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)

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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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