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
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Using the Remainder Theorem, factorise the following completely:
2x3 + x2 – 13x + 6
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
Find without division, the remainder in the following:
5x3 - 7x2 +3 is divided by (x-1)
What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
