Question

x^4-5x^2+4=0
find the real or imaginary solutions by factoring

Answer 1

Did you find the imaginary roots of the last one? Or just need help w/ this one?

Answer 2

need help with this one

Answer 3

Factoring x4-5x2+4

The first term is, x4 its coefficient is 1
The middle term is, -5x2 its coefficient is -5
The last term, "the constant", is +4

Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4

Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -5

-4 + -1 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, (-4) and (-1)
x4 - 4x2 - 1x2 - 4

Step-4 : Add up the first 2 terms, pulling out like factors :
x2 • (x2-4)
Add up the last 2 terms, pulling out common factors :
1 • (x2-4)
Now add up the four terms of step 3 :
(x2-1) • (x2-4)

Answer 4

But we are far from done, take the first half (x2-1) Factoring: x2-1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1
Check : x2 is the square of x1
Factorization is :
(x + 1) • (x - 1)

For the second half (x^2-4)
Factoring: x2 - 4

Check : 4 is the square of 2
Check : x2 is the square of x1
Factorization is :
(x + 2) • (x - 2)

Now add them together to get
(x + 1) • (x - 1) • (x + 2) • (x - 2)

Answer 5

Now solve each single variable equation to get 4 solutions. Post if you want to see if they are correct :)

Answer 6

@Nexxus ??? Do want me to double-check your work and any q's?