Question

Write a linear factorization of the function.

f(x) = x^4 + 49x^2

Answer 1

straight away i see x^2 can be taken out as common to write

x^2(x^2 + 49)
x^2 + 49 will have complex roots

if you are working in real plane factorization is (x)(x)(x^2 + 49)

Answer 2

then would you make it into x^4+49?

Answer 3

@Andreshoyos23 you mean to say the final answer would be x^4+49 ?

Answer 4

yes ? im a bit confused with what im supposed to do .

Answer 5

@harsimran_hs4

Answer 6

no lets check it step by step

= x^4 + 49x^2
= x(x^3 + 49x)
= x^2(x^2 + 49)

clear till now ?

Answer 7

yes

Answer 8

@harsimran_hs4 but then where would u go from here? i need to work it into an imaginary number but i dont know how to do that would it just factor the x^2 and 49? or foil i forget the names.

Answer 9

ok now we had reached
x^2(x^2 + 49)

now forget every thing and tell me the values of x which satisfy
x^2 + 49 = 0

Answer 10

@harsimran_hs4 (+- 7)?

Answer 11

@harsimran_hs4 7i

Answer 12

yes +7i and -7i

so finally
x^2 (x^2 + 49)
= x^2(x - 7i) (x+7i)
is the final answer

Answer 13

the one - is because when u place it on the other side it becomes negative and you have to show that in the equation right ? and thank you so much u were lots of help