Advertisements
Advertisements
प्रश्न
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
Advertisements
उत्तर १
Let p(x) = x3 – ax2 + 6x – a
x - a = 0
∴ x = a
∴ Remainder = (a)3 - a(a)2 + 6(a) - a
= a3 - a3 + 6a - a
= 5a
Therefore, the remainder obtained is 5a.
उत्तर २
By long division,
Therefore, when x3 − ax2 + 6x − a is divided by x − a, the remainder obtained is 5a.
संबंधित प्रश्न
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
A polynomial f(x) when divided by (x - 1) leaves a remainder 3 and when divided by (x - 2) leaves a remainder of 1. Show that when its divided by (x - i)(x - 2), the remainder is (-2x + 5).
The polynomial f(x) = ax4 + x3 + bx2 - 4x + c has (x + 1), (x-2) and (2x - 1) as its factors. Find the values of a,b,c, and remaining factor.
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 3x3 – 7x2 + 4x + 11
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
Find the remainder when 3x3 – 4x2 + 7x – 5 is divided by (x + 3)
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = 4x3 – 12x2 + 14x – 3, g(x) = 2x – 1
