Advertisements
Advertisements
Question
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
Advertisements
Solution
Given, p(x) = 4x3 – 12x2 + 14x – 3 and g(x) = 2x – 1
Here, zero of g(x) is `1/2`.
When we divide p(x) by g(x) using remainder theorem, we get the remainder `p(1/2)`.
∴ `p(1/2) = 4(1/2)^3 - 12(1/2)^2 + 14(1/2) - 3`
= `4 xx 1/8 - 12 xx 1/4 + 14 xx 1/2 - 3`
= `1/2 - 3 + 7 - 3`
= `1/2 + 1`
= `(1 + 2)/2`
= `3/2`
Hence, remainder is `3/2`.
APPEARS IN
RELATED QUESTIONS
Check whether 7 + 3x is a factor of 3x3 + 7x.
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
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’.
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.
When 2x3 – x2 – 3x + 5 is divided by 2x + 1, then the remainder is
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (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
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
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
