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A factored polynomial reveals its roots, a key concept in understanding the behavior of these expressions.
If \(x=18,\) what is the value of \[\frac{x^3-4x^2-21x}{x^2-7x} ?\]
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If \(x:y=4:7,\) what is the value of \[\frac{5x^2+xy+y^2}{x^2+y^2}?\]
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If \(x=13,\) what is the value of \[\frac{x^2+7x-8}{x^2-6x+5} \times \frac{x^2-4x-5}{x^2+9x+8} ?\]
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If \(\displaystyle \frac{x}{3}=\frac{y}{8}=\frac{z}{7} \neq 0,\) what is the value of \[\frac{x^2+y^2+z^2}{xy+yz+zx}?\]
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If \[\frac{x+4}{x^2+3x-4}=a,\] what is the value of \(a\) when \(x=\frac{14}{13}\)?
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