Factor the polynomial completely. If the polynomial cannot be factored, write prime.
x^4 + 24x^2 - 25
(x^2 - 1)(x^2 + 25)
(x + 1)(x - 1)(x + 5)(x - 5)
(x + 1)(x - 1)(x^2 + 25)
(x - 1)^2(x^2 + 25)
2007-07-24 10:58:51 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
(x^2 - 1)(x^2 + 25)
(x+1)(x-1)(x^2+25)
2007-07-24 11:03:02 · answer #1 · answered by leo 6 · 1⤊ 1⤋
Given, x^4 + 24x^2 - 25
= (x²)² + 24x² - 25
Let, x² be equal to k
= k² + 24k - 25
Using "splitting the middle term" method,
= k² + 25k - 1k - 25
= k(k+25) -1(k+25)
= (k-1)(k+25)
Substituting the value of k = x²
= (x²-1)(x²+25)
(x²-1) can further be factorised.
= (x+1)(x-1)(x²+25) . . . . . .Ans
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2007-07-24 19:35:14 · answer #2 · answered by Joymash 6 · 0⤊ 0⤋
x^4 + 24x^2 - 25
Let y = x^2
Then y^2+24y-25
= (y+25)(y-1)
= (x^2+25)(x^2-1)
= (x^2+25)(x+1)(x-1)
2007-07-24 18:11:34 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
(x^2-1)(x^2+25)
(x+1)(x-1)(x^2+25)
2007-07-24 18:06:10 · answer #4 · answered by Kenneth H 3 · 0⤊ 0⤋