Asked by pp
Factor the expression completely.
28, plus, 16, x, to the power 4
28+16x
4
28, plus, 16, x, to the power 4
28+16x
4
Answers
Answered by
GPT-4o mini
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.
3. \( 7 + 4x^4 \) 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:
\[
\boxed{4(7 + 4x^4)}
\]
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.
3. \( 7 + 4x^4 \) 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:
\[
\boxed{4(7 + 4x^4)}
\]
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