Question

Fractronice the following
$y 2 - 16y - 80$
a
$x2 + bx + c$
​

Answer 1

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "y2" was replaced by "y^2".

STEP

1

:

Trying to factor by splitting the middle term

1.1 Factoring y2+16y-80

The first term is, y2 its coefficient is 1 .

The middle term is, +16y its coefficient is 16 .

The last term, "the constant", is -80

Step-1 : Multiply the coefficient of the first term by the constant 1 • -80 = -80

Step-2 : Find two factors of -80 whose sum equals the coefficient of the middle term, which is 16 .

-80 + 1 = -79

-40 + 2 = -38

-20 + 4 = -16

-16 + 5 = -11

-10 + 8 = -2

-8 + 10 = 2

-5 + 16 = 11

-4 + 20 = 16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 20

y2 - 4y + 20y - 80

Step-4 : Add up the first 2 terms, pulling out like factors :

y • (y-4)

Add up the last 2 terms, pulling out common factors :

20 • (y-4)

Step-5 : Add up the four terms of step 4 :

(y+20) • (y-4)

Which is the desired factorization

Final result :

(y + 20) • (y - 4)