# How do you factor by grouping #6c^2+29c-42#?

##### 2 Answers

We are looking for factors,

and

factors,

such that

- this is because
#(mc+p)*(nc+q) = mnc^2+(mq+np)c +pq#

factors of 6

factors of (-42) # = {(6,-7),(3,-14),(2,-21),(1,-42)} and their negatives

A bit of testing combinations comes up with the pairs

and

that satisfy the requirement for the middle term

Multiply

Now we look for factor of

Because the product is negative and the sum is positive, we want the smaller number to be negative and the larger positive:

-1 252 does not add up to 29

-2 126 does not add up to 29

-3 84

-4 63

-5 is not a factor

-6 42

-7 36 does add up to 29

In

(or