Factoring polynomials

Factoring polynomials is the inverse process of multiplying polynomials. After factoring a polynomial, if we divide the polynomial with the factors then the remainder will be zero. Whenever we factor a polynomial we should always look for the greatest common factor(GCF) then we determine if the resulting polynomial factor can be factored again.

Here are the most common factoring techniques used with polynomials:

If we have any number of terms then we use GCF:

$$a^{4}b^{2}+a^{2}b^{2}-a^{3}b^{2}=a^{2}b^{2}(a^{2}+1-a)$$

If we have two terms then we could use either the difference of two squares, the sum of two cubes or the difference of two cubes:

$$a^{2}-b^{2}=(a+b)(a-b)$$

$$a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$$

$$a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$$

If we have three terms then we use either perfect square trinomials or general trinomials:

$$a^{2}+2ab+b^{2}=(a+b)^{2}$$

$$a^{2}-2ab+b^{2}=(a-b)^{2}$$

$$aex^{2}+(ad+be)x+bd=(ax+b)(ex+d)$$

Lastly if we have four or more terms we use grouping:

$$xa+xb+ya+yb=x(a+b)+y(a+b)$$

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Video lesson

Factor 2x²-4xy+2y²=2(x²-2xy+y²)=2(x-y) ²