Question

17. (a) By remainder theorem find the remainder, when p(x) is divided by g(x) where
p(x) = x2 - 6x + 2x - 4. g(x) = x + 6​

Answer 1

To Find :

• we need to find the remainder .

Solution :

p(x) = x² - 6x + 2x - 4

• p(x) = x² - 4x - 4
• g(x) = x + 6

⠀⠀x + 6)x² - 4x - 4( x - 10

⠀⠀⠀⠀⠀ x² + 6x

⠀⠀⠀⠀⠀ -- ⠀--⠀⠀⠀

⠀⠀⠀⠀⠀ ⠀⠀-10x - 4

⠀⠀⠀⠀⠀ ⠀⠀- 10x - 60

⠀⠀⠀⠀⠀ ⠀⠀ ⠀+⠀⠀+⠀⠀⠀

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀⠀56 R

When we Divide p(x) = x² - 6x + 2x - 4 by g(x) = x + 6 ,

Then,

• Remainder = 56

Verification :-

• Dividend = Divisor × quotient + Remainder.

›› p(x) = (x + 6)(x - 10) + 56

›› p(x) = x(x - 10) + 6(x - 10) + 56

›› p(x) = x² - 10x + 6x - 60 + 56

›› p(x) = x² - 4x - 4

›› x² - 4x - 4 = x² - 4x - 4

LHS = RHS

Hence Verified

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

56

Step-by-step explanation:

p(x) = x² - (6x - 2x) - 4

p(x) = x² - (4x) - 4

p(x) = x² - 4x - 4

We have to divide (x² - 4x - 4) by (x + 6). To find the remainder .

x+6)x² - 4x - 4(x-10

.......x² + 6x (change signs)

_______________

,..............-10x - 4

..............- 10x - 60 (change the signs)

_______________________

....................... 56

_______________________

When we Divide p(x) = x² - 6x + 2x - 4 by g(x) = x + 6 we get 56 as a remainder.

Hence, the remainder is 56.