Question

what is the LCM of 14x^2+28 and 7x^2+42x+56 what is the LCM of 14x^2+28 and 7x^2+42x+56 @Mathematics

Answer 1

i think i have the 14x^2+28 factored right is it 14x(x+2)=2x7x(x)x(x+2)

Answer 2

first you want to find their GCD. Then use the formula:
\[LCM(a,b)=\frac{a\cdot b}{GCD(a.b)}\]

Answer 3

14(x2 +2)=
7(x2 +6x +8)=7(x+4)(x+2)

Answer 4

\[14x^2+28=14(x^2+2)\]

Answer 5

Looks like their GCD is only 7. So the LCM would be:\[\frac{(14x^2+28)(7x^2+42x+56)}{7}\]

Answer 6

the GCD is 7, not the LCM. The LCM will be bigger than the two polynomials.

Answer 7

so after i factor the second is where i get lost

Answer 8

14(x2 +2)=(2(7(x+2) on exponent2) - 4x) and hence LCM will be 7(x+2)

Answer 9

you factor the first and get:\[14(x^2+2)=2\cdot7(x^2+2)\]
factoring the second gives:\[7x^2+42x+56=7(x^2+6x+8)=7(x+2)(x+4)\]
Their only common factor is 7, that is the GCD. Then use the formula i posted above.

Answer 10

somehow i came up with 14x(x+2)(x+4)

Answer 11

there is no way the LCM can be 7(x+2). what would you multiply 14x^2+28 by to get 7x+14?

Answer 12

yes joe u were ryt LCM is
14*(x^2+2)*(x+2)*(x+4)

Answer 13

but how i got that answer i have no idea lol

Answer 14

sheg has the correct answer.

Answer 15

thanks all!

Answer 16

Think of how you would do this with numbers.

What is the LCM of 6 and 9? its 18 because 6*3 is 18, and 9*2 is 18, and 18 is the smallest common multiple between the two.

Using the formula above, the GCD of 6 and 9 is 3, so the LCM = 6*9/3=18.