Question

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

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(3+4a2)

Answer 1

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

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

Combining these, the GCF of \(30a^3 + 40a^5\) is \(10a^3\).

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

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

Thus, the correct response is:

**10a³(3 + 4a²)**.