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Factor out the GCF from the polynomial.

\[
\begin{array}{l}
28x^7 + 16x^4 - 20x^6 + 12
\end{array}
\]

\[
28x^7 + 16x^4 - 20x^6 + 12 = \square
\]

(Type your answer in factored form.)

Answer :

To factor out the greatest common factor (GCF) from the polynomial [tex]\( 28x^7 + 16x^4 - 20x^6 + 12 \)[/tex], follow these steps:

1. Identify the GCF of the coefficients:

- First, look at the coefficients: 28, 16, -20, and 12.
- Find the largest number that can divide all these coefficients evenly.
- The GCF of 28, 16, -20, and 12 is 4.

2. Factor the GCF out of the entire polynomial:

- Divide each term of the polynomial by the GCF (4):
- [tex]\( 28x^7 \div 4 = 7x^7 \)[/tex]
- [tex]\( -20x^6 \div 4 = -5x^6 \)[/tex]
- [tex]\( 16x^4 \div 4 = 4x^4 \)[/tex]
- [tex]\( 12 \div 4 = 3 \)[/tex]

3. Write the polynomial in its factored form:

- Combine the results from the division above:
- The polynomial becomes: [tex]\( 4(7x^7 - 5x^6 + 4x^4 + 3) \)[/tex]

Therefore, the polynomial [tex]\( 28x^7 + 16x^4 - 20x^6 + 12 \)[/tex] factored by its GCF is [tex]\( 4(7x^7 - 5x^6 + 4x^4 + 3) \)[/tex].

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