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4.4A Factoring GCFs

Total questions: 14

Worksheet time: 4hrs 30mins

Name
Class
Date
1.

Factor the expression completely.

 9k369k-36  

a)

 4(k9)4\left(k-9\right)  

b)

 9(k4)9\left(k-4\right)  

c)

 3(3k12)3\left(3k-12\right)  

d)

 9(k27)9\left(k-27\right)  

2.

Factor the expression completely.

 12m3+8n212m^3+8n^2  

a)

 8(4m3+n2)8\left(4m^3+n^2\right)  

b)

 2(6m3+4n2)2\left(6m^3+4n^2\right)  

c)

 4(3m3+2n2)4\left(3m^3+2n^2\right)  

d)

 6(6m3+2n2)6\left(6m^3+2n^2\right)  

3.

Factor the expression completely.

 27ac3+6ac218a27ac^3+6ac^2-18a  

a)

 3a(9c3+2c26)3a\left(9c^3+2c^2-6\right)  

b)

 3(9ac3+2ac26a)3\left(9ac^3+2ac^2-6a\right)  

c)

 3ac(9c2+2c6)3ac\left(9c^2+2c-6\right)  

d)

 3c(9ac2+2ac6a)3c\left(9ac^2+2ac-6a\right)  

4.

Factor the expression completely.

 14v11+24v714v^{11}+24v^7  

a)

 2v7(7v4+12)2v^7\left(7v^4+12\right)  

b)

 2(7v11+12v7)2\left(7v^{11}+12v^7\right)  

c)

 v7(14v4+24)v^7\left(14v^4+24\right)  

d)

 14v7(v4+10)14v^7\left(v^4+10\right)  

5.

Factor the expression completely.

 4h4+h36h-4h^4+h^3-6h  

a)

 h(4h3+h26)h\left(-4h^3+h^2-6\right)  

b)

 h(4h3+h26)-h\left(4h^3+h^2-6\right)  

c)

 2h(2h3+h23)2h\left(2h^3+h^2-3\right)  

d)

 h(4h3h2+6)-h\left(4h^3-h^2+6\right)  

6.

Factor the expression completely.

 49t57t4+14t2-49t^5-7t^4+14t^2  

a)

 7t2(42t3+t27)-7t^2\left(42t^3+t^2-7\right)  

b)

 7t2(7t3t2+2)7t^2\left(7t^3-t^2+2\right)  

c)

 7t2(7t3+t22)-7t^2\left(7t^3+t^2-2\right)  

d)

 7t2(42t3t2+7)7t^2\left(42t^3-t^2+7\right)  

7.

Factor the expression completely.

 4m5+16m3+24m4m^5+16m^3+24m  

a)

 4m(m4+12m2+20)4m\left(m^4+12m^2+20\right)  

b)

 2m(2m4+8m2+12)2m\left(2m^4+8m^2+12\right)  

c)

 2m(2m4+14m2+22)2m\left(2m^4+14m^2+22\right)  

d)

 4m(m4+4m2+6)4m\left(m^4+4m^2+6\right)  

8.

Factor the expression completely.

 3x4y+18x2y333xy3x^4y+18x^2y^3-33xy  

a)

 3x2y(x2+6y211)3x^2y\left(x^2+6y^2-11\right)  

b)

 3xy(x3+6xy211)3xy\left(x^3+6xy^2-11\right)  

c)

 xy(3x3+18xy233)xy\left(3x^3+18xy^2-33\right)  

d)

 x2y(3x2+18y233)x^2y\left(3x^2+18y^2-33\right)  

9.

Factor the expression completely.

 4u8+2u528u2-4u^8+2u^5-28u^2  

a)

 4u(u72u4+7u)-4u\left(u^7-2u^4+7u\right)  

b)

 2u5(2u3u+14)-2u^5\left(2u^3-u+14\right)  

c)

 u2(4u62u3+28)-u^2\left(4u^6-2u^3+28\right)  

d)

 2u2(2u6u3+14)-2u^2\left(2u^6-u^3+14\right)  

10.

Factor the expression completely.

 r1014r928r4-r^{10}-14r^9-28r^4  

a)

 14r4(r6r52)14r^4\left(-r^6-r^5-2\right)  

b)

 r4(r6+14r5+28)-r^4\left(r^6+14r^5+28\right)  

c)

 r4(r614r528)-r^4\left(r^6-14r^5-28\right)  

d)

 r2(r814r728r2)r^2\left(r^8-14r^7-28r^2\right)  

11.

Factor the expression completely.

 4w3+4w228w4w^3+4w^2-28w  

a)

 2w(2w2+2w14)2w\left(2w^2+2w-14\right)  

b)

 4w(w2+w7)4w\left(w^2+w-7\right)  

c)

 4w(w2+w24)4w\left(w^2+w-24\right)  

d)

 w(4w2+4w28)w\left(4w^2+4w-28\right)  

12.

Factor the expression completely.

 6a312a2+32a-6a^3-12a^2+32a  

a)

 2a(3a2+6a16)-2a\left(3a^2+6a-16\right)  

b)

 6a(a2+6a26)-6a\left(a^2+6a-26\right)  

c)

 2a(3a26a+16)-2a\left(3a^2-6a+16\right)  

d)

 6a(a26a+26)-6a\left(a^2-6a+26\right)  

13.

Factor the expression completely.

 6e6+18e424e3+3e26e^6+18e^4-24e^3+3e^2  

a)

 3e2(2e4+6e28e)3e^2\left(2e^4+6e^2-8e\right)  

b)

 3e2(3e3+15e221e)3e^2\left(3e^3+15e^2-21e\right)  

c)

 3e2(3e4+15e221e+1)3e^2\left(3e^4+15e^2-21e+1\right)  

d)

 3e2(2e4+6e28e+1)3e^2\left(2e^4+6e^2-8e+1\right)  

14.

Factor the expression completely.

 10m5n30m4n2400m2n10m^5n-30m^4n^2-400m^2n  

a)

 10mn(m43m3n40m)10mn\left(m^4-3m^3n-40m\right)  

b)

 10m2n(m33m2n40)10m^2n\left(m^3-3m^2n-40\right)  

c)

 5m2n(2m46m3n80m)5m^2n\left(2m^4-6m^3n-80m\right)  

d)

 5mn(2m46m3n80)5mn\left(2m^4-6m^3n-80\right)