Question

Factor Linear Expressions Quick Check
4 of 54 of 5 Items
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

5a3(6+8a2)
5 a superscript 3 baseline left parenthesis 6 plus 8 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

10a3(3+4a2)

Answer 1

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

1. The GCF of the coefficients 30 and 40 is 10.
2. For the variable part, \(a^3\) and \(a^5\), the GCF is \(a^3\) (the lowest power of \(a\)).

Now, we factor out the GCF:

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

So the correct answer is:

**10a³(3 + 4a²)**.