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Manu needs to determine weather x+4 is a factor of f(x)=-x^4-6x^3+15x-72 how can manu use the factor theorem to determine weather x+4 is a factor of f(x)? Drag a value, expression or phrase into each box to correctly complete the statements.

Manu needs to determine weather x4 is a factor of fxx46x315x72 how can manu use the factor theorem to determine weather x4 is a factor of fx Drag a value expres class=

Respuesta :

[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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