Question

factor out the gcf $10x^{9}+15x^{8}+30x^{7}$.

Explanation:

Step1: Find GCF of coefficients

Coefficients: 10, 15, 30.
Factors of 10: 1, 2, 5, 10
Factors of 15: 1, 3, 5, 15
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
GCF(10,15,30) = 5.

Step2: Find GCF of variables

Variables: \(x^9\), \(x^8\), \(x^7\).
The lowest power of \(x\) is \(x^7\).

Step3: Factor out GCF

GCF is \(5x^7\).
Divide each term by \(5x^7\):
\(10x^9 \div 5x^7 = 2x^2\)
\(15x^8 \div 5x^7 = 3x\)
\(30x^7 \div 5x^7 = 6\)
So, \(10x^9 + 15x^8 + 30x^7 = 5x^7(2x^2 + 3x + 6)\).

Answer:

\(5x^7(2x^2 + 3x + 6)\)