document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105249>Question 1105249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Polynomial Function for Volume\r<BR>\n" );
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document.write( "The polynomial function given below represents the volume of a rectangular prism with a square base. Each binomial factor of the polynomial represents one dimension of the rectangular prism.\r<BR>\n" );
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document.write( "f(x) = x^3 + x^2 – 21x – 45\r<BR>\n" );
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document.write( " Use the Remainder Theorem to determine whether the binomials x – 5 and x + 1 represent dimensions of the rectangular prism. Enter your answer and explanation in the box.\r<BR>\n" );
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document.write( "Rewrite the given function as a product of binomial factors. Enter your answer and explanation in the box.\r<BR>\n" );
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document.write( "The area of the base of the rectangular prism is 289 cm2. What are the dimensions of the rectangular prism? Enter your answer and explanation in the box. </SPAN>\n" );
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document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29+=+5%5E3%2B5%5E2-21%2A5-45+=+125%2B25-105-45+=+0 ALIGN=MIDDLE  ALT=\"f%285%29+=+5%5E3%2B5%5E2-21%2A5-45+=+125%2B25-105-45+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Yes, (x-5) is a factor of f(x), so (x-5) represents a dimension of the prism.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29+=+%28-1%29%5E3%2B%28-1%29%5E2-21%28-1%29-45+=+-1%2B1%2B21-45+=+-24 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+%28-1%29%5E3%2B%28-1%29%5E2-21%28-1%29-45+=+-1%2B1%2B21-45+=+-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "No, (x+1) is not a factor of f(x), so (x+1) does not represent a dimension of the prism.<br><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bx%5E2-21x-45+=+%28x-5%29%28x%5E2%2B6x%2B9%29+=+%28x-5%29%28x%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E3%2Bx%5E2-21x-45+=+%28x-5%29%28x%5E2%2B6x%2B9%29+=+%28x-5%29%28x%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2+=+289 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2+=+289\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3+=+17 ALIGN=MIDDLE  ALT=\"x%2B3+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+14 ALIGN=MIDDLE  ALT=\"x+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The dimensions are (x+3) by (x+3) by (x-5) = 17x17x9. </SPAN>\n" );
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