How do I factor a function with with a degree of four? (again)?

Question

p(x)=4X^2-37X+9

I understood how the first one I posted was solved, thank you guys :)

but now this one really threw me off the bat, my math is kinda rusted :(

my mistake i meant

p(x)= 4X^4-37x^2+9

Answer 1

Errmmmm.... This one only has a degree of 2 ☺
and it factors as (4x - 1)(x-9)


Doug

Answer 2

That factors as

4x^4 - 37x^2 + 9
(4x^2 - 1)(x^2 - 9)

Then those can be broken down into

(2x - 1)(2x + 1)(x - 3)(x + 3)

Answer 3

Simple: 4 x 9 = 36 so the 2 numbers you choose need to mult ot 36
and add to -37 since it's the non exponent term. the 2 number are
-1 and -36 so 4X^2 -1X - 36X + 9. Now factor it half way like this
X(4x - 1) -9(4x - 1) the numbers in both perentheses must match.
Then the last step is to combine the outside like this (x - 9)(4x - 1).
To check and see if it's right just mult the 2. (mult mean multiply)

Answer 4

The easiest way is using the Ruffini method, it is done like a division... It's to late for me to do it (I'm tired!). First you start by "completing" (filling?, sorry I'm not a native English speaker...) But in this case the polinomial is of a degree of 2 (two) not 4 (four). 4X^2 (X^2 power of 2 not 4)

Answer 5

4x^2-37x+9
splitting the middle term such that you geta sum of -37 and a product od 36 it will be -36 and -1
4x^2-36x-x+9
4x(x-9)-1(x-9)
(x-9)(4x-1)
revised sum
in place of x you will have x^2
(x^2-9)(4x^2-1)
(x+3)(x-3)(2x+1)(2x-1)

Answer 6

The answer is....
(4x-1)(x-9)

I just use trial and error with the factors that are applicable.

Answer 7

Put x^2 = y.
4y^2-37y-9=(4y-1)(y-9)
now replace y by x^2
You get (4x^2-1)(x^2-9)
Factorize to get (2x+1)(2x-1)(x+3)(x-3)

Answer 8

let x ^2 = y
so given function = 4y^2-37y +9
= 4y^2- 36y-y+9
= 4y(y-9) -1(y-9)
= (y-9)(4y-1)
= (x^2-9)(4x^2-1)
= (x+3)(x-3)(2x+1)(2x-1)