Question

Find the quotient and remainder using synthetic division.x4 − x3 + x2 − x + 2 /x − 3quotient remainder

Answer 1

Answer:
`\begin{gathered} Quotient\text{ = x}^3\text{ + 2x}^2\text{ + 7x + 20} \\ Remainder\text{ = 62} \end{gathered}`

Step-by-step explanation:

Given:

`\frac{x^4-x^3+x^2-x+2}{x\text{ - 3}}`

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:

`\begin{gathered} f(x)\text{ = Quotient + }(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}`