A polynomial function has zeros at x = 5, x=5/3, x= 2/5 and x = 7 and a leading coefficient of -5. Write the polynomial function in factored form.

The polynomial function in the factored form is P(x) = -5 ( x - 5) (x -   ) ( x - ) (x - 7)

Step-by-step explanation:

Let P(x) be a polynomial

As given, zeroes of the polynomial are at x = 5 ,x = ,  x = , 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 = is(x -   )

the factors of the polynomial for the root x =   is( x - )

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 -   ) ( x - ) (x - 7)

∴ we get,

The polynomial function in the factored form is P(x) = -5 ( x - 5) (x -   ) ( x - ) (x - 7)

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