Advertisements
Advertisements
प्रश्न
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
उत्तर
For x=2, the value of the given
expression `3x^3+2x^2-19x+6`
= `3(2)^3+2(2)^2-19(2)+6`
=`24+8-38+6`
= 0
⇒ x-2 is a factor of `3x^3+2x^2-19x+6`
Now let us do long division
Thus we have ,
`3x^3+2x^2-19x+6` =`(x-2) (3x^2+8x-3) `
=`(x-2)(3x^2+9x-x-3)`
=`(x-2)(3x(x+3)-(x+3))`
= (x-2) (3x-1) (x+3)
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by `x - 1/2`
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 2x2 – 5x + 1
Find the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
What number must be subtracted from 2x2 – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
Check whether p(x) is a multiple of g(x) or not:
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
If x25 + x24 is divided by (x + 1), the result is ______.
