Question

How do you factor 6v^2 + 48v + 72?

Answer 1

first; divide by six

Answer 2

48 divided by 6 is 8 and 72 divided by 6 is 12 and 6 divided by 6 is 1

Answer 3

This is assuming of course that the equation above equals zero, or else you will have to divide both sides (essentially, you are anyways).

So now the equation is
\[v^2+8v+12=0\]
Do you know how to factor this?

Answer 4

is it (v + 6) (v + 2) ?

Answer 5

Yep.

Answer 6

thanks

Answer 7

You're welcome!

Answer 8

what about x^2 - 4x - 12?

Answer 9

so
\[ 6v^2 + 48v + 72=6(v+6)(v+2)\]

Answer 10

ya that's what I got

Answer 11

for \[x^2 - 4x - 12\]
the difference between two numbers is 4 and their product is -12

Answer 12

Same way:
Two numbers that multiply to equation -12, and add up to -4.
In this case, -6 and 2
\[(x-6)(x+2)\]

Answer 13

um 5w^2 - 20?

Answer 14

I don't know how to factor this without having a middle number

Answer 15

Factor out the 5 first.

Answer 16

ok

Answer 17

for
\[5w^2 - 20\]
first factor out the multiple of five

Answer 18

\[5(w^2-4)\]
That is the pattern known as the difference of two squares. w is a square, 4 is a square. It follows the pattern:
\[(a^2-b^2)=(a+b)(a-b)\]
Apply that two \(w^2-4\) and see what you get.