Find the difference between the quotient and remainder when( x³-6x²

1.	Find the difference between the quotient and remainder when( x³-6x² + 11x-6)is divided by (x+1).
Answer» Given us a polynomial, p(x) = x³ - 6x² + 11x - 6 And we have to find the difference between remainder and quotient when the given polynomial is divided by G(x) = x + 1 To Find the remainder when p(x) is divided by g(x), Substitute x = -1 in p(x), ⇒ p(-1) = (-1)³ - 6(-1)² + 11(-1) - 6 ⇒ p(-1) = -1 - 6 - 11 - 6 ⇒ p(-1) = -18 - 6 ⇒ p(-1) = -24 Refer to the diagram for the DIVISION process. Here we got the quotient Q(x) as q(x) = x² - 7x + 18 Now, We have to find the difference between quotient and remainder, so ⇒ q(x) - r ⇒ x² - 7X + 18 - (-24) ⇒ x² - 7x + 18 + 24 ⇒ x² - 7x + 42 Hence, The difference between quotient and Remainder is x² - 7x + 42

Find the difference between the quotient and remainder when( x³-6x² + 11x-6)is divided by (x+1).

Answer»

Given us a polynomial,

And we have to find the difference between remainder and quotient when the given polynomial is divided by G(x) = x + 1

To Find the remainder when p(x) is divided by g(x), Substitute x = -1 in p(x),

⇒ p(-1) = (-1)³ - 6(-1)² + 11(-1) - 6

⇒ p(-1) = -1 - 6 - 11 - 6

⇒ p(-1) = -18 - 6

⇒ p(-1) = -24

Refer to the diagram for the DIVISION process.

Here we got the quotient Q(x) as

Now, We have to find the difference between quotient and remainder, so

⇒ q(x) - r

⇒ x² - 7X + 18 - (-24)

⇒ x² - 7x + 18 + 24

⇒ x² - 7x + 42

Hence, The difference between quotient and Remainder is x² - 7x + 42