Math 10 - factoring

1. Factor using GCF

ex. 6x4 – 2x2 GCF = 2x2

then = 3x2 – 1now put together > 2x2(3x2 – 1) >this is the final answer

a)12rt2 – 4r2tb) 14p4 + 21p2 + 35p3

c) 18m2n3 + 12m3n2d) 3a3b2 + 12a2b – 9a2b2

e) 15y4z2 – 5y3z3 + 10y2z4e) 12d5 – 15d10

2. Factor the trinomials of form x2 + bx + c

ex. x2 – 16x + 39 think>what (+) -16 and (x) 39 1,39 or 3,13 or -1,-39 or -3,-13 >these two work!

(x - 3)(x - 13)right into brackets, and done

a) x2 – x – 6 b) x2 – 5x + 4

c) x2 + 15x + 56d) x2 + 4x – 21

e) x2 – 12x + 11f) x2 + 11x + 24

3. Sometimes you have to take the GCF before factoring a trinomial.

ex. 2x2 – 12x + 16 GCF = 2

2(x2 – 6x + 8) now what (+) -6 and (x) 8 >1,8 or 2,4 or -1,-8 or -2,-4 these work

2(x - 2)(x - 4) done

a) 4x2 + 16x – 128b) 3a3 + 24a2 + 45a

c) 4p3 + 4p2 – 24pd) x4 + x3 – 20x2

e) 2c4 + 18c3 + 28c2

4. Factoring trinomials of form ax2 + bx + c.

We covered a few methods for this ex. 2x2 – 17x + 30>begins same way (+) -17 and (x) 2x30=60

-5,-12 work

Decomposition
Replace middle term with 2 new
2x2 – 5x – 12x + 30
GCF from first 2 and last 2
x(2x - 5) -6(2x - 5)
GCF is bracket, followed by
second bracket of remaining
terms in front of brackets
(2x - 5)(x - 6) / Box
first term top left
last term bottom right
other two -5x, -12x
now GCF of each column and row
2x -5
x / 2x2 / -5x
-6 / -12x / 30
top side
(2x - 5)(x - 6) / Division
Place numbers you found into brackets
(x - 5)(x - 12)
Divide both numbers by the
“a” value
(x - )(x - )
If divide evenly great or lowest terms
(x - )(x - 6)
Now move denom. In front of letter in same bracket
(2x - 5)(x - 6)

a) 3x2 + 7x – 6b) 14a2 + a – 3

c) 6x2 + x – 2d) 2m2 – 11m + 15

e) 18x2 – 39x + 18 (hint: GCF first)

5. Factor – remember GCF first ALWAYS

a) -8c3 - 2c10b) -4d2 – 10d

c) 18t2 + 48t + 32d) 2u2 + 13u + 6

e) 6h9 + 4h4f) 2f2 + 13f + 20

g) 4m2 – 5m – 6h) 6c2 – c – 2

i) 6k2 – 19k + 10

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