Advertisements
Advertisements
प्रश्न
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Advertisements
उत्तर
Let p(y) = y3 − 5y2 + 7y + m
When the polynomial is divided by (y + 2), the remainder is 50. This means that the value of the polynomial when y = −2 is 50.
By remainder theorem,
Remainder = p(−2) = 50
∴ (−2)3 − 5 × (−2)2 + 7 (−2) + m = 50
⇒ − 8 − 5 × 4 -14 + m = 50
⇒ − 8 − 20 − 14 + m = 50
⇒ − 42 + m = 50
⇒ m = 50 + 42 = 92
Thus, the value of m is 92.
APPEARS IN
संबंधित प्रश्न
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
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.
Find without division, the remainder in the following:
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)3
When x3 + 3x2 – kx + 4 is divided by (x – 2), the remainder is k. Find the value of k.
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
If on dividing 4x2 – 3kx + 5 by x + 2, the remainder is – 3 then the value of k is
Find the remainder when 2x3 – 3x2 + 4x + 7 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
If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k = ?
If x51 + 51 is divided by x + 1, then the remainder is
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
If x25 + x24 is divided by (x + 1), the result is ______.
