Factoring Grouping Polynomials

[igor_iv837]

Hi, can anybody help me with the factoring grouping polynomials ? i get stuck on negative or positive signs, I don't know how they get negative or positive

1. y(a+2) + 7(a+2) = (a+2) (y+7) ....how you know its y+7???

2. 3r(a-b) + s(a-b) = (a-b) (3r+s) ....how you know its 3r+s?? why not 3r-s?

3. t(m-7) + 7(7-m) = (m-7) (t-7)...how you know its t-7???

4. 2y(4a-b) - (b-4a) = (4a-b) (2y+1)...how you know its 2y+1???? why not -1?? its a negative sign, why it became positive??


Anybody Knows?????? Ill be gratefull for ur answer

 

[Loren]

>y(a+2) + 7(a+2) = (a+2) (y+7) ....how you know its y+7???

If the problem were to factor ym + 7m how do you know it's m(y+7)?

>2y(4a-b) - (b-4a) = (4a-b) (2y+1)...how you know its 2y+1???? why not -1?? its a negative sign, why it became positive??

4a-b = -(b-4a) and b-4a = -(4a-b). etc.

 

[igor_iv837]

I Don't get it....Does anybody Else Knows?

 

[Loren]

The answers to your questions are contained in my previous response(s). Go back and read them carefully and put your brain to work analyzing and applying my responses (questions) to your problems.

 

[mmm4444bot]

1. y(a+2) + 7(a+2) = (a+2) (y+7) ....how you know its y+7???

Because the given exercise contains a + sign (as shown above in red).

2. 3r(a-b) + s(a-b) = (a-b) (3r+s) ....how you know its 3r+s?? why not 3r-s?

Because the given exercise contains a + sign (as shown above in red).

3. t(m-7) + 7(7-m) = (m-7) (t-7)...how you know its t-7???

Because we begin by recognizing from the given exercise that the factor (m-7) is not the same as the factor (7-m), and we ALSO recognize that we can make them the same by factoring out a -1 from (7-m).

-(m-7) = (7-m)

Factoring out the -1 changes the original + sign to a - sign (as shown below in blue).

t(m-7) + 7(7-m) becomes t(m-7) - 7(m-7)

4. 2y(4a-b) - (b-4a) = (4a-b) (2y+1)...how you know its 2y+1???? why not -1?? its a negative sign, why it became positive??

Same reason as #3 above; the factors (4a-b) and (b-4a) are not the same. We need for them to be the same before we can factor the entire expression by grouping.

(b-4a) = -(4a-b)

This is where the - sign comes from.

2y(4a-b) - (4a-b)

Cheers!

~ Mark