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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $8x^2 - 6$

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Factor out a monomial

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Q. Factor out the greatest common factor. If the greatest common factor is

1

, just retype the polynomial.

\newline

8x^2 - 6

Find GCF: We need to find the greatest common factor (GCF) of the terms $8x^2$ and $-6$ . The GCF is the largest factor that divides both terms. $\newline$ For $8x^2$ , the prime factors are $2 \times 2 \times 2 \times x \times x$ . $\newline$ For $-6$ , the prime factors are $-1 \times 2 \times 3$ . $\newline$ The common factor between these two is just $2$ .
Identify Prime Factors: Now that we have identified the GCF as $2$ , we can factor it out from the polynomial. $\newline$ $8x^2$ can be written as $2 \times 4x^2$ . $\newline$ $-6$ can be written as $2 \times -3$ . $\newline$ So, the polynomial $8x^2 - 6$ can be factored as $2(4x^2 - 3)$ .

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