Question

apply division algorithm to check if g x equals to x^2-3x+2 is a factor of polynomial. Fx. x^4-2x^3-x+2

Answer 1

Answer:

Step-by-step explanation:

Dividing F(x) = x⁴ - 2x³ - x + 2   by g(x) = x² - 3x + 2

(x⁴ - 2x³ - x + 2)/(x² - 3x + 2) =  x²   + (x³ - 2x² - x + 2)/(x² - 3x + 2)

Again dividing (x³ - 2x² - x + 2) by (x² - 3x + 2) we get

(x⁴ - 2x³ - x + 2)/(x² - 3x + 2) = x² + x + (x² - 3x + 2)/(x² - 3x + 2)

Again dividing (x² - 3x + 2) by (x² - 3x + 2) we get

(x⁴ - 2x³ - x + 2)/(x² - 3x + 2) = x² + x + 1

Hence,

(x⁴ - 2x³ - x + 2) = (x² - 3x + 2) (x² + x + 1)

Hence (x² - 3x + 2) is a factor of (x⁴ - 2x³ - x + 2)

I hope the answer helps you, please feel free to ask any doubts in the comment section.

Answer 2

Answer:

Step-by-step explanation: