High School

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------------------------------------------------ Factor the GCF out of the polynomial below:

\[ 8x^6 + 12x^4 + 28x^3 \]

Answer :

The polynomial 8x⁶+12x⁴+28x³ factored with the GCF is 4x³(2x³ + 3x + 7).

To factor out the Greatest Common Factor (GCF) from the polynomial 8x⁶+12x⁴+28x³, we first need to identify the GCF of the coefficients and the variable parts.

Step 1: Identify the GCF of the coefficients

Coefficients: 8, 12, and 28

The GCF of 8, 12, and 28 is 4.

Step 2: Identify the GCF of the variable parts

Variable Parts: x⁶, x⁴, and x³

The GCF of x⁶, x⁴, and x³ is x³.

Step 3: Combine the GCFs

GCF of 8x⁶, 12x⁴, and 28x³ is 4x³.

Step 4: Factor the GCF out of the polynomial

We rewrite the polynomial by factoring out 4x³ from each term:

8x⁶ + 12x⁴ + 28x³ = 4x³(2x³) + 4x³(3x) + 4x³(7) = 4x³(2x³ + 3x + 7)

Step-by-step explanation:

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