Answer:
[tex]\boxed {\boxed {\sf (5g^2+2)(2g-5)}}[/tex]
Step-by-step explanation:
We are given the expression:
[tex]10g^3-25g^2+4g-10[/tex]
There are no common factors between the four numbers, however the first two have a common factor and the last two do too. Therefore, we can factor by grouping.
Group the first two terms and the last two.
[tex](10g^3-25g^2)+(4g-10)[/tex]
Find the greatest common factor (GCF) of the first group. It is 5g². Factor it out of the first group. You can do this by dividing both terms by the GCF.
- 10g³/5g²= 2g
- -25g²/5g² = -5
[tex]5g^2 (2g-5) + (4g-10)[/tex]
Repeat with the second group. The GCF is 2.
[tex]5g^2 (2g-5) + 2(2g-5)[/tex]
There is another GCF: 2g-5. We can factor this out of both terms.
- 5g²(2g-5)/2g-5= 5g²
- 2(2g-5)/ 2g-5=2
[tex](5g^2+2)(2g-5)[/tex]
This cannot be factored further, so it is the answer.
