Answer:
The polynomial resulting from the division will be [tex]x^{2} -3*x+2[/tex]
Step-by-step explanation:
To divide the equations of third degree or greater, or put another way, for equations of degree greater than two with a first degree divisor of the form x-a, as in this case, Ruffini's rule is used.
The attached image shows how to solve Ruffini's rule.
To perform the division, first the dividend coefficients (in this case the third degree polynomial) are placed in a row ordered by their degree of major or minority and in a complete manner. That is to say that if it were not complete, that is, if we did not have for example any term that has x², in the place of degree 2, a 0 would be placed. In this case the polynomial is complete.
To the left of the vertical line, the opposite (that is, the changed sign number) of the independent term of the divisor is placed (that is, if the divisor in this case is x-5, the number 5 will be placed). To begin, the sum of the first column is made. Then that coefficient is multiplied by the divisor and placed below the next term in the second column. The sum of the second column is done. The number on the left of the vertical line is multiplied by the result of the sum of the second column and below the next term in the third column. This procedure is continued successively until the result of the sum is obtained in the last column.
The result of the sum obtained in the last column is a remainder, while the rest of the numbers correspond to the coefficients of the polynomial obtained as a response of the division. These coefficients obtained are placed in a complete and orderly manner; and the polynomial resulting from the division will be a degree less than the dividend. In this case the dividend is grade 3, then the resulting polynomial will be grade 2.
Then, the polynomial resulting from the division will be [tex]x^{2} -3*x+2[/tex]
