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## Polynomial Factoring

A factored polynomial reveals its roots, a key concept in understanding the behavior of these expressions.

# Rational Expressions

If $$x=18,$$ what is the value of $\frac{x^3-4x^2-21x}{x^2-7x} ?$

If $$x:y=4:7,$$ what is the value of $\frac{5x^2+xy+y^2}{x^2+y^2}?$

If $$x=13,$$ what is the value of $\frac{x^2+7x-8}{x^2-6x+5} \times \frac{x^2-4x-5}{x^2+9x+8} ?$

If $$\displaystyle \frac{x}{3}=\frac{y}{8}=\frac{z}{7} \neq 0,$$ what is the value of $\frac{x^2+y^2+z^2}{xy+yz+zx}?$

If $\frac{x+4}{x^2+3x-4}=a,$ what is the value of $$a$$ when $$x=\frac{14}{13}$$?

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