Question

How would you rewrite the expression 30a3+40a5 by factoring out the GCF?(1 point) Responses 10a3(3a+4a2) 10 a superscript 3 baseline left parenthesis 3 a plus 4 a superscript 2 baseline right parenthesis 10a3(3+4a2) 10 a superscript 3 baseline left parenthesis 3 plus 4 a superscript 2 baseline right parenthesis 10a2(3+4a2) 10 a superscript 2 baseline left parenthesis 3 plus 4 a superscript 2 baseline right parenthesis 5a3(6+8a2)

Answer 1

To factor out the greatest common factor (GCF) from the expression \(30a^3 + 40a^5\), we first determine the GCF of the coefficients (30 and 40) and the variable part \(a^3\).

1. The GCF of 30 and 40 is 10.
2. The GCF of \(a^3\) and \(a^5\) is \(a^3\).

Thus, the GCF of the entire expression is \(10a^3\).

Now, we can factor out \(10a^3\) from the expression:

\[
30a^3 + 40a^5 = 10a^3(3 + 4a^2)
\]

So the correct rewritten expression is:

**10 a³(3 + 4 a²)**.