Check if (x + 2) and (x – 4) are the sides of a rectangle whose area

1.	Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem.
Answer» Let P(x) = x² – 2x² – 8 By using factor theorem,(x + 2) is a factor of P(x), if P (-2) = 0 P(-2) = (-2)² – 2(-2) – 8 = 4 + 4 – 8 = 0 And also (x - 4) is a factor of P(x), if P(4) = 0 p(4) = 4² – 2(4) – 8 = 16 – 8 – 8 = 0 ∴ (x + 2), (x – 4) are the sides of a rectangle whose area is x² – 2x – 8.

Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem.

Answer»

Let P(x) = x² – 2x² – 8

By using factor theorem,(x + 2) is a factor of P(x), if P (-2) = 0

P(-2) = (-2)² – 2(-2) – 8 = 4 + 4 – 8 = 0

And also (x - 4) is a factor of P(x), if P(4) = 0

p(4) = 4² – 2(4) – 8 = 16 – 8 – 8 = 0

∴ (x + 2), (x – 4) are the sides of a rectangle whose area is x² – 2x – 8.