Question

Lmc of x^2-4 and x^2-5x-14

Answer 1

`\left(x+2\right)\cdot \left(x-2\right)\cdot \left(x-7\right)`

Explanation:

`\mathrm{Find\:Least\:Common\:Multiplier\:of\:}x^2-4,\:x^2-5x-14`

`\mathrm{The\:LCM\:of\:}a,\:b\:\mathrm{is\:the\:smallest\:multiplier\:that\:is\:divisible\:by\:both\:}a\mathrm{\:and\:}b`

`x^2-4`

`\mathrm{Rewrite\:}4\mathrm{\:as\:}2^2`

`=x^2-2^2`

`x^2-2^2=\left(x+2\right)\left(x-2\right)`

`=\left(x+2\right)\left(x-2\right)`

`x^2-5x-14`

`=\left(x^2+2x\right)+\left(-7x-14\right)`

`=x\left(x+2\right)-7\left(x+2\right)`

`=\left(x+2\right)\left(x-7\right)`

`\mathrm{Multiply\:each\:factor\:with\:the\:highest\:power:}`

`\left(x+2\right)\cdot \left(x-2\right)\cdot \left(x-7\right)`