Which of the following is a polynomial function in standard form with zeros at –8, –1, and 3?

a) f(x) = (x + 8)(x + 1)(x – 3)
b) f(x) = x^3 – 6x^2 – 19x + 24
c) f(x) = x^3 + 6x^2 – 19x – 24
d) f(x) = (x – 8)(x – 1)(x + 3)

Option: C is the correct answer.

The polynomial in standard form is:

   C)    

The standard form of a equation of a polynomial is written as :

  We arrange the terms from least to highest power of x.

We know that if a polynomial has roots as:

a, b and c then the equation of the polynomial is given by:

Here we  have: a= -8 , b= -1 and c=3

Hence, the equation of the circle is given  by:

which on expanding gives:

Hence, the standard equation of the polynomial is:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

the correct option is b

step-by-step explanation: