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gcf assignment factor the common factor out of each expression. 1) $6p …

Question

gcf assignment
factor the common factor out of each expression.

  1. $6p + 12$
  2. $-10m^2 - 10$
  3. $3m^4 + 24m^6$
  4. $48p^2 + 6$
  5. $-30xz^2y + 5xz^4$
  6. $-4q^4r + 8qrp$
  7. $2p^2q^2 + 2p^2m^2$
  8. $42x^2 + 35x - 49$
  9. $56x + 64x^2 + 64x^4$
  10. $6a^5 - 24a + 9$
  11. $-60 + 54n - 42n^3$
  12. $24x^4y^7 - 36x^4y^3 - 16xy$
  13. $5xy^5 + 7x^3y^3 - 5xy^3$
  14. $-4y^2x + 8y^3 - y^5$
  15. $-6yx^2 - 3y^3 - 21y^2$

Explanation:

Step1: Identify GCF of 6p,12

GCF is 6, factor it out:
$6p + 12 = 6(p + 2)$

Step2: Identify GCF of $-10m^2,-10$

GCF is $-10$, factor it out:
$-10m^2 - 10 = -10(m^2 + 1)$

Step3: Identify GCF of $3m^4,24m^6$

GCF is $3m^4$, factor it out:
$3m^4 + 24m^6 = 3m^4(1 + 8m^2)$

Step4: Identify GCF of $48p^2,6$

GCF is 6, factor it out:
$48p^2 + 6 = 6(8p^2 + 1)$

Step5: Identify GCF of $-30xz^2y,5xz^4$

GCF is $5xz^2$, factor it out:
$-30xz^2y + 5xz^4 = 5xz^2(-6y + z^2)$

Step6: Identify GCF of $-4q^4r,8qrp$

GCF is $4qr$, factor it out:
$-4q^4r + 8qrp = 4qr(-q^3 + 2p)$

Step7: Identify GCF of $2p^2q^2,2p^2m^2$

GCF is $2p^2$, factor it out:
$2p^2q^2 + 2p^2m^2 = 2p^2(q^2 + m^2)$

Step8: Identify GCF of $42x^2,35x,-49$

GCF is 7, factor it out:
$42x^2 + 35x - 49 = 7(6x^2 + 5x - 7)$

Step9: Identify GCF of $56x,64x^2,64x^4$

GCF is $8x$, factor it out:
$56x + 64x^2 + 64x^4 = 8x(7 + 8x + 8x^3)$

Step10: Identify GCF of $6a^5,-24a,9$

GCF is 3, factor it out:
$6a^5 - 24a + 9 = 3(2a^5 - 8a + 3)$

Step11: Identify GCF of $-60,54n,-42n^3$

GCF is $-6$, factor it out:
$-60 + 54n - 42n^3 = -6(10 - 9n + 7n^3)$

Step12: Identify GCF of $24x^4y^7,-36x^4y^3,-16xy$

GCF is $4xy$, factor it out:
$24x^4y^7 - 36x^4y^3 - 16xy = 4xy(6x^3y^6 - 9x^3y^2 - 4)$

Step13: Identify GCF of $5xy^5,7x^3y^3,-5xy^3$

GCF is $5xy^3$, factor it out:
$5xy^5 + 7x^3y^3 - 5xy^3 = 5xy^3(y^2 + \frac{7}{5}x^2 - 1)$

Step14: Identify GCF of $-4y^2x,8y^3,-y^5$

GCF is $-y^2$, factor it out:
$-4y^2x + 8y^3 - y^5 = -y^2(4x - 8y + y^3)$

Step15: Identify GCF of $-6yx^2,-3y^3,-21y^2$

GCF is $-3y$, factor it out:
$-6yx^2 - 3y^3 - 21y^2 = -3y(2x^2 + y^2 + 7y)$

Answer:

  1. $6(p + 2)$
  2. $-10(m^2 + 1)$
  3. $3m^4(1 + 8m^2)$
  4. $6(8p^2 + 1)$
  5. $5xz^2(-6y + z^2)$
  6. $4qr(-q^3 + 2p)$
  7. $2p^2(q^2 + m^2)$
  8. $7(6x^2 + 5x - 7)$
  9. $8x(7 + 8x + 8x^3)$
  10. $3(2a^5 - 8a + 3)$
  11. $-6(10 - 9n + 7n^3)$
  12. $4xy(6x^3y^6 - 9x^3y^2 - 4)$
  13. $5xy^3(y^2 + \frac{7}{5}x^2 - 1)$
  14. $-y^2(4x - 8y + y^3)$
  15. $-3y(2x^2 + y^2 + 7y)$