Question

2. Find the other polynomial q (x) h of each of the following, given that LCM and GCD and one polynomial p(x) respectively

Answer 1

SOLUTION IS IN THE ATTACHMENT

Greatest Common Divisor (GCD) :
Greatest Common Divisor (GCD) or (HCF) of two or more algebraic expressions is the expression of highest degree which divides each of them without remainder.

Least Common Multiple(LCM): The least common multiple of two or more algebraic expressions is the expression of lowest degree which is divisible by each of them without remainder.

RELATION BETWEEN LCM AND GCD :

The product of any two polynomials is equal to the product of their LCM and GCD. f(x) g(x) = LCM (f(x) , g(x)) × GCD (f(x) , g(x)).

HOPE THIS WILL HELP YOU…

Answer 2

Solution:-

given by:-

》lcm = (x^3-4x)(5x+1)
》 = x(x^2-2^2)(5x+1)
》 = x(x-2)(x+2)(5x+1)

》gcd = 5x^2+x = x(5x+1)

》q(x) = 5x^3-9x^2-2x
》 = x(5x^2-9x-2x)
》 = x(5x^2-10x+x-2x)
》 = x[5x(x-2)+1(x-2)]
》 = x(x-2)(5x+1)

we know that.
》lcm×gcd = q(x)×p(x)

》= x(x-2)(x+2)(5x+1) × x(5x+1)= x(x-2)(5x+1)× p(x).

p(x) =
x(x-2)(x+2)(5x+1) × x(5x+1)
____________________
x(x-2)(5x+1)

[p(x).= x(x+2)(5x+1)] ans

☆i hope its help☆