Find the zeros of the polynomial function.

f(x) = x^{3} + x^{2} - 42x

zeros of the function are where the value of function is zero.

f(x)=0

x3 + x2 - 42x=0

x (x2+x-42)=0

Hence, x=0 or x2+x-42=0

now, x2-x-42=0

x2-7x+6x-6*7=0

x(x-7)+6(x-7)=0, thus (x+6)(x-7)=0

so, x= -6 or x=7

Hence the zeros of the function are at x=0, -6, 7

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