Advertisements
Advertisements
प्रश्न
Find the LCM and GCD for the following and verify that f(x) × g(x) = LCM × GCD
(x3 – 1) (x + 1), (x3 + 1)
उत्तर
p(x) = (x3 – 1) (x + 1) = (x – 1) (x2 + x + 1) (x + 1)
g(x) = x3 + 1 = (x + 1) (x2 – x + 1)
G.C.D = (x + 1)
L.C.M = (x + 1) (x – 1) (x2 + x + 1) (x2 – x + 1)
L.C.M × G.C.D = (x + 1) (x – 1) (x2 + x + 1) (x2 – x + 1) × (x + 1)
= (x + 1)2 (x – 1) (x2 + x + 1) (x2 – x + 1) ...(1)
p(x) × g(x) = (x – 1) (x2 + x + 1) (x + 1) (x + 1) (x2 – x + 1)
= (x + 1)2 (x – 1) (x2 + x + 1) (x2 – x + 1) ...(2)
From (1) and (2) we get
L.C.M. × G.C.D. = p(x) × g(x)
APPEARS IN
संबंधित प्रश्न
Find the G.C.D. of the given polynomials
x4 + 3x3 – x – 3, x3 + x2 – 5x + 3
Find the L.C.M. of the given expressions
4x2y, 8x3y2
Find the L.C.M. of the given expressions
– 9a3b2, 12a2b2c
Find the L.C.M. of the given expressions
2x2 – 5x – 3, 4x2 – 36
Find the L.C.M. of the given expressions
(2x2 – 3xy)2, (4x – 6y)3, (8x3 – 27y3)
Find the LCM and GCD for the following and verify that f(x) × g(x) = LCM × GCD
21x2y, 35xy2
Given the LCM and GCD of the two polynomials p(x) and q(x) find the unknown polynomial in the following table
| LCM | GCD | p(x) | q(x) |
| (x4 – y4)(x4 + x2y2 + y2) | (x2 – y2) | (x4 – y4)(x2 + y2 – xy) |
If (x – 6) is the HCF of x2 – 2x – 24 and x2 – kx – 6 then the value of k is
Find the least common multiple of xy(k2 + 1) + k(x2 + y2) and xy(k2 – 1) + k(x2 – y2)
Find the GCD of the following by division algorithm
2x4 + 13x3 + 27x2 + 23x + 7, x3 + 3x2 + 3x + 1, x2 + 2x + 1
