Factor each of the following polynomials completely. -3s^2 - 10s + 8?

I'd start this one by factoring out a negative one.

-1 (3 s^2 + 10s - 8)

-1 (3s - 2)(s + 4)

First factor out -1 to make it easier to deal with the factorization process. Then factor the resulting polynomial.

-(3s² +10s - 8) = -(3s - 2)(s + 4).

Now, since we factored out -1 to make the polynomial easier to factor, we can put it back again by multiplying either one of the factors by it. Apparently some of the other responders forgot this little detail. We can also switch the order of the terms and produce the same result.

-(3s - 2)(s + 4) = (-3s + 2)(s + 4) = (2 - 3s)(s + 4)

-(3s - 2)(s + 4) = (3s - 2)(-s - 4)

In the last equation, there is no point in switching the order of the terms of the second factor on the right side, because both of them are negative anyway. We can check to see if each of these expressions are equal simply by performing the indicated operations.

(2 - 3s)(s + 4) = (3s - 2)(-s - 4)

2s + 8 - 3s² - 12s = -3s² -12s + 2s + 8

-3s² - 10s + 8 = -3s² - 10s + 8

So all of the above expressions are equivalent to each other.

(-3s-4)(s-2)

Side Note : Factoring out the -1 is not necessary, nor is it good math. If so you would be stuck forever...... example

(-1)(-1)(-1)(-1)(-3s-4)(s-2)

And so on and on and on.....you could also factor out one....

(1)(1)(1)(-1)(-1)(-3s-4)(s-2)

Factoring out 1 or -1 is not needed to "completely" factor anything....

However you can do this if it makes it simpler for you....

if the trinomial can be factorised, then the equation with one hand side is the trinomial and the other is 0 must have at least one root:

-3s2-10s+8=0 (1)

delta' = (-10/2)^2 - (-3)*8 = 25 + 24 = 49 (>0) (so we have 2 roots to this equation)

sqrt(delta') = 7

s1 = (-(-10/2) + 7)/-3 = 12/-3 = -4

s2 = (-(-10/2) - 7)/-3 = 2/3

so, we can rewrite (or retype??lol) (1) as (s + 4)(s - 2/3) =0

we finally have the trinomial factorised out: (s + 4)(s - 2/3).

take out a minus to get (3s^2+10s-8)

then factorise to get -(3s-2)(s+4)

-3s^2-10s+8

= -(3s^2+10s-8)

= -(3s^2+12s-2s-8)

= -{3s(s+4)-2(s+4)}

= -(s+4)(3s-2)

-(3s-2)(s+4)

The trinomial seems to be prime.

No numbers will mulitply to give you -24 and add to give you -10.