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प्रश्न
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
विकल्प
0
– 4
2
4
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उत्तर
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is – 4.
Explanation:
We know that when f(x) is divided by x – a
Then remainder = f(a)
Let f(x) = x3 – x2 + x – 1
When f(x) is divided by x – (– 1)
Then remainder
= f(– 1)
= (– 1)3 – (– 1)2 – 1 – 1
= – 1 – 1 – 1 – 1
= – 4
संबंधित प्रश्न
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
If x3 + ax2 + bx + 6 has x – 2 as a factor and leaves a remainder 3 when divided by x – 3, find the values of a and b.
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 the polynomial x3 + 2x2 – 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial x3 + ax2 – 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0.
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
Find without division, the remainder in the following :
x3 + 8x2 + 7x- 11 is divisible by (x+4)
Find without division, the remainder in the following:
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
