write 2 equations for a polynomial whose graph has x-intercepts at x= -3, -1, and 5

Answer 1

a(x+1)(x+3)(x-5) = 0 where a = any number such as

a =1 or a=2

x^2 +4x +3)(x-5) =

x^3 -x^2-17x -15=0

or double or triple each term

2x^3 -2x^2 -34x -30=0

or 3x^3 -3x^2 -51x -45 =0

Answer 2

The x-coordinates of the x-intercepts of a polynomial function are given as -3, -1, and 5.

That means (x + 3)(x + 1)(x - 5) are factors of the polynomial function.

P(x) = A(x + 3)(x + 1)(x - 5) is one way to write the polynomial function where A is any real number except zero.

If you multiply the binomials:

P(x) = A(x³ - x² - 17x -15)

Let A = 1 or A = 2 for example to get two different polynomials with the target roots/x-intercepts.

P₁(x) = x³ - x² - 17x - 15

P₂(x) = 2x³ - 2x² - 34x - 30

desmos.com/calculator/ku4lyxzjog

Note:

(x + 1)(x + 3) = x² + 4x + 3

and:

(x² + 4x + 3)(x - 5) = x³ + 4x²+3x - 5x² - 20x - 15 = x³ - x² - 17x -15