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Question
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
Solution
Let the area of a rectangle be p(x)
p(x) = x2 – 2x – 8
When x + 2 is the side of the rectangle
p(–2) = (–2)2 – 2(–2) – 8
= 4 + 4 – 8
= 8 – 8
= 0
When x – 4 is the side of the rectangle.
P(4) = (4)2 – 2(4) – 8
= 16 – 8 – 8
= 16 – 16
= 0
(x + 2) and (x – 4) are the sides of a rectangle
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