3.2 Factoring a Common Factor
1. Multiply the following. Collect like terms and simplify as needed. Identify the greatest common
factor in each expression.
a. 6(5 + 4t2 +3t3)
b. 4m2 (–6m3p + 2mp + 4mp5)
c. (3x + 4y)(3x – 5y)
d.
– 6a2b (2ab2 – 4ab2 +6)
e. 4x(x – 5) + 6x
f.
(Remember BEDMAS!!)
2
5h2 (3 + 5g) + (3 + g)(4 + h2)
2. Factor the common factor out of each equation.
a. 90 – 50x + 50x2
b. 30 + 24p2 +12p
c. –25p4 – 45p – 50p2
d. –35x2 + 49x – 42
e. 25a3 – 15a2 + 15a
f.
20m6n4 – 30m2n4 – 20 mn4
g. –8b5 + 18b3a + 14b3
h. 8u3v3 + 40u2v4 + 56 u2v2
i.
24xy3 – 16y + 8
j.
13c2 – 4b2 + 5
3. Identify which of the expressions in questions 1 and 2 have a factor that is in the form:
ax2 + bx + c (Remember that b can be zero.)
Answers:
1.
a. 30 + 24t2 + 18t3 (GCF = 6)
b. – 24m5p + 8m3p + 16m3p5 (GCF = 8m3p)
c. 9x2 – 3xy – 20y2 (GCF = 1)
d. 12a3b3 – 36a2b (GCF = 12a2b)
e. 10x2 – 20x (GCF = 10x)
f. 18h2 + 26h2g + 4g + 12 (GCF = 2)
a. 10 (9 – 5x + 5x2)
b. 6(4p2 + 2p + 5)
c. – 5p2 (5p3 + 10p + 9)
d. – 7(5x2 – 7x + 6)
e. 5a(5a2 – 3a + 3)
f. 10mn4 (2m5 – 3m – 2)
g. 2b3 (–4b2 + 9a + 7)
h. 8u2v2 (uv + 5v2 + 7)
i. 8(3xy3 – 2y + 1)
j. not factorable GCF is 1
2.
4. Question 1 c and e (c = zero in e) and question 2 a, b (b = 3y and c = 20y2), d (It is okay if c is also a variable )and d
Tkarras
IAPR2S
2/20/2019