Question

Having trouble FACTORING this...

n^2+21n = 0

Answer 1

@mathmate Are you available for some help?

Answer 2

think of n^2 as n*n

`n^2+21n = 0` is the same as `n*n+21*n = 0`

we can divide both terms (n*n and 21*n) by the common factor n so we can pull it out

In other words,

n*n+21*n = n*(n+21)

hopefully you can see that if you distribute the n back in, you get n*n + 21*n back again?

Answer 3

@jim_thompson5910 I'm still kind of confused...

Answer 4

Let's say we replace n with a number. What number do you want to replace n with?

Answer 5

You can pick any number

Answer 6

@jim_thompson5910 2

Answer 7

so we would go from `n*n + 21*n` to `2*2 + 21*2` agreed?

Answer 8

yes

Answer 9

the common factor here is 2

we can pull this out

2*2 + 21*2 = 2*(2+21)

think of it as distribution but in reverse

Answer 10

if n = 3, then we'd have

3*3 + 21*3 = 3*(3+21)

Answer 11

so in 2(2+21), 2 before the () would actually be n, correct?

Answer 12

yes because n represents any number (not just 2)

Answer 13

ok. but how am i going to find n?

Answer 14

same with the 2 inside the parentheiss

Answer 15

or am i not supposed to? because it just says to factor it.

Answer 16

you leave n as itself. There's no need to actually find the value of n

Answer 17

oh. ok.

Answer 18

you just go from `n^2+21n` to `n(n+21)`

Answer 19

so
n^2+21n = 0
is the same as
n(n+21) = 0

Answer 20

right....so then it would be (-21+21)=0
so -21 would be the answer, correct?

Answer 21

-21 is one solution since it is the solution to n+21 = 0

Answer 22

n(n+21) = 0 means that n = 0 or n+21 = 0

Answer 23

so if n(n+21) = 0, then n = 0 or n = -21

Answer 24

oh......so if there is x^2 (or another variable) + a number (lets say 32)x, then x would automatically equal 0?

Answer 25

no, in your original equation, you have n^2+21 set equal to zero

Answer 26

n^2+21n I mean

Answer 27

remember that if A*B = 0 then either A = 0 or B = 0

Answer 28

well if it was set equal to zero
so if it was like:
x^2 + 32x +0 it would automatically equal 0?

Answer 29

i mean =0

Answer 30

if you had x^2 + 32x = 0, then it would factor to x*(x+32) = 0