Any algebra helpers out there to help a mom explain an algebra problem to 16 yr old. I'm lost too.?

Question

I know, I know..... tell her to "do your own homework" but just thought I'd ask for some reference as to how to do this so I could help her as she needs all extra pts she can get.

Factor each polynomial by grouping.

5b4 - 15b3 + 3 - b

Answer 1

let us group b4 and b3 together and b and 3(b^0) together

5b^4-15b^3-b+3
= 5b^3(b-3)-1(b-3) (take 5b^3 common in 1st 2 and -1 in second 2
=(b-3)(5b^3-1)

now 5b^3-1 cannot be factored as rational roots

Answer 2

(-5b^3 + 1)(-b + 3)

First factor the term: 5b^4 - 15b^3:

1) divide by 5

5(b^4 - 3b^3)

2) divide by b^3

5b^3(b - 3)

Now you have something like this:

5b^3(b - 3) + (3 - b)

Note that the expressions in parenthesis are almost the same, so in the expression one divide by -1:

-5b^3(3 - b) + (3 - b)

as you can see now both expressions are identical. Also the expression (3 - b) (the one in the right) has a 1 outside, that multiplies the wole expression. in other words:

-5b^3(3 - b) + 1(3 - b)

now:

(-5b^3 + 1)(3 - b)

if you want, you can multiply by -1:

(5b^3 - 1)(b - 3)

both are the same thing.

THAT'S ALL!!

Answer 3

5b^4 - 15b^3 + 3 - b
(5b^4 - 15b^3) + (3 - b) ---> Group into two binomials.
5b^3 (b - 3) - 1 (-3 + b) ---> Factor GCF out of each binomial.
(5b^3 - 1)(b - 3) ---> Since the parentheses are the same, it can be simplified like this.

= (5b^3 - 1)(b - 3)

Hope that helps! :)

Answer 4

I'm assuming you meant 5b to the fourth power - 15b squared .......

Take the first two terms and the last two terms and put them in parenthesis.

(5b^4 - 15b^3) + (3 - b)

Find the common factors.

5b^3(b - 3) - 1(b - 3)

Then take the 5b^3 and the 1 and put that in parenthesis, and take the (b - 3) and put that afterwards. This gives you:

(5b^3 - 1)(b - 3)

Answer 5

5b4-15b3-b+3
You split the terms:
(5b4-15b3) (-b+3)
Factor both groups:
5b3(b-3) -1(b-3)
Now that you have a common factor in the parentheses, you can make that one term:
(b-3)
Make the factors into another term:
(5b3-1)
Here is the result:
(b-3)(5b3-1)

Answer 6

5b^4 -15b^3 +3 -b (multiply by -1)

= -5b^4 +15^3 -3+ b

= -5b^4 + 15b^3 +b -3

= -5b^3(b -3) + (b -3)

= (b -3)(1 - 5b^3)

Answer 7

For this one,
5b^3(b-3) -1(b-3) =
(5b^3 - 1)(b-3)
for more on how to do these, have her see this
http://www.purplemath.com/modules/factquad.htm
http://www.purplemath.com/modules/solvpoly2.htm
http://www.math.unt.edu/mathlab/emathlab/factoringbygrouping.htm