Question
Factor.
x squared plus 32 x plus 256
Question content area bottom
Part 1
x squared plus 32 x plus 256equals
enter your response here (Factor completely.)
x squared plus 32 x plus 256
Question content area bottom
Part 1
x squared plus 32 x plus 256equals
enter your response here (Factor completely.)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To factor the quadratic expression \( x^2 + 32x + 256 \), we can look for two numbers that multiply to the constant term (256) and add to the linear coefficient (32).
In this case, the two numbers are 16 and 16 because:
- \( 16 \times 16 = 256 \)
- \( 16 + 16 = 32 \)
Thus, we can write the expression as:
\[
x^2 + 32x + 256 = (x + 16)(x + 16)
\]
This can also be expressed as:
\[
(x + 16)^2
\]
Therefore, the factored form of \( x^2 + 32x + 256 \) is:
\[
(x + 16)^2
\]
In this case, the two numbers are 16 and 16 because:
- \( 16 \times 16 = 256 \)
- \( 16 + 16 = 32 \)
Thus, we can write the expression as:
\[
x^2 + 32x + 256 = (x + 16)(x + 16)
\]
This can also be expressed as:
\[
(x + 16)^2
\]
Therefore, the factored form of \( x^2 + 32x + 256 \) is:
\[
(x + 16)^2
\]
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