Advertisements
Advertisements
प्रश्न
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
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(–2) = 2(–2)3 + 3(–2)2 – 5(–2) – 6
= –16 + 12 + 10 – 6
= 0
Thus, (x + 2) is a factor of the polynomial f(x).
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Check whether 7 + 3x is a factor of 3x3 + 7x.
Find the remainder when x3 + 3x2 – 12x + 4 is divided by x – 2.
Find the remainder when x4 + 1 is divided by x + 1.
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)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).
Check whether p(x) is a multiple of g(x) or not:
p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
