Real confused still!

Question

12c^2 13c-35

these have to be in the order ( ) ( - )

Please explain what to do thank you

Answer 1

12c^2+13c-35 to factor into ( c+ )( c- )

We are looking for a specific combination of the factors of 12 and the factors of 35.

Factors of 12:

1x12

2x6

3x4

Factors of 35:

1x35

5x7

Multiply the pairs together first...for example:

2x5=10 (the 2 is from the 2x6 factor; the 5 is from the 5x7 factor)

6x7=42 (these are the other numbers in those pairs)

*Subtract* those answers (subtract because there is a "-" in front of the 35):

42-10=32

We are looking for the answer of 13 (the middle number), and this combination failed. Keep trying combinations until you get one that works. The one that works is:

5x3=15

7x4=28

28-15=13

To figure out which one goes where, set up the parentheses:

( c+ )( c- )

To start with, the 3 and the 4 must go with the "c", since those two must multiply to 12:

(3c+ )(4c- )

This takes care of the "F" of FOIL.

For the FOIL to work (because this has to multiply back out to equal the original equation), the 3 will be multiplied by the 5...so it must go at the end (this takes care of the "O" of FOIL):

(3c+ )(4c-5)

There's only one place for the 7 to go:

(3c+7)(4c-5)

To be sure everything is ok, be sure to check the "I" -- inside -- part of FOIL. 7x4 is 28, and it is positive...just like the 13 is positive in the original equations. (If it had been negative, switch the + and - signs.)

Hope that helps!