Question

the LCM and GCD of two polynomial is q (x) is (x4-y4)(x2+y2-xy) find other polynomial ​

Answer 1

Answer:

GCD= Greatest Common Divisor.

x

2

−xy−xy+y

2

=x(x−y)−y(x−y)

=

(x−y)

(x−y)

x

4

−y

4

=

(x−y)

(x+y)(x

2

+y

2

)

GCD=

x−y

Factors of x

4

−y

4

=(x

2

−y

2

)(x

2

+y

2

)

=(x−y)(x+y)(x

2

+y

2

)

Factors of x

2

(x−y)+y

2

(x−y)+y−x

=x

2

(x−y)+y

2

(x−y)−(x−y)

=(x−y)(x

2

+y

2

−1)

Common factors of (x

4

−y

4

,x

2

(x−y)+y

2

(x−y)+y−x)=x−y

∴ H.C.F of (x

4

−y

4

,x

2

(x−y)+y

2

(x−y)+y−x)=x−y

Step-by-step explanation:

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