Trinomials and Factoring

[halojono91]

I have been working away at some questions i can most of them but they just threw me a curve ball in my book on a couple different sections

First series i have problems with is to "expand and simplify each expression":

5(3y - 2)(y+7)

Second series are factoring with:

5n(to the power of 2) - 25n - 70

any support is greatly appreciated, thanks

 

[mmm4444bot]

5(3y - 2)(y+7)

The instruction "expand" means to multiply out everything and combine like terms.

You could use the FOIL algorithm to first multiply (3y - 2) times (y + 7).

Then multiply the resulting polynomial by 5, to finish.



5n^2 - 25n - 70

You could factor this polynomial by using a method called "Factor by Grouping".

However, there's a shortcut.

Do you recognize that each of the coefficients is a multiple of five ? In other words, any Integer that ends with the digit 0 or the digit 5 can be evenly divided by 5.

Therefore, start by factoring out 5. Then, factor the remaining part in the usual way.

I welcome specific questions; please, show whatever work that you can.

 

[halojono91]

For question 5(3y - 2)(y+7) I got
5(3y)x(y) +(3y)x7-2x(y)-2x7
5 x 3y^2+19y-2y-14
5 x 3y^2+19y-14
15y^2 + 95y - 70

is this correct? Thanks for responding so quickly this really helps me.

I am working on
5n(to the power of 2) - 25n - 70 right now will post answer soon.

 

[halojono91]

For 5n^2 - 25n - 70 I got these results...

n^2 - 5n - 14

(factoring)
1,-14
-1,14
2,-7
-2,7

(-2)+7=5

(n-2)(n+7)

 

[Deleted member 4993]

For 5n^2 - 25n - 70 I got these results...

5(n^2 - 5n - 14)

(factoring)
1,-14
-1,14
2,-7
-2,7

(-2)+7=5

5(n + 2)(n - 7)

 

[mmm4444bot]

For question 5(3y - 2)(y+7) I got
5(3y)x(y) +(3y)x7-2x(y)-2x7
5 x 3y^2+19y-2y-14
5 x 3y^2+19y-14
15y^2 + 95y - 70

is this correct?

The end result is correct, but your typing lacks a bunch of grouping symbols.

Also, for showing multiplication, please use an asterisk (or parentheses) instead of the letter x. In algebra, the letter x has a different meaning.

5[3y*y + 3y*7 - 2*y - 2*7]

OR

5[(3y)(y) + (3y)(7) + (-2)(y) + (-2)(7)]

et cetera …