Slip and slide trinomials (x^2+bx+c)

Question

What trinomial do you get when you multiply a times c? Type the answer in the form: x^2+bx+c

the trinomial I am trying to solve is: 8m^2+6m-5

Answer 1

What you are trying to do is FACTOR the trinomial.

The slip & slide method works this way (in your problem.

"Slide" the 8 to the right and multiply it by the constant term to get: m² +6m -40.

Factor this easily as (m+10)(m-4).

Divide the roots by the 8 you started with: (m+10/8)(m-4/8), i.e. (4m+5)(2m+1).

To understand why this works; start with Ax² + Bx + C = 0

Substitute u=x/A to get: u²/A + Bu/A + C = 0

Multiply by A: u² + Bu + AC = 0

Now apply the quadratic formula to get the roots.

The get x by dividing u by A.