Question

Given 2x3 + 3x2 + 2xy2 + y3 = (x + y)ƒ(x, y), use polynomial long division to find ƒ(x, y). A. x2 + 2xy + y3 B. 2x2 + 2xy + y2 C. x2 + xy + y2 D. 2x2 + xy + y2

Answer 1

The correct option is option (D).

f(x,y)=2x²+xy+y²

Explanation:

Given that,

`2x^3+3x^2+2xy^2+y^3=(x+y)f(x,y)`

`\Rightarrow f(x,y)=(2x^3+3x^2+2xy^2+y^3)/((x+y))`

x+y) 2x³ + 3x²y + 2xy² + y³ ( 2x²+xy+y²

2x³ +2x²y

- -

________________________

x²y + 2xy² + y³

x²y + xy²

- -

_________________________

xy² + y³

xy² + y³

- -

________________________

×

Therefore f(x,y)=2x²+xy+y²