Alg1, Unit 13, Lesson04_absent-student, page 1
Using GCF to factor a polynomial
In the problem below, distribute 3x2 into the parenthesis:
3x2(x3 + 5x + 2a)
Working backwards on this process, we could say that
the factored form of 3x5 + 15x3 + 6ax2 is 3x2(x3 + 5x + 2a).
We say that we “factored out” 3x2.
It is important to notice that 3x2 is the GCF of 3x5 + 15x3 + 6ax2
To factor a GCF out of a polynomial:
• Find the GCF of all the terms
• Write this GCF in front of a parenthesis
• Inside the parenthesis, write each original term of the polynomial
divided by the GCF.
Example 1: Factor 5x2 – 10
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Example 2: Factor 6x3 – 12mx2
Alg1, Unit 13, Lesson04_absent-student, page 2
Example 3: Factor 4y5 – 8y4 + 16y2
Example 4: Factor 12p3q5r2 – 8pq3r7 + 20 p3q3r3
Example 5: -3m4 – 9m5n2 – 18m3n2
It is possible to check your work by multiplying the two factors
together. The result should be the original polynomial that was to be
factored.
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Alg1, Unit 13, Lesson04_absent-student, page 3
Assignment: Factor.
1. 9x3 – 6
2. 12 + 48k2
3. 25x2 + 5x
4. 32m5 – 8m4
5. 9ab – 6a2b
6. 18h2 + 12h – 36
7. 11x2 – 33x3 + 22x5
8. 6xy2 – 10x2y
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Alg1, Unit 13, Lesson04_absent-student, page 4
9. 4g2 + 10g + 1
10. 2p2q2 + 10pq
11. 16d2c – 4d2c2
12. –16x3y – 24x5y2
13. 5bz2 + 10b2z – 15b4z
14. 14a3b3 – 21a2b2 + 42ab
15. 72x2y3 + 48 x3y2
16. 77w6d6 + 84w5d4
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Alg1, Unit 13, Lesson04_absent-student, page 5
17. 14f2 – 21f
18. 30a – 25ab + 35
19. 11xy2z3 + 22x3y2z
20. 8ab + 9xy
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