Advertisements
Advertisements
प्रश्न
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
Advertisements
उत्तर
f(x) = 3x3 + 2x2 – 23x – 30
For x = –2,
f(x) = f(–2)
= 3(–2)3 + 2(–2)2 – 23(–2) – 30
= –24 + 8 + 46 – 30
= –54 + 54
= 0
Hence, (x + 2) is a factor of f(x).
3x2 – 4x – 15
`x + 2")"overline(3x^3 + 2x^2 - 23x - 30)`
3x3 + 6x2
– 4x2 – 23x
– 4x2 – 8x
– 15x – 30
– 15x – 30
0
∴ 3x3 + 2x2 – 23x – 30 = (x + 2)(3x2 – 4x – 15)
= (x + 2)(3x2 + 5x – 9x – 15)
= (x + 2)[x(3x + 5) – 3(3x + 5)]
= (x + 2)(3x + 5)(x – 3)
APPEARS IN
संबंधित प्रश्न
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
Find the values of a and b when the polynomial f(x)= ax3 + 3x2 +bx -3 is exactly divisible by (2x+3) and leaves a remainder -3 when divided by (x+2).
Find the values of m and n when the polynomial f(x)= x3 - 2x2 + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).
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 value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x2 + 5x + 3
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 3x2 + 4x + 50; g(x) = x – 3
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 2x2 – 4x – 1, g(x) = x + 1
