Question

6.1 greatest common factor: probl
(1 point)

factor out the greatest common factor:

15x²y⁴ + 10xy + 20x =

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Explanation:

Step1: Find the GCF of coefficients

The coefficients are \(15\), \(10\), and \(20\).
The factors of \(15\) are \(1,3,5,15\).
The factors of \(10\) are \(1,2,5,10\).
The factors of \(20\) are \(1,2,4,5,10,20\).
The greatest common factor of \(15\), \(10\), and \(20\) is \(5\).

Step2: Find the GCF of variables

For the variable \(x\):
In \(15x^{2}y^{4}\), the power of \(x\) is \(2\).
In \(10xy\), the power of \(x\) is \(1\).
In \(20x\), the power of \(x\) is \(1\).
The lowest power of \(x\) is \(1\).
There is no \(y\) in the term \(20x\), so the GCF for \(y\) - terms is \(y^{0}=1\) (since we need a factor common to all terms).
The GCF of the variables is \(x\).

Step3: Factor out the GCF

Factor out \(5x\) from each term:

$$
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$$

Answer:

\(5x(3xy^{4}+2y + 4)\)