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# GCF and Factoring

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1. Find the GCF of the set of monomials of 252, 468

2. Factor the polynomial 35 y + 14, if possible.

3. Factor the polynomial 7 a ^6 b ^7 c^ 5 - 35 a ^7 b ^5 c ^6, if possible.

4. Factor the expression 2(x + y) - 19 t(x + y).

5. Factor 17 x ^2 + 17 x y + 2 x + 2 y by grouping.

6. Factor the polynomial.

25 y ^2 - 4

7. Factor the polynomial.

9 a ^8 b ^6 c ^6 - 64 d ^8

8. Complete the factorization. x^2 + 5x - 6 = x + 6) . ____

9. Use a special product formula to factor the perfect square trinomial.

b2 + 8b + 16

10. True or False?
The trinomial b 2 + 7 b + 20 is prime.

11. Factor the trinomial.
If the lead coefficient is negative, begin by factoring out -1.

- x ^2 - 4 x + 45.

12. Factor the trinomial. Factor out all common monomials first.

35 x ^3 - 61 x ^2 + 8 x.

13. True or False?
a ^4 - 10 a ^2 + 16 = ( a ^2 - 8)( a ^2 - 2)

14. Use a special product formula to factor the perfect square trinomial.

49x^2 - 56x + 16

##### Solution Summary

The following posting helps with problems involving greatest common factor and factoring.

##### Solution Preview

1. GCF - you can read more here http://www.purplemath.com/modules/lcm_gcf.htm

252 - factors = 2 x 2 x 3 x3 x7

468 - factors = 2x2x3x3x13

GCF = 2X2X3X3 =36

2. 35Y +14 = 7(5Y+2)

3. 7 a ^6 b ^7 c^ 5 - 35 a ^7 b ^5 c ^6 = 7a^6b^5c^5(b^2 -5ac)

4. 2(x + y) - 19 t(x + y).

= (x+y) (2-19t)

5. 17 x ^2 + 17 x y + 2 x + ...

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###### Education
• BE, Bangalore University, India
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