Question

2a^2 + 30a + 100
Is it prime when factored?

Answer 1

i got prime

Answer 2

when i did it

Answer 3

so you factored to this?
\[2a^2 + 30a + 100 = (2a +10)(a+10) = 2(a+5)(a+10)\]

Answer 4

well isnt that wrong?

Answer 5

im not sure quite what you mean by prime in this case

Answer 6

well, can you factor this equation?

Answer 7

i cant seem to

Answer 8

yes i did so above :D

Answer 9

i'll help

Answer 10

because there are no factors of ten that add to 30

Answer 11

i mean 100 not 10

Answer 12

ah i see your problem, here we go:

we have 2a^2 and not just a^2 , so when we factor it will effect what numbers we are looking for.

we are going to have

(2a + (something) )( a + (something else) )

so you're right the numbers we are looking for will multiply to 100
but we need to think about the 2a term when we think how they add to get 30

10*10 = 100 and 2*10 + 10 = 30

so it becomes (2a+10)(a+10)

you can check by multiplying out

Answer 13

ok thanks! :D:D

Answer 14

:) happy to help

Answer 15

wait hold on

Answer 16

sure

Answer 17

sorry, but why do you do the 2 * 10 + 10 = 30 part. Where do you get it from?

Answer 18

its from how we multiply out the brackets, because factorising is just the reverse of expanding:

lets pretend we dont know about the 10's

we are looking for two numbers C and D

first we see that one of the a's in the brackets has to be multiplied by 2:

2a^2 + 30a + 100 = (2a + C)(a + D)

lets expand that right hand side:

(2a + C)(a + D) = 2a(a+D) + C(a+D) = 2a^2 + 2aD + aC + CD

now we know

2a^2 + 30a + 100 = 2a^2 + 2aD + aC + CD

so CD = 100

and 2aD + aC = 30a

so our numbers multiply to get 100

and if we double one of them and add the other we get 30

im really sorry if this has confused you more

Answer 19

hmmm...

Answer 20

i sort of get this.

Answer 21

prime.