Factoring Polynomials with Common Factors
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
3cd
3cd
-12c2d2
3cd
+3cd = 2c2 - 4cd + 1
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
20)
2ma + 4mb + 2mc
10) 10x – 15x3
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)
1C
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
22. 3x2 + 13x + 12
23. 4x2 - 9
25. y2 + 13y - 48
26. 7k3 - 35k2 + 70k
21. x2 - 6x - 7
24. x2 - 9x - 36
27. a2 - 9a + 14