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
The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.
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, factorise the following completely:
4x3 + 7x2 – 36x – 63
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
Find the values of a and b when the polynomial f(x)= ax3 + 3x2 +bx -3 is exactly divisible by (2x+3) and leaves a remainder -3 when divided by (x+2).
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x3 – 7x2 + 3
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
