Thursday

December 18, 2014

December 18, 2014

Posted by **Anonymous** on Monday, March 25, 2013 at 7:53pm.

X^4+x^3=16-8x-6x^2. Answer: -2,1,+-√8

3x^3+4x^2+6=x. (-2,1/3, i√8/3)

Please help so I know how to figure these equations out.A big THANKS

- college algebra -
**Reiny**, Monday, March 25, 2013 at 8:50pmX^4+x^3=16-8x-6x^2

x^4 + x^3 + 6x^2 + 8x - 16 = 0

you must know the factor theorem to do these

look at the constant of 16

if there are factors of the type ( ?x + c) , c must be a factor of 16

so try ±1, ±2, ±4, ... that is, try factors of 16

e.g.

let x = 1 , we get

1 + 1 + 6 + 8 - 16 = 0 ahhhh, so x-1 is a factor, that was lucky

try some more:

x = 2, we get

16 + 8 + 24 + 16 - 16 ≠ 0

x = -2

16 - 8 + 24 - 16 - 16 = 0 , aahhh again, so x+2 is a factor

now do a long algebraic division by first x-1, and then x+2

both must divide evenly.

I got

x^4 + x^3 + 6x^2 + 8x - 16 = (x-1)(x+2)(x^2 + 8)

so x = 1 , -2 or

x^2 = -8 = 2√-2 = ±2√2 i , yours should have been ±√8 i

2nd:

3x^3 + 4x^2 - x + 6 = 0

try x = ±1, ±2, ±3

x=1 ---> 1 + 4 - 1 + 6 ≠0

x=-1 --> -3 + 4 + 1 + 6 ≠ 0

x = 2 --> 24 + 16 ...... ≠ 0

x = -2 --> -24 + 16 + 2 + 6 = 0 ..... finally, x+2 is a factor

division:

3x^3 + 4x^2 - x + 6 = (x+2)(3x^2 - 2x + 3)

so x = -2

or

x = (2 ±√-32)/6

= ( 2 ± 4√2 i)/6

= (1 ± 2√2 i)/3

I don't see how you got your answers.

**Answer this Question**

**Related Questions**

Algebra - How would i complete these problems? 1. (√6mn)^5 2. ^3√16x...

Algebra - How would i solve for this problems? also what is the answer(s) 5.)...

math - How would I come about to the solution and what the answers to the ...

Math - Find an equation of the line that bisects the obtuse angles formed by the...

Math - Help with radicals please - Please show work Simplify rational 1. 4√...

Algebra Work Check - 1. 5√6 * 1/6√216 5/6 * √1296 5/6 * √...

Algebra - Simplify the expressions and solve the equations 1. 2√3 - √...

Algebra 2 Answer Check - Simplify by rationalizing each denominator. 1. 2/√...

math - I tried solving these problems and get stuck . Can you please tell me ...

math grade 11 - i need help with this quretsion ; i dont know if im right, and i...