Answer: [tex]\begin{gathered} Quotient\text{ = x}^3\text{ + 2x}^2\text{ + 7x + 20} \\ Remainder\text{ = 62} \end{gathered}[/tex]
Explanation:
Given:
[tex]\frac{x^4-x^3+x^2-x+2}{x\text{ - 3}}[/tex]
To find:
the quotient and the remainder using synthetic division
x - 3 = 0
x = 3
We will use the coefficients of the term in the synthetic division:
[tex]\begin{gathered} f(x)\text{ = Quotient + }\frac{remainder}{divisor} \\ \\ Remainder\text{ is the last number after the synthetic division is done} \\ Remainder\text{ = 62} \\ \\ Quotient\text{ are the coefficient of the terms numbers before the last number:} \\ 1\text{ 2 7 20} \\ Quotient\text{ = 1x}^3\text{ + 2x}^2\text{ + 7x + 20 } \\ \\ Quotient\text{ = x}^3\text{ + 2x}^2\text{ + 7x + 20} \end{gathered}[/tex]
