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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_rings.html" title="">rings</a> > <a href="_factoring_sppolynomials.html" title="">factoring polynomials</a></div>
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<div><h1>factoring polynomials</h1>
<div>Polynomials can be factored with <a href="_factor.html" title="factor a ring element or a ZZ-module">factor</a>. Factorization works in polynomial rings over prime finite fields, ZZ, or QQ.<table class="examples"><tr><td><pre>i1 : R = ZZ/10007[a,b];</pre>
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<tr><td><pre>i2 : f = (2*a+3)^4 + 5
4 3 2
o2 = 16a + 96a + 216a + 216a + 86
o2 : R</pre>
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<tr><td><pre>i3 : g = (2*a+b+1)^3
3 2 2 3 2 2
o3 = 8a + 12a b + 6a*b + b + 12a + 12a*b + 3b + 6a + 3b + 1
o3 : R</pre>
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<tr><td><pre>i4 : S = factor f
2
o4 = (a - 402)(a + 405)(a + 3a - 2301)(16)
o4 : Expression of class Product</pre>
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<tr><td><pre>i5 : T = factor g
3
o5 = (a - 5003b - 5003) (8)
o5 : Expression of class Product</pre>
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The results have been packaged for easy viewing. The number of factors is obtained using<table class="examples"><tr><td><pre>i6 : #T
o6 = 2</pre>
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Each factor is represented as a power (exponents equal to 1 don't appear in the display.) The parts can be extracted with <a href="__sh.html" title="length, or access to elements">#</a>.<table class="examples"><tr><td><pre>i7 : T#0
3
o7 = (a - 5003b - 5003)
o7 : Expression of class Power</pre>
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<tr><td><pre>i8 : T#0#0
o8 = a - 5003b - 5003
o8 : R</pre>
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<tr><td><pre>i9 : T#0#1
o9 = 3</pre>
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