Introduction to factoring polynomials

Page
4

(2r + a)

a

– 1

2ra + a2 – 2r – a =

(2r + a)(a – 1)

Slide 23

Your Turn to Try a Few

Slide 24

To factor a polynomial completely, ask

Do the terms have a common factor (GCF)?

Does the polynomial have four terms?

Is the polynomial a special one?

Is the polynomial a difference of squares?

a2 – b2

Is the trinomial a perfect-square trinomial?

a2 + 2ab + b2 or a2 – 2ab + b2

Is the trinomial a product of two binomials?

Factored completely?

Slide 25

Special Polynomials

Is the polynomial a difference of squares?

a2 – b2 = (a – b)(a + b)

Is the trinomial a perfect-square trinomial?

a2 + 2ab + b2 = (a + b)2

a2 – 2ab + b2 = (a – b)2

Slide 26

Ex: Factor x2 – 4

Notice the terms are both perfect squares

x2 = (x)2

4 = (2)2

 x2 – 4 = (x)2 – (2)2

a2 – b2

and we have a difference

= (x – 2)(x + 2)

 difference of squares

= (a – b)(a + b)

factors as

Slide 27

Ex: Factor 9p2 – 16

Notice the terms are both perfect squares

9p2 = (3p)2

16 = (4)2

 9a2 – 16 = (3p)2 – (4)2

a2 – b2

and we have a difference

= (3p – 4)(3p + 4)

 difference of squares

= (a – b)(a + b)

factors as

Slide 28

Ex: Factor y6 – 25

Notice the terms are both perfect squares

y6 = (y3)2

25 = (5)2

 y6 – 25 = (y3)2 – (5)2

a2 – b2

and we have a difference

= (y3 – 5)(y3 + 5)

 difference of squares

= (a – b)(a + b)

factors as

Slide 29

Ex: Factor 81 – x2y2

Notice the terms are both perfect squares

81 = (9)2

x2y2 = (xy)2

 81 – x2y2 = (9)2 – (xy)2

a2 – b2

and we have a difference

= (9 – xy)(9 + xy)

 difference of squares

= (a – b)(a + b)

factors as

Slide 30

Your Turn to Try a Few

Slide 31

To factor a polynomial completely, ask

Do the terms have a common factor (GCF)?

Does the polynomial have four terms?

Is the polynomial a special one?

Is the polynomial a difference of squares?

a2 – b2

Is the polynomial a sum/difference of cubes?