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:-
$lcm = {(4x + 5)}^{3} {(3x - 7)}^{3} \\ gcd = (4x + 5) {(3x - 7)}^{2} \\ q(x) = {(4x + 5)}^{3} {(3x - 7)}^{2} \\ we \: know \: that \: \\ lcm \times gcd \: = q(x) \times p(x) \\ {(4x + 5)}^{3} {(3x - 7)}^{3} \times (4x + 5) {(3x - 7)}^{2} = {(4x + 5)}^{3} {(3x - 7)}^{2} \times p(x) \\ p(x) = \frac{ {(4x + 5)}^{3} {(3x - 7)}^{3} \times (4x + 5) {(3x - 7)}^{2} }{{(4x + 5)}^{3} {(3x - 7)}^{2}} \\ p(x) = {(3x - 7)}^{3} (4x + 5)ans$
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