Advertisements
Advertisements
Question
Find without division, the remainder in the following:
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
Advertisements
Solution
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
Putting 2x - 3 = 0, we get : x = `3/2`
Substituting this value of x in the equation, we get
`2 xx 3/2 xx 3/2 xx 3/2 - 3 xx 3/2 xx 3/2 + 6 xx 3/2 - 4`
`= 27/4 - 27/4 + 9 - 4`
= 5
APPEARS IN
RELATED QUESTIONS
Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.
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.
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
When x3 – 3x2 + 5x – 7 is divided by x – 2,then the remainder is
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
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
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 3x2 + 4x + 50, g(x) = x – 3
If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3, find the value of a.
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
