Limits by Factoring Polynomials Questions with Solutions

Eliminating the common factor from rational functions by factoring its polynomials avoids the indeterminate form while finding the limits. Here is a worksheet of problems with examples on finding the limits by factorization for your practice and solutions with understandable steps to learn how to evaluate the limits by factoring polynomials in numerator and denominator of rational functions.

Evaluate $\displaystyle \large \lim_{x\,\to\,2}{\normalsize \dfrac{x^2-4}{x-2}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 1}{\normalsize \dfrac{x^2-3x+2}{x^2-5x+4}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,1}{\normalsize \dfrac{x^2-2x+1}{x-1}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,2}{\normalsize \dfrac{x^3-8}{x-2}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,-3}{\normalsize \dfrac{x^2-9}{x^2+3x}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,1}{\normalsize \dfrac{x-1}{x^2+x-2}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,2}{\normalsize \dfrac{x^2+4x-12}{x^2-2x}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,-1}{\normalsize \dfrac{x^3+1}{x+1}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,3}{\normalsize \dfrac{x^2-9}{x-3}}$

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