Question

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.

Answer 1

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

Explanation:

Let P(x) be a polynomial

As given, zeroes of the polynomial are at x = 5 ,x =
`(5)/(3)`, x =
`(2)/(5)` , 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 =
`(5)/(3)` is(x -
`(5)/(3)` )

the factors of the polynomial for the root x =
`(2)/(5)` is( x -
`(2)/(5)` )

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 -
`(5)/(3)` ) ( x -
`(2)/(5)` ) (x - 7)

∴ we get,

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