help please. 2tsquared+ 5t -3 = 0. factor out?

Answer 1

In this case you need to consider factors of 3 and factors of 2 that when comined subtract to 5. The reason we think of subtraction is that the 3 is negative which tells us the signs are different.

2t^2 +5t - 3, since 2 and 3 are both prime we have no other choices than 2, 1 and 3, 1 and factor pairs.

(2t -1)(t+3)

If you multiply the inner and outer terms:
2t(3) = 6t
-1(t) = -1t
6t + -1t = 5t, so that is correctly factored.

Answer 2

First thing you need to do is set it up. 2 has no factors except 2 and 1, so you know the answer has to have the form

(2t +/- )(t +/- ) = 0

3 has no factors except 3 and 1. Now the question becomes what combination of 2, 1, +/-3, and +/-1 will get you -5.

You know that either the 3 or the 1 has to be negative while the other is positive, since their product needs to be -3.

Our possible cominations, then, are
2x1 - 1x3 = -1
-2x1 + 1x3 = 1
-2x3 + 1x1 -5
2x3 - 1x1 = 5

The last one provides us with the desired result, so this is the comination we want to use. Plugging these values into our earlier set up, we get

(2t - 1)(t +3) = 0

The zero product property tells us that 2t-1=0 or t+3=0

Solving for t in both of these gives us t=1/2 or t=-3

Answer 3

2t^2 + 5t - 3

think about what multiplies to make -3
1 * -3 or -1 * 3
so your choices would be
(2t +1)(t - 3) or (2t - 1)(t +3)
which works?