How would you rewrite the expression 30a3+40a5

Question

by factoring out the GCF?(1 point)
Responses

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)
5 a superscript 3 baseline left parenthesis 6 plus 8 a superscript 2 baseline right parenthesis

10a3(3a+4a2)

Answer 1

To factor the expression \(30a^3 + 40a^5\), we first need to identify the greatest common factor (GCF) of the coefficients and the variable terms.

1. The coefficients are 30 and 40. The GCF of 30 and 40 is 10.
2. The variable terms are \(a^3\) and \(a^5\). The GCF for \(a^3\) and \(a^5\) is \(a^3\).

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

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

Therefore, the correct response is:

10 a superscript 3 baseline left parenthesis 3 plus 4 a superscript 2 baseline right parenthesis.