Mathematics
Using factor theorem, show that:
(x - 3) is a factor of (x3 + x2 - 17x + 15).
Factorisation
13 Likes
Answer
Let f(x) = (x3 + x2 - 17x + 15).
Given,
Divisor :
⇒ x - 3 = 0
⇒ x = 3
By factor theorem,
(x - a) is a factor of f(x), if f(a) = 0.
Substituting x = 3 in f(x), we get :
⇒ f(3) = (3)3 + (3)2 - 17(3) + 15
= 27 + 9 - 51 + 15
= 51 - 51
= 0.
Since, f(3) = 0, thus (x - 3) is a factor of f(x).
Hence, proved that (x - 3) is factor of x3 + x2 - 17x + 15.
Answered By
4 Likes
Related Questions
If (2x3 + ax2 + bx - 2) when divided by (2x - 3) and (x + 3) leaves remainders 7 and -20 respectively, find values of a and b.
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 + 1) is a factor of (x3 + 4x2 + 5x + 2).
Using factor theorem, show that:
(3x - 2) is a factor of (3x3 + x2 - 20x + 12).