Question

How do you factor the expression `-6x^2-25x-25`?

Answer 1

the factors are `-(3x+5)(2x+5)`

Explanation:

Given `-6x^2-25x-25`
common monomial factor `=-1`

so `-6x^2-25x-25=-(6x^2+25x+25)`

factors of 6: could be (3 and 2)
or (6 and 1)

factors of 25: could be (5 and 5)
or (25 and 1)

by inspection and thru practice

best numbers are 3, 2, 5, 5 which could result to 15+10=25
because `3*5+2*5=25` giving us the middle number

so

`-6x^2-25x-25=-(6x^2+25x+25)=-(3x+5)(2x+5)`

God bless ....I hope the explanation is useful.

Answer 2

y = -(3x + 5)(2x + 3)

Explanation:

I use the new systematic, non-guessing new AC Method to factor trinomials (Socratic Search)
y = -(6x^2 + 25x + 25) = -6(x + p)(x + q)
Converted trinomial: y' = - (x^2 + 25x + 150) = - (x + p')(x + q').
p' and q' have same sign since ac > 0.
Compose factor pairs of (ac = 150) --> ...(6, 25)(10, 15). This sum is 15 = b. Then p' = 10 and q' = 15.
Therefor: `p = (p')/a = 10/6 = 5/3` and `q = (q')/a = 15/6 = 5/2`.
Factored form: `y = -(x + 5/3)(x + 5/2) = -(3x + 5)(2x + 5)`