document.write( "Question 974211: Find a polynomial p of degree 3 such that −2, −1, and 4 are zeros of p and
\n" ); document.write( "p(1) = 2 \n" ); document.write( "

Algebra.Com's Answer #596175 by Boreal(15235) $\"\"$ $\"About$

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a(x^3+x^2+x+d)=0\r
\n" ); document.write( "\n" ); document.write( "factors are inverses of roots
\n" ); document.write( "(x+2)(x+1)(x-4)
\n" ); document.write( "Multiply them:
\n" ); document.write( "first two are x^2+3x+2
\n" ); document.write( "multiply by (x-4)
\n" ); document.write( "x^3-4x^2+3x^2-12x+2x-8
\n" ); document.write( "=x^3-x^2-10x-8, the general form of the polynomial\r
\n" ); document.write( "\n" ); document.write( "a(x^3-x^2-10x-8)=2, when x=1\r
\n" ); document.write( "\n" ); document.write( "a(1-1-10-8)=2
\n" ); document.write( "-18a=2
\n" ); document.write( "a=-1/9\r
\n" ); document.write( "\n" ); document.write( "polynomial is (-1/9)(x^3-x^2-10x-8)\r
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\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F9%29%28x%5E3-x%5E2-10x-8%29%29\"$ \r
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