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Subtraction of Polynomials

If 2x2+xy-3...

Question

If $2 x^{2} + x y - 3 y^{2} + x + a y - 10 = (2 x + 3 y + b) (x - y - 2)$ , the value of a and b are

A

11 a n d 5

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B

1

and

- 5

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C

- 1

and

- 5

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D

- 11

and

5

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Solution

The correct option is D $- 11$ and $5$
$∵ 2 x^{2} + x y - 3 y^{2} + x + a y - 10$
$= (2 x + 3 y + b) (x - y - 2)$
$= 2 x^{2} + x y - 3 y^{2} + (b - 4) x - (b + 6) y - 2 b$
Compare the coefficients of x, y and constant on both sides,
$b - 4 = 1 ⟹ b = 5$
$- (b + 6) = a ⟹ a = - 11$
$2 b = 10 ⟹ b = 5$
$∴ a = - 11$ and $b = 5$

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