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Let's address the two parts of the question:

### Part (a)
We are asked to rewrite the quadratic expression \( x^2 - 10x + 35 \) in the form \( (x - p)^2 + q \).

This involves **completing the square**. Let's work through it:

Given: 
\[
x^2 - 10x + 35
\]

Step 1: Take the coefficient of \(x\), divide it by 2, and square it. The coefficient of \(x\) is -10, so:

\[
\left(\frac{-10}{2}\right)^2 = 25
\]

Step 2: Rewrite the quadratic by adding and subtracting 25:

\[
x^2 - 10x + 25 - 25 + 35 = (x - 5)^2 + 10
\]

Thus

a) Write x^2 - 10x + 35 in the form (x - p)^2 + q. b) Hence, or otherwise, find the maximum value of 1 / (x^2 - 10x + 35)^2.

Learn how to complete the square for the quadratic expression x^2 - 10x + 35 and find the maximum value of the rational function 1 / (x^2 - 10x + 35)^2. This step-by-step guide explains key algebraic techniques for Grades 10-12 students.

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