Advertisements
Advertisements
Question
Check whether p(x) is a multiple of g(x) or not:
p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
Advertisements
Solution
According to the question,
g(x) = 2x + 1
Then, zero of g(x),
g(x) = 0
2x + 1 = 0
2x = –1
x = `-1/2`
Therefore, zero of g(x) = `-1/2`
So, substituting the value of x in p(x), we get,
`p(-1/2) = 2 xx (-1/2)^3 - 11 xx (-1/2)^2 - 4 xx (-1/2) + 5`
= `-1/4 - 11/4 + 7`
= `16/4`
= 4 ≠ 0
Hence, p(x) is not the multiple of g(x), the remainder ≠ 0.
APPEARS IN
RELATED QUESTIONS
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
Find the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by x + 3
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
What is the remainder when x2018 + 2018 is divided by x – 1
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
If x25 + x24 is divided by (x + 1), the result is ______.
