trying to figure out factoring

Question

what 2 numbers add to make 14 and multiply to make 240?

Answer 1

We need 2 different numbers.  Lets call one x and the other y.  If we have 2 unknowns, we need 2 equations.

 

so, 

x+y=14

 

(x)*(y)=240

 

solve for x or y ⇒ y=14-x ;  then substitute into the other equation

 

x(14-x)=240 ⇒ 14x-x²=240 therefore -x²+14x=240 ⇒ x²-14x+240=0  ,  using the quadratic formula; there are no Real solutions to this second degree polynomial, only complex solutions. which are 7±√(191)i. Using the positive value and plug into  y=14-x , hence,  x=7+i√(191) and y=7-i√(191)   Now check:  Note: i²=-1

7+i√(191)+7-i√(191)=14

[7+i√(191)]*[7-i√(191)]=49-7i√(191)+7i√(191)-i²*191=49+191=240

 

Answer 2

Your two numbers add to 14, so call them x and 14-x. Then, multiply them to equal 240:

 

x(14-x) = 240, or

x²-14x+240 = 0. This is where Jim B got your polynomial for you. Off you go!

Answer 3

24 and 10 have a difference of 14, so it this is part of a polynomial factoring problem be sure to check the signs in the problem. For example:

 

x² + 14x - 240 = (x + 24) (x -10)