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What strategies can I use to factorize polynomials?
in Mathematics by Gold Status (12,917 points) | 18 views

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A Strategy for Factoring a Polynomial

1. If there is a common factor, factor out the GCF.

2. Determine the number of terms in the polynomial and try factoring as follows


If there are two terms, then can the binomial be factored by any of the special forms? i.e.

  • Difference of two squares $a^{2}-b^{2}=(a+b)(a-b)$
  • Sum of two cubes $a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right)$
  • Difference of two cubes $a^{3}+b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)$

If there are three terms, then is the trinomial a perfect square trinomial? i.e. $\mathrm{a}^{2}+2 \mathrm{ab}+\mathrm{b}^{2}=(\mathrm{a}+\mathrm{b})^{2}$ and $a^{2}-2 a b+b^{2}=(a-b)^{2}$

If there are four or more terms, try factoring by grouping.

3. Check to see if any factors with more than one term in the factored polynomial can be factored further. If so, factor completely.

by Gold Status (12,917 points)

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