Question

use factor theorem to determine the value of K for which x+2 is a factor of (x+1)⁷ + (2x + k)³​

Answer 1

Answer:

Using factor theorem, which says if x - a is a factor of a poly. f(x), then value of f(x) is 0 for all values of a.

Here,

( x - (-2) ), so for x = - 2,

= > ( x + 1 )^7 + ( 2x + k )^3 = 0

= > ( - 2 + 1 )^7 + ( 2(-2) + k )^3 = 0

= > (-1)^7 + ( k - 4 )^3 = 0

= > - 1 + ( k - 4 )^3 = 0

= > ( k - 4 )^3 = 1

= > k - 4 = 1

= > k = 1 + 4

= > k = 5

Satisfying value of k is 5.