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# Given that \$x\$ is a multiple of \$23478\$, what is the greatest common divisor of \$f(x)=(2x+3)(7x+2)(13x+7)(x+13)\$ and \$x\$?

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Given that x is a multiple of 23478, what is the greatest common divisor of \(f(x)=(2x+3)(7x+2)(13x+7)(x+13)\)  and x?

Feb 2, 2018

### Best Answer

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Since 23478 prime factors are = 2 * 3 * 7 * 13 * 43, and the first 4 factors are common to the polynomial f(x)=(2x+3)(7x+2)(13x+7)(x+13), therefore no matter what value x takes, the GCD of the polynomial and x will ALWAYS be = 2 x 3 x 7 x 13 = 546 !!.

Feb 2, 2018

### 1+0 Answers

#1
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Best Answer

Since 23478 prime factors are = 2 * 3 * 7 * 13 * 43, and the first 4 factors are common to the polynomial f(x)=(2x+3)(7x+2)(13x+7)(x+13), therefore no matter what value x takes, the GCD of the polynomial and x will ALWAYS be = 2 x 3 x 7 x 13 = 546 !!.

Guest Feb 2, 2018