Factorization of a Polynomial Expression
The expression given in the image is:
\( 5r^3t^2 - 25r^5t^4 + 10r^2t^2 \)
To factorize this expression, we should look for a common factor in each term. You can see that each term contains at least one factor of \( r \), \( t \), and the number \( 5 \).
The greatest common factor (GCF) that can be factored out of each term is:
\( 5r^2t^2 \)
When we factor \( 5r^2t^2 \) out of each term in the expression, we get:
\( 5r^2t^2(r - 5r^3t^2 + 2) \)
This simplifies to:
\( 5r^2t^2(1 - 5r^2t^2 + 2) \)
Which is choice (C) from the options shown in the image:
\( 5r^2t^2(1 - 5r^3t^2 + 2) \)
