] , x = 7
So , the factors of the polynomial for the root x = 5 is ( x - 5)
the factors of the polynomial for the root x = [tex]\frac{5}{3}[/tex] is(x - [tex]\frac{5}{3}[/tex] )
the factors of the polynomial for the root x = [tex]\frac{2}{5}[/tex] is( x - [tex]\frac{2}{5}[/tex] )
the factors of the polynomial for the root x = 7 is(x - 7)
Also leading coefficient is of -5
⇒ P(x) = -5 ( x - 5) (x - [tex]\frac{5}{3}[/tex] ) ( x - [tex]\frac{2}{5}[/tex] ) (x - 7)
∴ we get,
The polynomial function in the factored form is P(x) = -5 ( x - 5) (x - [tex]\frac{5}{3}[/tex] ) ( x - [tex]\frac{2}{5}[/tex] ) (x - 7)
