# How do you use synthetic division to find factors for #x^3 + 2x^2 - 5x - 6#?

##### 1 Answer

Noting that

Complete factors:

#### Explanation:

**Part 1: The initial Factor**

If

then setting the negative terms on one side and the positive terms on the other:

then testing a few values:

#{: (x,color(white)("XX"),x^3+2x^2,color(white)("XX"),5x+6), (0,color(white)("XX"),0,color(white)("XX"),6), (1,color(white)("XX"),3,color(white)("XX"),11), (2,color(white)("XX"),16,color(white)("XX"),16) :}#

So if#x=2# then#x^3+2x^2-5x-6 =0#

#rarr (x-2)# is a factor of#x^3+2x^2-5x-6#

**Part 2: Use of synthetic division**

So

**Part 3: Factoring the remaining quadratic**

By observation or using the quadratic formula we can factor:

**Part 4: Summarize results**