Factoring Polynomials with Common Factors
Factoring Polynomials with Common Factors 1C
To factor a polynomial:
1) We look at all of the terms in the polynomial, then find their GCF
2) We then divide each term of the polynomial by the GCF
3) The polynomial is then expressed as the product of the two factors
4) We can check by multiplying the factors to obtain the original polynomial
Factor: 6c3d - 12c2d2+ 3cd
1) 3cd is the GCF
2) To find the other factor: divide 6c3d - 12c2d + 3cd by 3cd
6c3d -12c2d2 + 3cd = 6c3d -12c2d2 +3cd = 2c2 - 4cd + 1
3cd 3cd 3cd 3cd
3) Express the two factors as products
3cd (2c2-4cd + 1)
4) Check by distributing 3cd
Factor the following polynomials
1) 2a + 2b 11) 3ab2-6a2b
2) 5c + 5d 12) 21r3s2 – 14r2s
3) 8m+8n 13) 3x2 - 6x - 30
4) bx + by 14) c3 - c2 +2c
5) 3m -6n 15) 9ab2 - 6ab - 3a
6) 18c - 27d 16) l0xy-l5x2y2
7) 3y4 + 2y2 17) 28m4n3 – 70m2n4
8) y2 – 3y 18) 15x3y3z3 - 5xyz
9) 2x2 + 5x 19) 8a4b2c3 + 12a2b2c2
10) 10x – 15x3 20) 2ma + 4mb + 2mc
Factoring the difference of Two Squares “DOTS”
An expression of the form a2 – b2 is DOTS
Ex: a2 – b2 = (a – b)(a + b) 25x2 – y2 = (5x – y)(5x + y)
r2 – 9 = (r – 3)(r + 3) 1 – c6d4 = (1 – c3d2)(1 + c3d2)
NAME___________________________________ Date ___________
MATH A REVIEW PRACTICE: FACTORING
Factor completely.
1. x2 – 14x + 24 2. 2x2 + 6x + 12 3. x2 - 11x -12
4. x2 – y2 5. 4x2 - 100 6. x2 + 14x + 48
7. 4x2 + 9 8, 3x2+l3x-10 9. x2 +18x + 32
10. xy + xz U. 4x2 - 24x + 32 12. 2x2 + x
13. x2 + 7x - 18 14. 6a2b3 - 2a5b 15. p + prs
16. 25a2 - 36b2 17. x2 - 13x + 40 18. 36x2 - 16y2
19. l0x-l5x3 20. 3x3 - 12x 21. x2 - 6x - 7
22. 3x2 + 13x + 12 23. 4x2 - 9 24. x2 - 9x - 36
25. y2 + 13y - 48 26. 7k3 - 35k2 + 70k 27. a2 - 9a + 14
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