Advertisements
Advertisements
Question
Find the GCD pair of the following polynomials
(x3 + y3), (x4 + x2y2 + y4) whose LCM is (x3 + y3) (x2 + xy + y2)
Advertisements
Solution
p(x) = x3 + y3
= (x + y)(x2 – xy + y2)
g(x) = x4 + x2y2 + y4 = [x2 + y2]2 – (xy)2
= (x2 + y2 + xy) (x2 + y2 – xy)
L.C.M. = (x3 + y3) (x2 + xy + y2)
(x + y) (x2 – xy + y2) (x2 + xy + y2)
G.C.D. = `("p"(x) xx "g"(x))/("L"."C"."M".)`
= `((x + y)(x^2 - xy + y^2) xx (x^2 + y^2 + xy)(x^2 + y^2 - xy))/((x + y)(x^2 - xy + y^2)(x^2 + xy + y^2))`
G.C.D. = x2 – xy + y2
APPEARS IN
RELATED QUESTIONS
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
– 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 pair of the following polynomials
a2 + 4a – 12, a2 – 5a + 6 whose GCD is a – 2
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 least common multiple of xy(k2 + 1) + k(x2 + y2) and xy(k2 – 1) + k(x2 – y2)
