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Which of the following is the value of m for which the polynomial $$x^{4}+10x^{3}+25x^{2}+15x+m $$ is exactly divisible by $$x+7$$?
$$f(x)=x^{4}+10x^{3}+25x^{2}+15x+m $$ is exactly divisible by $$x+7$$. Thus, $$x+7$$ is a factor of $$f(x)$$
Therefore, using the remainder theorem, $$f(-7)=0$$
$$(-7)^{4}+10(-7)^{3}+25(-7)^{2}+15(-7)+m=0$$
$$2401-3430+1225-105+m=0$$
$$-1134+1225+m=0$$
$$m=-91$$
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