Solve by completing the square. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION. \[ r^{2}-5 r=1 \]

Simplify each expression. Assume that the variables represent any real numbers. Use the absolute value button only when necessary. (a) \( \sqrt{y^{16}}=\square \) (b) \( \sqrt{x^{18}}=\square \)

Simplify the expression. Assume that the variable is unrestricted and use absolute value symbols when necessary. \[ \sqrt{y^{2}-2 y+1} \]

Multiply. \[ \begin{array}{l}(\sqrt{2}+7 \sqrt{5})(6 \sqrt{5}+\sqrt{2}) \\ \text { Simplify your answer as much as possible. }\end{array} \] II .

Faktoriseer in Afrikaans \( 4(m-2 n)^{2}-25 \)

Use the Factor Theorem to determine whether \( x-2 \) is a factor of \( P(x)=x^{3}-3 x^{2}-4 x+ \) Specifically, evaluate \( P \) at the proper value, and then determine whether \( x-2 \) is a factor. \( \begin{array}{l}P(\square)=\square \\ x-2 \text { is a factor of } P(x) \\ x-2 \text { is not a factor of } P(x)\end{array} \)