A gardener plans to convert a piece of land into a square garden

MATHEMATICS · Multi-part · GCSE · Mathematics · Algebra · Algebra

Problem

A gardener plans to convert a piece of land into a square garden. The area of the plot, expressed in square metres, is given by the polynomial

2x^{2}-16x+32

. Answer the following: (i) Show that the polynomial representing the area can be rewritten in the form

2(x-r)^{2}

for some real number

r

. (ii) Determine the value of

r

and hence write an expression for the length of one side of the square garden in terms of

x

. (iii) If the actual area of the garden is

98\text{ m}^{2}

, calculate the length of each side of the garden.