SOLUTION: Form a polynomial whose zeros and degree are given. ​Zeros: negative −2​, 2​, 4​, 5​; degree 4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Form a polynomial whose zeros and degree are given. ​Zeros: negative −2​, 2​, 4​, 5​; degree 4      Log On


   

Question 1097564: Form a polynomial whose zeros and degree are given.
​Zeros: negative −2​, 2​, 4​, 5​; degree 4
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, for a zero at -2, that means you'll have a factor (x + 2) (its always the opposite sign because the zero 'a' is the value that makes x + a = 0 and that happens at x = -a). Similarly, for the zero at 2, you have a factor (x-2)...
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Applying this idea to each zero gives you the four factors:
(x + 2)(x - 2)(x - 4)(x-5) =
+%28x%5E2+-+4%29%28x+-+4%29%28x+-+5%29+ =
+%28x%5E3+-+4x%5E2+-+4x+%2B+16%29%28x-5%29+ =
+x%5E4+-4x%5E3+-+4x%5E2+%2B+16x+-5x%5E3+%2B20x%5E2+%2B+20x+-+80+ =
+highlight%28x%5E4+-9x%5E3+%2B16x%5E2+%2B+36x+-+80%29+
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Check:
x=4: +4%5E4+-+9%2A4%5E3+%2B+16%2A4%5E2+%2B+36%2A4+-+80+=+256+-+576+%2B+256+%2B+144+-+80+=+0+
x=2: +2%5E4+-+9%2A2%5E3+%2B+16%2A2%5E2+%2B36%2A2+-+80+=+16+-+72+%2B+64+%2B+72+-+80+=+0+
and similar for x=-2 and x=5.