Mathematics, 05.04.2020 01:26 jjau834

Need help solving this math problem.

Use synthetic division to show that 5 is a solution of the equation shown below. Then solve the polynomial equation. Hint: Use factoring by grouping when working with the quotient factor.
x^4 -3x^3 -19x^2 +27x +90 =0

The quotient is _ and the remainder is . Therefore, the number 5 is a solution because the of the division, x^4 -3x^3 -19x^2 +27x +90 divided by x-5, is ___.

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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 x^3 + 2x^2 - 9x - 18 and the remainder is zero. Therefore, the number 5 is a solution because the remainder of the division, x^4 - 3x^3 - 19x^2 + 27x + 90 divided by, x - 5 is zero.

The polynomial entered in this exercise is described as:

x^4 - 3x^3 - 19x^2 + 27x + 90 = 0

Knowing that the value of 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 x^3 + 2x^2 - 9x - 18 and the remainder is zero. Therefore, the number 5 is a solution because the remainder of the division, x^4 - 3x^3 - 19x^2 + 27x + 90 divided by, x - 5 is zero.

See more about polynomial division at link

Answer from: casianogabriel2004

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.

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Answer from: Quest

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step-by-step explanation:

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