Factor: g^2+3g-54 plz help?

g² + 3g - 54

It is in the quadratic form (ax² + bx + c), so find what multiplies to give c, but adds to give b. Make a list of the factors until you find the right one:

Since we want them to add to give a positive number and multiply to give a negative number, we need to have a positive number and a negative number multiplied by eachother. We need to have the negative number on the left so as to achieve a positive addition

-1 × 54
-2 × 27
-3 × 18
-6 × 9 ← these add to give 3

Substitute them into the unknown brackets:

( g _ __ )( g _ __ )

( g - 6 )( g + 9 )

( g + 9 ) ( g - 6 )

g^2 + 9g - 6g -54
g(g+9) - 6(g+9)
= (g-6)(g+9)

(g + 9) (g - 6) = 0

g^2 + 3g - 54
= g^2 + 9g - 6g - 54
= (g^2 + 9g) - (6g + 54)
= g(g + 9) - 6(g + 9)
= (g + 9)(g - 6)

g^2+3g-54

(x+9)(x-6)