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Chapter 0: Problem 4

Factor out the greatest common factor. $$4 x^{2}-8 x$$

Short Answer

Expert verified
The factored form of the polynomial \(4x^2 - 8x\) with the GCF factored out is \(4x(x - 2)\).

Step by step solution

01

Identify the GCF

The GCF of the given polynomial is determined by taking the largest common factor of the coefficients and the smallest power of x. The GCF between 4 and 8 is 4. For \(x^2\) and x, the smallest power of x is 1 (from x). Hence, the GCF of the polynomial is \(4x\).
02

Factor out the GCF

Remove \(4x\) from each term in the polynomial \(4x^2 - 8x\) by dividing each term by \(4x\). This gives \(x - 2\).
03

Write the factored form of the polynomial

The factored form of the polynomial is obtained by multiplying the GCF and the result from step 2. This gives \(4x(x - 2)\).

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