Question

How do you factor the trinomial `b^2 - 5bf -14f^2`?

Answer 1

`(b-7f)(b+2f)`

Explanation:

Noting that
`color(white)("XXX")(color(cyan)(-7))xx(color(brown)(+2)) = (color(red)(-14))`
and
`color(white)("XXX")(color(cyan)(-7))+(color(brown)(+2))=(color(blue)(-5))`

`b^2color(blue)(-5)bfcolor(red)(-14)f^2`
`color(white)("XXX")=(bcolor(cyan)(-7)f)(bcolor(brown)(+2)f)`