Mathematics
Answer
Let f(x) = (x3 + 4x2 + 5x + 2)
Given,
Divisor:
⇒ x + 1 = 0
⇒ x = -1
By factor theorem,
(x - a) is a factor of f(x), if f(a) = 0.
Substituting x = -1 in f(x), we get :
⇒ f(-1) = (-1)3 + 4(-1)2 + 5(-1) + 2
= -1 + 4(1) - 5 + 2
= -1 + 4 - 5 + 2
= 6 - 6
= 0.
Since, f(-1) = 0, thus (x + 1) is a factor of f(x).
Hence, proved that (x + 1) is factor of x3 + 4x2 + 5x + 2.
Related Questions
Using the Remainder Theorem, find the remainders obtained when x3 + (kx + 8)x + k is divided by x + 1 and x - 2. Hence find k if the sum of the two remainders is 1.
Using factor theorem, show that:
(x - 3) is a factor of (x3 + x2 - 17x + 15).
Using factor theorem, show that:
(3x - 2) is a factor of (3x3 + x2 - 20x + 12).
Using factor theorem, show that:
(3 - 2x) is a factor of (2x3 - 9x2 + x + 12).