Example Question - greatest common factor
Here are examples of questions we've helped users solve.
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: \( 5r^2t^2(1 - 5r^3t^2 + 2) \)
Factorization of a Quadratic Expression
The expression given in the image is: \[ x^2 - 5x \] To factorize this expression, we need to find the greatest common factor (GCF) of the terms present in the expression. Here, the GCF of \( x^2 \) and \( -5x \) is \( x \). Now we'll factor out the GCF from each term: \[ x^2 - 5x = x(x - 5) \] The expression has been factorized into the product of \( x \) and \( (x - 5) \).
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