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
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x3 – 7x2 + 3
Find the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
