document.write( "Question 1097564: Form a polynomial whose zeros and degree are given.
\n" ); document.write( "Zeros: negative −2, 2, 4, 5; degree 4 \n" ); document.write( "

Algebra.Com's Answer #712006 by math_helper(2461) $\"\"$ $\"About$

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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)...\r
\n" ); document.write( "\n" ); document.write( "—
\n" ); document.write( "Applying this idea to each zero gives you the four factors:
\n" ); document.write( "(x + 2)(x - 2)(x - 4)(x-5) =
\n" ); document.write( " $\"+%28x%5E2+-+4%29%28x+-+4%29%28x+-+5%29+\"$ =
\n" ); document.write( " $\"+%28x%5E3+-+4x%5E2+-+4x+%2B+16%29%28x-5%29+\"$ =
\n" ); document.write( " $\"+x%5E4+-4x%5E3+-+4x%5E2+%2B+16x+-5x%5E3+%2B20x%5E2+%2B+20x+-+80+\"$ =
\n" ); document.write( " $\"+highlight%28x%5E4+-9x%5E3+%2B16x%5E2+%2B+36x+-+80%29+\"$
\n" ); document.write( "—
\n" ); document.write( "Check:
\n" ); document.write( " x=4: $\"+4%5E4+-+9%2A4%5E3+%2B+16%2A4%5E2+%2B+36%2A4+-+80+=+256+-+576+%2B+256+%2B+144+-+80+=+0+\"$
\n" ); document.write( " x=2: $\"+2%5E4+-+9%2A2%5E3+%2B+16%2A2%5E2+%2B36%2A2+-+80+=+16+-+72+%2B+64+%2B+72+-+80+=+0+\"$
\n" ); document.write( " and similar for x=-2 and x=5.\r
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