Question

divide 3x^2 - x^3 - 3x + 5 by x - 1 - x^2 , and verify the division algorithm. class 10th​

Answer 1

Step-by-step instruction

Let f(x) = 3x² - x³ - 3x + 5 and g(x) = x - 1 - x²

Long Division Method:

-x² + x - 1) -x³ + 3x² - 3x + 5(x - 2

-x³ + x² - x

-------------------------

2x² - 2x + 5

2x² - 2x + 2

----------------------

3

Verification:

Dividend = Divisor * Quotient + Remainder

= (-x² + x - 1) - (x - 2) + 3

= -x³ + x² - x + 2x² - 2x + 2 + 3

= 3x² - x³ - 3x + 5

Hope it helps!