Question

solving a polynomial equation by factoring 36d^3-121d=0

Answer 1

For this case we must factor the following equation:

$36d ^ 3-121d = 0$

It is observed that both terms contain the variable "d", so we can take it out as a common factor:

$d (36d ^ 2-121) = 0$

On the other hand, we look for the factors of 36 and 121:

36: 1,2,3,4,6,9,12,18,36

121: 1, 11,121

The greatest common factor between both numbers is 1.

Thus, the expression is factored as:

$d (36d ^ 2-121) = 0$

Thus, one of the roots of the polynomial is 0.

$36d ^ 2-121 = 0\\36d ^ 2 = 121\\d ^ 2 = \frac {121} {36}\\d = \pm \sqrt {\frac {121} {36}}\\d = \pm \frac {11} {6}$

Answer:

$d (36d ^ 2-121) = 0\\d_ {1} = 0\\d_ {2} = \frac {11} {6}\\d_ {3} = - \frac {11} {6}$