1. ## Factoring Polynomials

Hello, Im new to factoring polynomials:

6st + 15t -10s -25

(6st + 15t) + (-10s -25) <-- Grouped polynomials

Common factors of both groups:
(6st + 15t) --> 3t
(-10s -25) --> -5

Now factor out the common factor from each group:
= 3t(2s + 5) -5(2s + 5)

The common factor is the binomials but what are the steps to factoring this out? I lost here.

tyvm

2. Originally Posted by 4lgebra
Hello, Im new to factoring polynomials:

6st + 15t -10s -25

(6st + 15t) + (-10s -25) <-- Grouped polynomials

Common factors of both groups:
(6st + 15t) --> 3t
(-10s -25) --> -5

Now factor out the common factor from each group:
= 3t(2s + 5) -5(2s + 5)

The common factor is the binomials but what are the steps to factoring this out? I lost here.

tyvm
Hi 4lgebra,

(2s + 5) is common to both terms, so (2s + 5)(3t - 5) and you're done.

Maybe, look at it this way.

3t(2s + 5) -5(2s + 5)

Let x = (2s + 5)

3tx - 5x

Factor out the x

x(3t - 5)

Replace x with (2s + 5) and we have (2s + 5)(3t - 5).

3. ## Factoring Polynomials:

Masters,

Thank you for clearing that up for me, I appreciate you taking the time to respond.

In closing... When factoring, if I have "opposites" like a - b , how is -(a - b) its opposite? My text says these values are opposites, but it assumes I already know why they are opposites.

ty bye

4. Originally Posted by 4lgebra
Masters,

Thank you for clearing that up for me, I appreciate you taking the time to respond.

In closing... When factoring, if I have "opposites" like a - b , how is -(a - b) its opposite? My text says these values are opposites, but it assumes I already know why they are opposites.

ty bye
Hi 4lgebra,

The opposite of a value is defined as being the negative of the value. In other words, the opposite of 5 is -5. The opposite of -4 is 4, and so on. If a variable represents a value, then the opposite of x would be -x. The opposite of (a - b) would be -(a - b).

If you think of a value as being a certain distance from zero on the number line, it's opposite would be the same distance from zero going in the opposite direction.

5. ## Factoring Polynomials

masters,

That is exactly the information I needed. Thank you for all your help and God bless.

4~