SOLUTION: x^4-5x^2-36 Help me. How do you factorize this problem?

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Question 596272: x^4-5x^2-36
Help me. How do you factorize this problem?
Found 3 solutions by jim_thompson5910, Edwin McCravy, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4-5x%5E2-36

x%5E4-9x%5E2%2B4x%5E2-36 See Note at bottom

%28x%5E4-9x%5E2%29%2B%284x%5E2-36%29

x%5E2%28x%5E2-9%29%2B4%28x%5E2-9%29

%28x%5E2%2B4%29%28x%5E2-9%29

%28x%5E2-9%29%28x%5E2%2B4%29

%28x-3%29%28x%2B3%29%28x%5E2%2B4%29

So x%5E4-5x%5E2-36 completely factors to %28x-3%29%28x%2B3%29%28x%5E2%2B4%29


Note: the numbers -9 and 4 multiply to -36 (the last number) and add to -5 (the second coefficient)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
x4 - 5x² - 36

(x² - 9)(x² + 4)

(x - 3)(x + 3)(x² + 4)

Edwin

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E4+-+5x%5E2+-+36+
Let +z+=+x%5E2+
+z%5E2+-++5z+-+36+
Complete the square
+z%5E2+-++5z+-+36+=+0+
+z%5E2+-++5z+=+36+
+z%5E2+-+5z+%2B+%285%2F2%29%5E2+=+36+%2B+%285%2F2%29%5E2+
+z%5E2+-+5z+%2B+25%2F4+=+144%2F4+%2B+25%2F4+
+z%5E2+-+5z+%2B+25%2F4+=+169%2F4+
+%28+z+-+5%2F2+%29%5E2+=+%28+13%2F2+%29%5E2+
Take the square root of both sides
+z+-+5%2F2+=+13%2F2+
+2z+-+5+=+13+
+2z+-+18+=+0+
+z+-+9+=+0+
and, also
+z+-+5%2F2+=+-13%2F2+
+2z+-+5+=+-13+
+2z+%2B+8+=+0+
+z+%2B+4+=+0+
-------------
The factoring is
+%28+z+-+9+%29%2A%28+z+%2B+4+%29+
and, since
+z+=+x%5E2+
+%28+x%5E2+-+9+%29%2A%28+x%5E2+%2B+4+%29+
This can be further factored into
+%28+x+%2B+3+%29%2A%28+x+-+3+%29%2A%28+x%5E2+%2B+4+%29+