Question
Which expression is the result of factoring the expression below by taking out its greatest common factor?
10x^2+50x=\,?
10x^2+50x=\,?
Answers
GPT-4o mini
To factor the expression \(10x^2 + 50x\) by taking out its greatest common factor (GCF), we first need to identify the GCF of the coefficients and the variable parts.
1. The coefficients of the terms are 10 and 50. The GCF of 10 and 50 is 10.
2. Both terms also have the variable \(x\). The smallest power of \(x\) present in the terms is \(x^1\).
Thus, the GCF of the entire expression is \(10x\).
Now, we can factor out \(10x\) from the expression:
\[
10x^2 + 50x = 10x(x) + 10x(5) = 10x(x + 5)
\]
So, the expression factored by taking out its greatest common factor is:
\[
10x(x + 5)
\]
1. The coefficients of the terms are 10 and 50. The GCF of 10 and 50 is 10.
2. Both terms also have the variable \(x\). The smallest power of \(x\) present in the terms is \(x^1\).
Thus, the GCF of the entire expression is \(10x\).
Now, we can factor out \(10x\) from the expression:
\[
10x^2 + 50x = 10x(x) + 10x(5) = 10x(x + 5)
\]
So, the expression factored by taking out its greatest common factor is:
\[
10x(x + 5)
\]