Question

Factor by grouping


`4r {}^(3) + 10r {}^(2) - 10r - 25`
A.

`(2r {}^(2) + 5)(2r - 5)`
B.

`(2r {}^+ 5)(2r {}^(2) - 5)`
C.

`(2r + 5)(2r {}^(2) - 5)`
D.

`(2r - 5)(2r {}^(2) - 5)`
​

Answer 1

C

Explanation:

Nice work using latex. I admire anyone who has skills with it.

It looks like this question can be grouped using to sets of brackets.

(4r^3 + 10r^2) : Pull out the common factor. 2r^2* (2r + 5)

The second set of brackets is a little bit tricker. Minus signs are not to be ignored.

(-10r - 25) : -5(2r + 5)

Now put both together,

2r^2(2r + 5) - 5(2r + 5)

Notice that there is a common factor on either side of that isolated minus sign. The common factor is 2r + 5. Use the distributive property to pull it out.

(2r + 5)(2r^2 - 5)

It looks like C will be the answer.