simplify k^4-5k^2+4?

Question

k^4-5k^2+4
I can't figure this out.

Pleas show your work, I need to know how to do it

yes factor

Answer 1

Start by assigning x = k²

Then you have x² - 5x + 4

This is easy to factor as:
(x - 4)(x - 1)

Put k² back in and you have:
(k² - 4)(k² - 1)

(Note: if this was all equal to zero, then you could solve this as k² = 4 or k² = 1. This would lead to four solutions of k = 1 or 2 or -1 or -2)

Answer 2

k^4 - 5k^2 + 4

*Rewrite the expression in alpha descending order:

First: factor > multiply the 1st and last coefficient (1*4 = 4). Find two numbers that give you 4 when multiplied and -5 (middle coefficient) when added/subtracted. The numbers are: -1, -4

Sec: rewrite the expression with the new middle numbers and group "like" terms >

k^4 - 1k^2 - 4k^2 + 4
(k^4 - 1k^2) - (4k^2 + 4)

Third: factor the expression >

k^2(k^2 - 1) - 4(k^2 - 1)
(k^2 - 1)(k^2 - 4)

"Factor into lowest terms, if possible.

(k+1)(k-1)(k+2)(k-2)

P.S. The only way to simplify the problem is to factor.

Answer 3

k^4- 5k^2+4 Factor

(k^2-1)(k^2-4) Factor each

(k+1)(k-1)(k+2)(k-2) Equal each eqation to 0 then solve

k+1= 0 k-1= 0 k+2= 0 k-2= 0
k= -1 k=1 k= -2 k= 2

{k= -1, 1, -2, 2}

Answer 4

k^4-5k^2+4
(k^2-4)(k^2-1)
(k+2)(k-2)(k+1)(k-1)

not much to show. I just did it in my head, but then I've had a LOT of practice :)

You can check by using FOIL to get back to the original trinomial.

Answer 5

(k^2-4)(k^2-1) first factor it into two polynomials

(k+2)(k-2)(k+1)(k-1) then factor the two remaining polynomials into 4 polynomials

Answer 6

nicely that's of route distinction of two squares..... y2-16 aspects into (y+4)(y-4) so that you at present have (y-4)/(y-4)(y+4) (y-4) cancels out interior the numerator and denominator and also you're left with a million/(y+4) D is your answer =D

Answer 7

(k^4 - 5k^2 + 4) is in its simplest form
Do not factorize unless it is a requirement
You need not do anything unless teacher instructs you

Answer 8

(k^2-4)(k^2-1)

Answer 9

(k^2-4)(k^2-1)

Answer 10

do you mean factor the equation?