Advertisements
Advertisements
प्रश्न
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
Advertisements
उत्तर
f(x) = x3 + x2 – 4x – 4
For x = –1,
f(x) = f(–1)
= (–1)3 + (–1)2 – 4(–1) – 4
= –1 + 1 + 4 – 4
= 0
Hence, (x + 1) is a factor of f(x).
x2 – 4
`x + 1")"overline(x^3 + x^2 - 4x - 4)`
x3 + x2
– –
– 4x – 4
– 4x – 4
+ +
0
∴ x3 + x2 – 4x – 4 = (x + 1)(x2 – 4)
= (x + 1)[(x)2 – (2)2]
= (x + 1)(x + 2)(x – 2)
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
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.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
When x3 + 3x2 – kx + 4 is divided by (x – 2), the remainder is k. Find the value of k.
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
If x51 + 51 is divided by x + 1, then the remainder is
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
