Advertisements
Advertisements
प्रश्न
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
उत्तर
According to the question,
Let p(x) = 4x2 + x − 2 and g(x) = x – 2
g(x) = x – 2
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) = 4(2)2 + 2 − 2
= 16 ≠ 0
Since, the remainder ≠ zero,
We can say that,
g(x) = x – 2 is not a factor of p(x) = 4x2 + x − 2
APPEARS IN
संबंधित प्रश्न
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
Find the values of a and b when the polynomials f(x)= 2x2 -5x +a and g(x)= 2x2 + 5x +b both have a factor (2x+1).
Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 3x3 + 7x2 – 5x + 1
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 3x3 – 7x2 + 4x + 11
Find the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 2x2 – 4x – 1; g(x) = x + 1
Find the remainder when 3x3 – 4x2 + 7x – 5 is divided by (x + 3)
