Advertisements
Advertisements
प्रश्न
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
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) = 2(1/2)^3 + 3(1/2)^2 - 5(1/2) - 6`
= `1/4 + 3/4 - 5/2 - 6`
= `-5/2 - 5`
= `(-15)/2 ≠ 0`
Thus, (2x – 1) is not a factor of the polynomial f(x).
APPEARS IN
संबंधित प्रश्न
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Use remainder theorem and find the remainder when the polynomial g(x) = x3 + x2 – 2x + 1 is divided by x – 3.
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
What number must be subtracted from 2x2 – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?
Use the Remainder Theorem to factorise the following expression:
2x3 + x2 – 13x + 6
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by 2x + 1
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
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x – 1
If x25 + x24 is divided by (x + 1), the result is ______.
