Advertisements
Advertisements
प्रश्न
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
Advertisements
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
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
If ( x31 + 31) is divided by (x + 1) then find the remainder.
Using remainder theorem, find the value of m if the polynomial f(x)= x3 + 5x2 -mx +6 leaves a remainder 2m when divided by (x-1),
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.
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
What number must be subtracted from 2x2 – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 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
