Question 1161068
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The graph passing through the origin means one root is 0; the polynomial has a factor of x.<br>
A zero of i means a zero of -i.  The quadratic factor producing those two roots is {{{x^2+1}}}<br>
A zero of 4-i means a zero of 4+1.  The quadratic factor producing those two roots is {{{x^2-8x+17}}}<br>
The polynomial is<br>
{{{a(x)(x^2+1)(x^2-8x+17)}}}<br>
The constant a is determined by the requirement that p(5) = 520.<br>
{{{a(5)(26)(2) = 520}}}
{{{260a = 520}}}
{{{a = 2}}}<br>
The polynomial function is<br>
{{{2(x)(x^2+1)(x^2-8x+17)}}}<br>