Advertisements
Advertisements
प्रश्न
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
Advertisements
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)
संबंधित प्रश्न
Use Remainder theorem to factorize the following polynomial:
`2x^3 + 3x^2 - 9x - 10`
Find the remainder when x3 + 3x2 – 12x + 4 is divided by x – 2.
When the polynomial x3 + 2x2 – 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial x3 + ax2 – 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0.
The polynomial f(x) = ax4 + x3 + bx2 - 4x + c has (x + 1), (x-2) and (2x - 1) as its factors. Find the values of a,b,c, and remaining factor.
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x3 – 7x2 + 3
When 2x3 – x2 – 3x + 5 is divided by 2x + 1, then the remainder is
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
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
