# How do you factor #18c^2-3c-10#?

##### 1 Answer

#### Answer:

#### Explanation:

We can use an AC method:

Look for a pair of factors of

The pair

Then use this pair to split the middle term and factor by grouping:

#18c^2-3c-10#

#=18c^2+12c-15c-10#

#=(18c^2+12c)-(15c+10)#

#=6c(3c+2)-5(3c+2)#

#=(6c-5)(3c+2)#

**Alternative method**

Alternatively, we can find this factorisation by completing the square then using the difference of squares identity:

#a^2-b^2 = (a-b)(a+b)#

with

To make the arithmetic easier, first multiply by

#8(18c^2-3c-10)#

#=144c^2-24c-80#

#=(12c^2)-2(12c)-80#

#=(12c-1)^2-1-80#

#=(12c-1)^2-81#

#=(12c-1)^2-9^2#

#=((12c-1)-9)((12c-1)+9)#

#=(12c-10)(12c+8)#

#=(2(6c-5))(4(3c+2))#

#=8(6c-5)(3c+2)#

So dividing both ends by

#18c^2-3c-10 = (6c-5)(3c+2)#

Why did I multiply by

If I multiplied by