Advertisements
Advertisements
प्रश्न
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
Advertisements
उत्तर
By remainder theorem we know that when a polynomial f(x) is divided by x – a, then the remainder is f(a).
Let f(x) = 2x3 + 3x2 – 5x – 6
f(–1) = 2(–1)3 + 3(–1)2 – 5(–1) – 6
= –2 + 3 + 5 – 6
= 0
Thus, (x + 1) is a factor of the polynomial f(x).
संबंधित प्रश्न
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
If ( x31 + 31) is divided by (x + 1) then find the remainder.
Find the values of a and b when the polynomials f(x)= 2x2 -5x +a and g(x)= 2x2 + 5x +b both have a factor (2x+1).
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.
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 6x2 + 2x – 4, g(x) = `1 - 3/2 x`
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
