Advertisements
Advertisements
प्रश्न
A polynomial in ‘x’ is divided by (x – a) and for (x – a) to be a factor of this polynomial, the remainder should be ______.
विकल्प
– a
0
a
2a
Advertisements
उत्तर
A polynomial in ‘x’ is divided by (x – a) and for (x – a) to be a factor of this polynomial, the remainder should be 0.
Explanation:
For (x – a) to be a factor of a polynomial P(x), the remainder when P(x) is divided by (x – a) should be 0. This is based on the Factor Theorem, which states that (x – a) is a factor of P(x) if and only if P(a) = 0.
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
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.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
Given f(x) = ax2 + bx + 2 and g(x) = bx2 + ax + 1. If x – 2 is a factor of f(x) but leaves the remainder – 15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression. f(x) + g(x) + 4x2 + 7x.
When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 3x2 + 4x + 50; g(x) = x – 3
Find the remainder when 3x3 – 4x2 + 7x – 5 is divided by (x + 3)
