Question

use synthetic division to find the result when $2x^4 - x^3 + 2x^2 - 10x + 2$ is divided by $x - 1$. if there is a remainder, express the result in the form $q(x) + \frac{r(x)}{b(x)}$.

Explanation:

Step1: Set up synthetic division

Root divisor: $x=1$, coefficients: $2, -1, 2, -10, 2$

1 |  2  -1   2  -10   2
        2   1    3   -7
      ----------------
        2   1   3   -7  -5

Step2: Identify quotient and remainder

Quotient degree = 4-1=3, coefficients: $2,1,3,-7$; Remainder: $-5$

Step3: Write final form

Quotient $q(x)=2x^3+x^2+3x-7$, remainder $r(x)=-5$, divisor $b(x)=x-1$

Answer:

$2x^3+x^2+3x-7+\frac{-5}{x-1}$