Question

Solve the following: (1) Divide: (x +4x²+x-16)÷(x - 1)​

Answer 1

Given to divide the following :–

4x² + x + x -16 ÷ x-1

SOLUTION:–

4x² + x + x -16 = 4x² + 2x-16

Dividend :- 4x² + 2x -16

Divisor :- x-1

x- 1 ) 4x² + 2x - 16 ( 4x +6

+ 4x² -4x

(-) (+)

___________

6x -16

+ 6x - 6

(-) (+)

___________

-10

So, the Quotient is 4x + 6

Remainder is -10

EXPLANATION :-

• Take the first term of Dividend (4x²) and first term of divisor (x) Divide each other i.e 4x²/x = 4x .

• Now , multiply '4x' with divisor (x-1) i.e 4x(x-1) = 4x²-4

• Now, subtract 4x²-4x from 4x²+2x-16

• After subtracting we get 6x-16.

• Now repeat the same process.

• Again, Take the first term of 6x-16 i.e 6x divide with first term of divisor (x) i.e 6x/x = 6

• Now , multiply 6 with divisor x-1 i.e 6(x-1) = 6x-6

• Again subtract 6x-6 from 6x-16

• After subtracting we get the remainder "-10".

We have to do this process..until the remainder degree must be less than the degree of Divisor.

__________________

Verification:-

As we know that,

Dividend = (Divisor)(Quotient) + Remainder .

Quotient is 4x + 6

Remainder is -10

Dividend :- 4x² + 2x -16

Divisor :- x-1

4x² + 2x -16 = (x-1) (4x+6) + (-10)

4x² + 2x -16 = x(4x+6) -1(4x+6) -10

4x² + 2x-16 = 4x²+6x-4x -6-10

4x² + 2x -16 = 4x²+2x-16

L.H.S = R.H.S

Henceforth, Verified!