Respuesta :

because the zeros are 1, -1, 2, 4, the factors are
(x-1)(x+1)(x-2)(x-4)
to put in standard form, you have to write the terms in order by degree, so you have to expand the above expression:
(x^2-1)(x^2-6x+8)
further expand it:
x^4-6x^3+7x^2+6x-8
fichoh

The polynomial function obtained from the Zeros given, written in standard form is x⁴ - 6x³ + 7x² + 6x - 8

Polynomial with Zeros 1, - 1, 2 and 4 can be expressed thus :

x = 1 :

  • x - 1

x = - 1 :

  • x + 1

x = 2 :

  • x - 2

x = 4 :

  • x - 4

Hence, we have :

(x - 1)(x + 1)(x - 2)(x - 4) = 0

We can then expand ;

(x - 1)(x + 1) = x² + x - x - 1 = x² - 1

(x² - 1)(x - 2) = x³ - 2x²-x + 2

(x³ - 2x² - x + 2)(x - 4)

x⁴ - 4x³ - 2x³ + 8x² - x² + 4x + 2x - 8

x⁴ - 6x³ + 7x² + 6x - 8

Hence, the polynomial function written in standard form is x⁴ - 6x³ + 7x² + 6x - 8

Learn more : https://brainly.com/question/10613585

Otras preguntas