Product 48 and sum 14 what are the factors

6 and 8

6*8 = 48

6+8 = 14

Step-by-step explanation:

Let's write a system.

Let's say that the variables are x and y.

xy=48

x+y=14

Solve for one of the variables, let's say, x.

x=14-y.

Now substitute x into the 1st equation.

(14-y) y=48

Simplify.

-y²+14y=48

Make it into a quadratic equation.

-y²+14y-48=0

Make sure y²'s coefficient is one. Divide everything by - 1

y²-14y+48=0

Now factor!

What factors add up to 14 and multiply to 48.

6 and 8!

Since the 2nd term is negative, and the 3rd term is positive, the factors have to be negative.

y²-6y-8y+48=0

Group.

(y²-6y) + (-8y+48) = 0

y (y-6) - 8 (y-6) = 0

(y-8) (y-6) = 0

y-8=0

y-6=0

y=8 y=6

now let's substitute each y value into y²-14y+48=0

8²-14 (8) + 48=0

64-112+48=0

0=0. so y=8 checks out!

6²-14 (6) + 48=0

36-84+48=0

0=0 so y=6 also checks out!

Choose one y value and solve for x, in each equation:

xy=48

x+y=14

8x=48

x+8=14

x=6

x=6

It checks out!

so the factors are

x=6 y=8.