Factoring and the Factor Theorem

Factoring and the Factor Theorem

Hints to determine each type

Difference of Perfect Squares

Simple Trinomial

Complex Trinomial

Factor by Grouping

Two Terms Three Terms Four Terms

Examine the Number of Terms

Each term is a perfect square separated by a “-” sign

Is of the formx2 +bx +c

Is of the formax2 +bx +c, wherea≠0.

Always look for a Greatest Common Factor

Group in pairs of terms

Should be able to factor twice

Finally, check each factor to see if it can be factored further.

Sum/Diff of Cubes

Sum and Difference of Cubes

Sum of cubes: x3+y3= (x+y)(x2-xy+y2)

Difference of cubes: x3-y3= (x-y)

(x2+xy+y2)Eg. x3-27

Eg. 8x6+125y3

= (x-3)(x2+3x+9)

=(2x2 +5y)(4x4-10x2y+25y2 )

Factor TheoremA polynomial P(x) has x – b as a

factor if and only if P(b) = 0.

37234521

2

23

xxxxxx

Factor: P(x) = 2x3 – 5x2 – 4x + 3Since P(-1) = 0, therefore x + 1 is a factor.

Try factors of +/-3 and +/- 3/2 to get

the root

Repeat the process to find other factors or use long division to find remaining factors

P(x) = (x+1)(2x-1)(x-3)

Factor Completely

1. x2 – 3x - 182. y2 -6y + 363. 2x2 +4x + 64. x2 – xy – x +y5. t3 + 646. x3 - 17. 16a4 - 256b12

8. x3 – x2 – 16x + 16 9. x3 + 5x2 – 2x - 24