Question

find the gcd of given polynomial 3x^3+3x^2+3x+3, 6x^3+12x^2+6x+12​

Answer 1

Answer:

3(x^2 + 1)

Step-by-step explanation:

Factor of 3x3+3x2+3x+3

=3x3+3x2+3x+3

=3(x3+x2+x+1)

=3((x3+1)+(x2+x))

=3((x3+1)+x(x+1))

=3((x+1)(x2-x+1)+x(x+1))

=3(x+1)((x2-x+1)+x)

=3(x+1)(x2+1)

= 3 (x + 1)(x2 + 1)

Factor of 6x3+12x2+6x+12

=6x3+12x2+6x+12

=6(x3+2x2+x+2)

=6(x2(x+2)+1(x+2))

=6(x+2)(x2+1)

=2×3(x+2)(x2+1)

= 2 × 3 (x + 2)(x2 + 1)

GCD = 3 (x2 + 1)

hope it helps

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Answer 2

Step-by-step explanation:

3(x+1)(x2 +2) for first one

3(x2+1) for second one

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