The given zeros [tex]-7,2,-3[/tex] are verified to the given function [tex]f(x)=x^{3}+8x^{2} +x-42[/tex].
The given function is [tex]f(x)=x^{3}+8x^{2} +x-42[/tex] has zeros located at [tex]-7, 2, -3[/tex].
What is zero?
A function's zero is any substitution for the variable that yields a zero result.
We need to verify the zeros of [tex]f(x)[/tex] and explain the verification.
You can use either the synthetic method or the factor theorem to verify the zeros.
Here, we use the factor theorem to verify.
By substituting [tex]x=-7[/tex], we get
[tex]f(-7)=(-7)^{3}+8(-7)^{2} +(-7)-42=-343+392-7-42=0[/tex]
By substituting [tex]x=2[/tex], we get
[tex]f(2)=(2)^{3}+8(2)^{2} +(2)-42=8+32+2-42=0[/tex]
By substituting [tex]x=-3[/tex], we get
[tex]f(-3)=(-3)^{3}+8(-3)^{2} +(-3)-42=-27+72-3-42=0[/tex]
Hence, the given zeros [tex]-7,2,-3[/tex] are verified to the given function [tex]f(x)=x^{3}+8x^{2} +x-42[/tex].
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