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 ___.

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    and the remainder is zero. Therefore, the number 5 is a solution because the remainder of the division,  divided by, is zero.

The polynomial entered in this exercise is described as:

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    and the remainder is zero. Therefore, the number 5 is a solution because the remainder of the division,  divided by, is zero.    

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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.                                                    

think about it deeply and passionately about this property

i am sorry

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4