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Factor the expression completely.

28, plus, 16, x, to the power 4
28+16x
4

1 answer

To factor the expression \( 28 + 16x^4 \) completely, we can start by factoring out the greatest common factor (GCF) from both terms.

  1. Identify the GCF of the coefficients 28 and 16:

    • The GCF of 28 and 16 is 4.

  2. Factor out the GCF: \[ 28 + 16x^4 = 4(7 + 4x^4) \]

Now we have \( 4(7 + 4x^4) \). Next, we can check if the expression \( 7 + 4x^4 \) can be factored further.

  1. \( 7 + 4x^4 \) can be thought of and recognized as a sum of squares, but it does not factor nicely over the integers or reals.

Thus, the completely factored form of the expression is: \[ \boxed{4(7 + 4x^4)} \]