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Polynomial Factoring

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

Simplifying Rational Expressions

         

Simplify \[\frac{x^2+11x+18}{x+2} \div \frac{x+9}{12}.\]

If \[\frac{x+2}{x^2+5x-6} \times \frac{x^2-6x+5}{3x+6} = \frac{x-c}{ax+b},\] where \(a\), \(b\) and \(c\) are constants, what is \(a+b+c\)?

If \[\frac{35x^{4}y^{3}}{3a^{8}b^{7}} \div \frac{5x^{6}y^{5}}{21a^{9}b^{8}} = \frac{pab}{x^my^n},\] where \(p\), \(m\) and \(n\) are constants, what is the value of \(p+m+n\)?

Simplify \[\frac{4x^2+20x+21}{3x+6} \times \frac{2x+3}{2x+7} \div \frac{4x^2+12x+9}{6x+12}.\]

If \[\frac{x}{x-7}-\frac{x}{x+9}=\frac{ax}{(x-7)(x+9)},\]

holds for all values of \(x\), what is the value of \(a\)?

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