Hey, I need help factoring this problem : x^4 - 19x^2 + 25
Please show your work and explain. THANKS!
2007-01-04 14:16:53 · 4 answers · asked by Choho855 1 in Science & Mathematics ➔ Mathematics
x^4 - 19x^2 + 25
= (x^4 - 10x^2 +25) - 9x^2... This is just regrouping terms.
= (x^2 - 5)^2 - (3x)^2... Rewrite as squares of something.
= (x^2 + 3x - 5)(x^2 - 3x - 5)... Difference of squares factoring.
The quadratics can't be factored over the integers, so that's it.
2007-01-04 14:23:35 · answer #1 · answered by bictor717 3 · 1⤊ 0⤋
You can't factor it. There are no 2 numbers that multiply to 25 and add to -19.. And it's not a perfect square trinomial.
If you are looking for the roots, then use the quadratic formula.
2007-01-04 22:22:37 · answer #2 · answered by teekshi33 4 · 0⤊ 0⤋
x⁴- 19x² + 25
x⁴- 19x² + (19/2)² - (19/2)² + 25
( x² - 19/2 )² - 261/4
there u go, this leaves only x² to get sqrt of the other side of the equation to get the value of x.
2007-01-05 11:29:54 · answer #3 · answered by xyeslam 3 · 0⤊ 0⤋
This can't be factored any more then it is. You can't multiply two numbers to get 25 and add them together to get -19.
2007-01-04 22:22:58 · answer #4 · answered by Nick R 4 · 0⤊ 0⤋