Advertisements
Advertisements
प्रश्न
Check whether p(x) is a multiple of g(x) or not:
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
Advertisements
उत्तर
According to the question,
g(x) = x – 2,
Then, zero of g(x),
g(x) = 0
x – 2 = 0
x = 2
Therefore, zero of g(x) = 2
So, substituting the value of x in p(x), we get,
p(2) = (2)3 – 5(2)2 + 4(2) – 3
= 8 – 20 + 8 – 3
= –7 ≠ 0
Hence, p(x) is not the multiple of g(x), the remainder ≠ 0.
APPEARS IN
संबंधित प्रश्न
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
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 ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3.
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(x2 − 7x + 9) ; (x + 1)
Use the Remainder Theorem to factorise the following expression:
2x3 + x2 – 13x + 6
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
If x51 + 51 is divided by x + 1, then the remainder is
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
