Question
Factor the following expression. \( z^{2}-1.6 z+0.64 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( z^{2}-1.6 z+0.64=\square \) (Simplify your answer. Use integers or decimals for any numbers in your expression.) B. The given polynomial is not factorable.
Ask by Chandler French. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( z^{2}-1.6z+0.64 = \frac{1}{25}(5z-4)^2 \)
Solution
Factor the expression \( z^{2}-1.6z+0.64 \).
Factor the expression by following steps:
- step0: Factor:
\(z^{2}-1.6z+0.64\)
- step1: Convert the expressions:
\(z^{2}-\frac{8}{5}z+\frac{16}{25}\)
- step2: Factor the expression:
\(\frac{1}{25}\left(5z-4\right)^{2}\)
The expression \( z^{2}-1.6z+0.64 \) can be factored as \( \frac{1}{25}(5z-4)^{2} \).
Therefore, the correct choice is:
A. \( z^{2}-1.6z+0.64=\frac{1}{25}(5z-4)^{2} \)
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Simplify this solution Bonus Knowledge
To factor the expression \( z^{2}-1.6 z+0.64 \), we look for two numbers that multiply to \( 0.64 \) (the constant term) and add up to \( -1.6 \) (the coefficient of the linear term). The factors of \( 0.64 \) that meet this requirement are \( -0.8 \) and \( -0.8 \). Therefore, we can write the expression as: \[ z^{2} - 1.6z + 0.64 = (z - 0.8)(z - 0.8) \text{ or } (z - 0.8)^{2} \] So, the answer is: A. \( z^{2}-1.6 z+0.64=(z-0.8)^{2} \)
