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The function f(x) is a cubic function and the zeros of f(x) are -5, -3 and 1. The y-intercept of f(x) is -45. Write the equation of the cubic polynomial in standard form.​

Respuesta :

ChoiSungHyun

Step-by-step explanation:

Since -5, -3 and 1 are the zeroes of f(x),

(x + 5), (x + 3) and (x - 1) are factors of f(x).

=> f(x) = a(x + 5)(x + 3)(x - 1),

where a is a real constant.

We are given that when x = 0, f(x) = -45.

=> a(0 + 5)(0 + 3)(0 - 1) = -45

=> -15a = -45, a = 3.

Hence, f(x) = 3(x + 5)(x + 3)(x - 1)

= 3x³ + 21x² + 21x - 45.

manissaha129

Answer:

The function f(x) is a cubic function and the zeros of f(x) are -5, -3 and 1. The y-intercept of f(x) is -45.

(x+5), (x+3) and (x-1) are the factors of f(x).

Form : f(x)=a(x+5)(x+3)(x-1)

When f(x)=-45 and x=0, we get a=3

Equation of the cubic polynomial in standard form is :---

[tex]f(x) = 3(x + 5)(x + 3)(x - 1)\\ =3 ( {x}^{2} + 8x + 15)(x - 1) \\=3({x}^{3} + 8 {x}^{2} + 15x - {x}^{2} - 8x - 15) \\ =3({x}^{3} + 7{x}^{2} + 7x - 15)\\=\boxed{3{x}^{3}+21{x}^{2}+21x-45}[/tex]

3x³+21x²+21x-45 is the right answer.

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