[tex](x+4)[/tex] is not the factor of [tex]f(x).[/tex]
Manu evaluates [tex]f(-4)=-(-4)^{4}-6(-4)^{3}+15(-4)-72[/tex] and determine its value to be [tex]-4[/tex]. Manu concludes that [tex]x+4[/tex] is not a factor of [tex]f(x)=-x^4-6x^3+15x-72.[/tex]
Given that:
[tex]f(x)=-x^4-6x^3+15x-72........(1)[/tex]
Now,
[tex]x+4=0[/tex]
or, [tex]x=-4[/tex]
We put [tex]x=-4[/tex] in equation [tex](1)[/tex].
[tex]f(-4)=-(-4)^{4}-6(-4)^{3}+15(-4)-72[/tex]
[tex]f(-4)=-256+384-60-72[/tex]
[tex]f(-4)=-4[/tex]
Therefore, [tex](x+4)[/tex] is not the factor of [tex]f(x)[/tex].
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