Answer:
The answer to your question is below
Step-by-step explanation:
Data
Polynomial x⁴ - 3x³ - 19x² + 27x + 90 = 0
root = 5
Process
Use synthetic division to prove if 5 is a factor of the polynomial
1 -3 -19 + 27 + 90 5
5 10 - 45 -90
1 2 -9 - 18 0
Result
Quotient = x³ + 2x² - 9x - 18
Remainder = 0
Paragraph: The quotient is x³ + 2x² - 9x - 18 and the remainder is 0. Therefore, the number 5 is a solution because the remainder of the division, x⁴ - 3x³ - 19x² + 27x + 90 divided by x - 5, is 0.
In this exercise it is necessary to have a knowledge of polynomial division to calculate the quotient and the rest of that division then:
The quotient is [tex]x^3 + 2x^2 - 9x - 18[/tex] and the remainder is zero. Therefore, the number 5 is a solution because the remainder of the division, [tex]x^4 - 3x^3 - 19x^2 + 27x + 90[/tex] divided by, [tex]x - 5[/tex] is zero.
The polynomial entered in this exercise is described as:
[tex]x^4 - 3x^3 - 19x^2 + 27x + 90 = 0[/tex]
Knowing that the value of [tex]5[/tex] is a solution, we will do the division of these polynomials being. Use synthetic division to prove if 5 is a factor of the polynomial:
So when doing the division by 5 the polynomial will have the final result equal to zero. This means that 5 is a precise division value where nothing is left.
The quotient is [tex]x^3 + 2x^2 - 9x - 18[/tex] and the remainder is zero. Therefore, the number 5 is a solution because the remainder of the division, [tex]x^4 - 3x^3 - 19x^2 + 27x + 90[/tex] divided by, [tex]x - 5[/tex] is zero.
See more about polynomial division at brainly.com/question/12978781
