# How to find the value of v in here?

How to solve for the value of v when 0= v^4 + 9v^3 -13v^2-213v-360. Find or solve the value of v.

### 2 Answers

- Anonymous7 years agoBest Answer
v^4 + 9v^3 - 13v^2 - 213v - 360 = 0

You start by testing out values that you think will work.

I notice a lot of 3's, 6's, 9's and also a few negative signs, so I will test out v = -3:

(-3)^4 + 9(-3)^3 - 13(-3)^2 - 213(-3) - 360

= 81 - 243 - 117 + 639 - 360

= 720 - 360 - 360

= 0

So it works. Now that means that v = -3 is a solution, so (v + 3) is a factor.

Divide the polynomial by (v + 3):

-3 [1 9 -13 -213 -360]

... [ -3 -18 93 360]

... 1 6 -31 -120 0

Therefore (v + 3)(v^3 + 6v^2 - 31v - 120) = 0

Divide the polynomial by (v + 3) again:

-3 [1 6 -31 -120]

... [ -3 -9 120]

... 1 3 -40 0

Therefore (v + 3)^2 * (v^2 + 3v - 40) = 0

As for the quadratic part:

v^2 + 3v - 40 = (v + 8)(v - 5)

So when you combine the whole thing:

(v + 8)(v - 5)(v + 3)^2 = 0

v = -8, v = 5 or v = -3