Question

Can you guys help me solve this
32 + 14x^2 -x^4

Answer 1

are you supposed to factor, or set equal to zero and solve?

Answer 2

factor

Answer 3

ok first we can try to factor \(32 + 14x -x^2\) and then replace \(x\) by \(x^2\)

Answer 4

there are a lot of factors of 32 but you know it has to look like
\((a-x)(b+x)\) because that is the only way you are going to get an \(x^2\) out of it.
so \(ab=32\) and \(a-b=14\)
really you have to guess and check, but after some trial and error you should see that \(a=16\) and \(b=2\) will work because \(16\times 2=32\) and \(16-2=14\)

Answer 5

for x i've got x=4, x=-16

Answer 6

actually 2 :) my hand writing suck

Answer 7

ok good,
first step would be to write as
\[32+14x-x^2=(16-x)(2+x)\]

Answer 8

now we really have \((16-x^2)(2+x^2)\) so we can continue to factor, because \(16-x^2\) is the difference of two squares

Answer 9

final answer would then be
\[(4+x)(4-x)(2+x^2)\]

Answer 10

tks

Answer 11

yw