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Factor Completely

The document contains examples of completely factoring polynomial expressions. It provides step-by-step workings and explanations for factoring expressions involving subtraction, greatest common factors, difference of squares, and grouping. Guidelines are given for identifying and factoring out negative signs in expressions with "backwards" subtraction. Further examples factor polynomials involving various variables and operations.

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Alma Richelle Ampong-Verdida
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64 views11 pages

Factor Completely

The document contains examples of completely factoring polynomial expressions. It provides step-by-step workings and explanations for factoring expressions involving subtraction, greatest common factors, difference of squares, and grouping. Guidelines are given for identifying and factoring out negative signs in expressions with "backwards" subtraction. Further examples factor polynomials involving various variables and operations.

Uploaded by

Alma Richelle Ampong-Verdida
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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Factor Completely.

4x2 + 5x 2x2 – 10

5x – 25 3x3 + 5x2 + 7x

2x + 4y – 3x2 – 6xy a2b + a4b2

8s + 12r – 6s2 – 9rs 10a2b – 15ab – 4a + 6


Factor Completely.

x2 + 5x + 4 2x2 – 8x – 90

x2 + 5x – 24 3a3 – 9a2 – 54a

x2 + 8x + 16 wz4 + 2wz3 – 80wz2

p2 – 24p + 63 3x2y – 6xy – 45y


Factor Completely.

4x2 – 68xy – 72y2 4y3 + 12y2 – 72y

3x2 + 15x + 18 5q – 50q2 – 120q3

15 + 2y – y2 10p2 – 100p + 90

4x2 + 5x + 1 x2 + 10x – 24

8x2 + 30x + 25 25b2 + 35b – 30

3c2 – 13c + 4 14a2 + 15a – 9


Factor Completely.

24y2 + 14y + 12 12z2 – 14z – 6

2x2 – 15x – 8 12 + 11x – x2

9x2 – 13x – 4 9x3 – 39x2 + 12x


Factor Completely.

1 2 x 1
4 2 x 1 x2 – 24x ay2 – by2 – a + b
2
4x – 1 (ay2 – by2) + (-a + b)

(ay2 – by2) – (a – b)

y2 (a – b) – 1(a – b)

(a – b)(y2 – 1)
(a – b)(y – 1)(y + 1)

16x2 + 24x + 9 2x2 – 12x – 18

72 – 2x2 4x4 – 38x3 + 48x2

w2 + 4w + 4 t4 – 1
Factor Completely.

49x2 + 42xy + 9y2 21x2 – 11x3 – 2x4

6x5y – 6xy5 49 – x4

3a2 + 4a + 1 15x2 – 19x + 6

12t2 – 28t – 5 8z2 – 36z + 1


16x2 – 16x – 12 2yz3 + 17yz2 + 8yz

2t2 + 5t – 12 24k2 + 41k + 12

4x2 + 6x + 2 12 – x – x2

ay2 – by2 – 9a + 9b 3w2 – zw2 – 3 + w

12y2 – 145y + 12 36p2 – 9p3 – p4

256 – m4 3y2 – 147


If subtraction is written backwards, factor out a negative.
When you factor out the negative sign, you write the subtraction switched around.

Beware of “backwards” subtraction.


C(x – y) + (y – x) d(3 – x) – f(x – 3)

C(x – y) – (x – y): not factored, still subtraction d(3 – x) + f(3 – x)

(x – y)(C – 1) (3 – x)(d + f)

Factor Completely.

y(x – 3) – (3 – x) 7x(y – 1) + 4(1 – y)

4x + 6y – 2ax – 3ay xw – yw – 5x + 5y
Factor:

example: ax – 3x + 2a – 6 x2 – y2 + 10y – 25
x(a – 3) + 2(a – 3)
(a – 3)(x + 2)

x2 + 4xy + 4y2 – 25 c2 – cu – 5c + 5u

y4 – 81 8x3 – 1

5z2 – 45w2 125 – y3

x2(x + 4) – 6x(x + 4) – 15( x + 4) (4x + y)2 + 4(4x+ y) + 4


Factor Completely:

b2 – bx – 2b + 2x 3d3 + 81

x2 – 6x + 9 – 36y2 (w – z)2 – 10(w – z) + 25

3x3 + 6x2 – 27x – 54 9y2 – x2 – 14x – 49

4x3 + 32y6 x4 – 16

27 + 8w3

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