Question

divide (2x³+x²-13x+6)by (x-2)​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given :-

2x³+x²-13x+6

To find :-

Divide (2x³+x²-13x+6) by (x-2) ?

Solution :-

Given Polynomial = 2x³+x²-13x+6

Given divisor = x-2

On dividing 2x³+x²-13x+6 by x-2

x-2 ) 2x³+x²-13x+6 ( 2x² + 5x -3

2x³-4x²

(-) (+)

__________

0 +5x² -13x

5x²- 10x

(-) (+)

___________

0 -3x+6

-3x+6

(+) (-)

____________

0

____________

Quotient = 2x² + 5x -3

Remainder = 0

Answer :-

Quotient = 2x² + 5x -3

Remainder = 0

Check :-

We know that

Division Algorithm on Polynomials is

P(x) = g(x)×q(x)+r(x)

=> (x-2)×(2x² + 5x -3) +0

=> x(2x² + 5x -3)+(-2)(2x² + 5x -3)+0

=> 2x³+5x²-3x-4x²-10x+6+0

=> 2x³+x²-13x+6

=> Given Polynomial

Verified the given relation.

Used formulae

• Division Algorithm on Polynomials is
• P(x) = g(x)×q(x)+r(x)

Where,

• P(x) = Dividend
• g(x) = Divisor
• q(x) = Quotient
• r(x) = Remainder