# How do you use synthetic substitution to find x=2 for f(x) = 3x^5-2x^2+x?

Jul 17, 2018

$\text{Quotient } 3 {x}^{4} + 6 {x}^{3} + 12 {x}^{2} + 22 x + 45$

$\text{Remainder } = \frac{90}{x - 2}$

#### Explanation:

$2 \text{ " | " " 3 " " 0 " " 0 " " -2 " " 1 " } 0$

$\text{ " | " " darr " " 6 " " 12 " " 24 " " 44 " } 90$

$\text{ " | " - - - - - - - - - - - - - - - - - - - - - }$

$\text{ " | " " 3 " "6 " " 12 " " 22 " " 45 " } 90$

$\text{ " | " - - - - - - - - - - - - - - - - - - - - - - }$

$\text{Quotient } 3 {x}^{4} + 6 {x}^{3} + 12 {x}^{2} + 22 x + 45$

$\text{Remainder } = \frac{90}{x - 2}$