Advertisements
Advertisements
प्रश्न
Find the LCM pair of the following polynomials
x4 – 27a3x, (x – 3a)2 whose GCD is (x – 3a)
उत्तर
p(x) = x4 – 27a3x = x[x3 – 27a3]
= x[x3 – (3a)3]
= x(x – 3a) (x2 + 3ax + 9a2)
g(x) = (x – 3a)2
G.C.D. = x – 3a
L.C.M. = `("p"(x) xx "g"(x))/("G"."C"."D".)`
= `(x(x - 3"a")(x^2 + 3"a"x + 9"a"^2) xx (x - 3"a")^2)/((x - 3"a"))`
L.C.M. = x (x – 3a)2 (x2 + 3ax + 9a2)
APPEARS IN
संबंधित प्रश्न
Find the G.C.D. of the given polynomials
3x4 + 6x3 – 12x2 – 24x, 4x4 + 14x3 + 8x2 – 8x
Find the G.C.D. of the given polynomials
3x3 + 3x2 + 3x + 3, 6x3 + 12x2 + 6x + 12
Find the L.C.M. of the given expressions
4x2y, 8x3y2
Find the L.C.M. of the given expressions
p2 – 3p + 2, p2 – 4
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
Find the GCD pair of the following polynomials
12(x4 – x3), 8(x4 – 3x3 + 2x2) whose LCM is 24x3 (x – 1)(x – 2)
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) |
| a3 – 10a2 + 11a + 70 | a – 7 | a2 – 12a + 35 |
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) |
Find the GCD of the following by division algorithm
2x4 + 13x3 + 27x2 + 23x + 7, x3 + 3x2 + 3x + 1, x2 + 2x + 1
