Question

factor out the greatest common factor.
$8x^8 + 8x^4 + 8x$
$?x(x^7 + x^{\square} + 1)$

Explanation:

Step1: Analyze the original expression

The original expression is \(8x^8 + 8x^4 + 8x\). We need to factor out the greatest common factor (GCF) from each term.
First, look at the coefficients: 8, 8, and 8. The GCF of 8, 8, 8 is 8.
Then, look at the variable part: \(x^8\), \(x^4\), and \(x\). The GCF of the variables is \(x\) (since the lowest power of \(x\) among the terms is 1).
So the GCF of the entire expression is \(8x\).

Step2: Factor out the GCF

When we factor out \(8x\) from each term:

• For \(8x^8\), dividing by \(8x\) gives \(\frac{8x^8}{8x}=x^7\)
• For \(8x^4\), dividing by \(8x\) gives \(\frac{8x^4}{8x}=x^3\)
• For \(8x\), dividing by \(8x\) gives \(\frac{8x}{8x}=1\)

So the factored form is \(8x(x^7 + x^3 + 1)\). Comparing with the given form \([?]x(x^7 + x^{\square}+ 1)\), we can see that the value of \([?]\) is 8 and the value of \(\square\) is 3.

Answer:

The value of \([?]\) is 8 and the value of the square is 3. So the filled - in form is \(8x(x^7 + x^{3}+ 1)\), with \([?]=8\) and the exponent in the square is 3.