CORNELL NOTES SHEET



Cornell NotesFoundations,Pre-Calc. 10Chapter:____4.2_________Topic: Common Factors __________________________Date:________________________Homework: Pg. 158 # 2,4-8,10Key Terms:Definition:Greatest Common Factorthe largest factor shared between two or more termsEx. GCF: 12 and 28 4Least Common MultipleThe smallest multiple shared by two or more termsEx. LCM: 6 and 8: 24The GFC of a polynomialThe largest factor shared by both the coefficients and the variablesTo factor a polynomial find the GFC for the coefficient and use thevariable with the lowest exponent as the GCF Questions/Examples:Notes:Example 1Find the GCF of 16x2y an 24x2y3Method 1: Prime Factorization16 = 2*2*2*2 GCF of the coefficient = 824 = 2*2*2*3 GFC of the variables = x2yx2y = x*x*y GFC of the polynomial = 8x2yx2y3 = x*x*y*y*yMethod 2: List the Factors16x2y = 1,2,4,8,16, x2,y24x2y3 = 1,2,3,4,6,8,12,24, x2,y,y2GFC of the polynomial = 8x2ycontinue notes on backSUMMARY: Write a summary – 2 to 3 key points in full sentences – of what you learned and need to remember about this lesson.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Questions:Notes:Example 2Factor the polynomials:divide each of the termsa) 5x5 + 10x3 + 20xGCF for the coeffients: 5in the polynomial by the 5x(x4 + 2x2 + 4) GCF for the variable: xGCF to factor the GCF for the polynomial: 5xb) 7a2b – 28ab + 14ab2GCF of the coeffiencets: 7 7ab(a – 4 + 2b) GCF for the variable: ab GCF for the polynomial: 7abFactoring by Groupingthe simplest expression to factor this way is a 4-term polynomial whosefirst two terms have a GCF and the last two terms have a different GCFgroup the first two terms and then the last two termsfactor out the GCF for each separate binomialfactor out the common binomialExample 3Write each expression in factored formthis binomial is the 3x(x – 4) + 5(x – 4) GCF: x – 4 common factor for (3x + 5)(x – 4)both; this leaves the othertwo terms to create thesecond binomialy2 + 8xy + 2y + 16x (y2 + 8xy) + (2y + 16x) GCF: y GCF: 2 y(y + 8x) + 2(y+8x) (y +2)(y +8x)758190161290Multiply0Multiply653415-2381250 5x+2=5x+10 4x22x-3=8x3-12x2 a2bab2-2a-b= a3b3-2a2b- a2b293916579375Factor0Factor615315-158760Self-assessment of C-notes: Write a Yes or No in the appropriate blank for the following:________ I have completed all the header information.________ I have done a thorough job of note-taking today’s subject.________ I have written questions in the left column that will remind me of the contents of my notes when I study.________I have written a detailed summary according the writing guidelines required. ................
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