For further information about factoring polynomials using a GCF, see pp. 214 - 219 of Mathematics 10.


Additional video examples are below:
Video Set 1:
GCFs of Monomials
 
 

Video Set 2:
Factoring Polynomials by GCF
 
 
 

 

Many polynomials can be factored by determining the GCF and using the distributive property in reverse. This process works for some products, but not all. Consider «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mo»(«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«mo»(«/mo»«mn»4«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mo»)«/mo»«mo»=«/mo»«mn»8«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mstyle»«/math». Is there a reliable way to factor «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mn»8«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/mstyle»«/math» into «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mo»(«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«mo»(«/mo»«mn»4«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mo»)«/mo»«/mstyle»«/math»? The next lesson explores this question.