Question

Completely factor the following expression.

Answer 1

\[t ^{2}+tv+4v ^{2}\]

Answer 2

spliiting term method

Answer 3

how do i do that @mayankdevnani lol

Answer 4

Find what is common between these first

Answer 5

ok got \[(t+2v)^{2}\] is it right?

Answer 6

No the letter t is present in\[t ^{2}+tv+4v ^{2}\]

Answer 7

grrr i dont get this lol

Answer 8

In this equation what number or letter is present in all the equation

Answer 9

well im guessing t?

Answer 10

Yes

Answer 11

So in factorization you have to take the common number or letter which is found in the equation

Answer 12

write (t) then open a bracket to make:\[t+v+4v ^{2}\]

Answer 13

You did that incorrectly, @Faris_Waleed . That would only work if the 4v^2 expression also consisted of a t, which it does not. @Vikt0r this question has no solutions on the real number plane, only in the imaginary number plane. Therefore, this question has no solutions, it is unfactorable.

Answer 14

@hkim then how my book is wrong *GASP*!!!!!!

Answer 15

Yes I figured that out

Answer 16

Sorry

Answer 17

SorryVikt0r

Answer 18

@Vikt0r your book is not wrong. It wants you to be able to come to that conclusion, that it is unfactorable, yourself.

Answer 19

grr then what do i answer lol!

Answer 20

Does your book require that you answer in imaginary number form? If so, then you should be able to get an answer. If not, then there are no actual answers to the factoring. If it crossed the horizontal plane of axis at any time, even once, then it is possible to provide an answer, but there is no real solution. You can see so for yourself here http://www.wolframalpha.com/input/?i=t%5E2%2Btv%2B4v%5E2

Answer 21

ok i got it!!!
i found an example of \[x ^{2}+11x18] where i need to find two positive factors of 18 which sum is 11 the factos 9 and 2 have a sum of 11 so they are the correct values of p and q so \[x ^{2}+11x+18=(x+9)(x+2) which if u simplify \it is =x ^{2}+11x+18 which is the answer\] @hkim @Faris_Waleed