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
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.
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
Find without division, the remainder in the following:
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
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).
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3)x – 6 leave the same remainder. Find the value of ‘p’.
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
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
