Question

7. Use the remainder's theorem to find the value of m for which x + 2 is a factor of
(x + 1) ^ 7 + (2x + m) ^ 3
(a) 3
(b) 5
(c) 4
(d) 2​

Answer 1

Given :

p(x) = (x + 1)⁷ + (2x + m)³ = 0

and, x + 2 is a factor of p(x)

⇒ x = -2

To Find :

value of m

Solution :

by substituting the x value in p(x) ,

⇒ (-2 + 1)⁷ + [(2)(-2) + m]³ = 0

⇒ (-1)⁷ + (-4 + m)³ = 0

⇒ -1 + (-64) + m³ - 3(-4)(m)(-4 + m) = 0

⇒ -1 - 64 + m³ + 12m(-4 + m) = 0

⇒ -63 + m³ - 48m + 12m² = 0

⇒ m³ + 12m² - 48m - 63 = 0

⇒ m = 2