Question - Factorization of a Polynomial Expression
mathalgebraic expressiongreatest common factorfactorization of polynomial expressionpolynomial factoring
Solution:
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:$$ 5r^2t^2(1 - 5r^3t^2 + 2) $$
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