If x = 3 is a zero of the polynomial function f(x) = 2x^3+ x2 - 25x + 12, which of the following is another zero of f(x)?
x= -3
x=4
x= -4
x = 12

From the given four options, another factor of polynomial is x = -4.

Solution:

Given that x = 3 is a zero of the polynomial function

Need to check if any other zeros is present in four given option. Let us understand what is zero of a polynomial. A zero for polynomial is that value of variable x for which dependent function of (x) = 0.

So we need to check for all four values of x,  

Corresponding value of polynomial and if it is equal to 0 that that value of x is zero of f of x.

On substituting x= -3, we get

As function of -3 =  42, which is not equal to 0,  

So x= -3 is not a zero of polynomial

On substituting x = 4, we get

As function of 4 =  56, which is not equal to 0,  

So x= 4 is not a zero of polynomial

On substituting x = -4, we get

As function of -4 = 0 , so x = -4 is a zero of a zero of polynomial

On substituting x = 12, we get

As function of 12 =  1584, which is not equal to 0,  

So, x= 12 is not a zero of polynomial

Therefore, the another zero is x=-4.

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answer: 2530

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