Mathematics: Given that a is a multiple of 456, find the greatest common divisor of 3a^3+a^2+4a+57 and a.

I believe the answer is C. 43 hope that I m right on this...

Given that a is a multiple of 456, find the greatest

chgraypto

31.01.2022

Step-by-step explanation:

Given: a is a multiple of 456

Let a = 456 x

Then, expression 3a^3+a^2+4a+57 =3(456x)^3+(456x)^2+4(456x)+57

Since 456 = 57 x 8

Then, $3(456x)^3+(456x)^2+4(456x)+57=3(57\times 8x)^3+(57\times 8x)^2+4(57\times 8x)+57$

$=3(57)^3\times (8x)^3+(57)^2\times (8x)^2+4(57)\times (8x)+57$

Taking 57 out as common

$=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1]$

Now, the greatest common divisor of a = 456 x and $3a^3+a^2+4a+57=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1]$ is 57.

Hence, the greatest common divisor of 3a^3+a^2+4a+57 and a is 57.

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