Question 1105249
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(1) {{{f(5) = 5^3+5^2-21*5-45 = 125+25-105-45 = 0}}}
Yes, (x-5) is a factor of f(x), so (x-5) represents a dimension of the prism.<br>
{{{f(-1) = (-1)^3+(-1)^2-21(-1)-45 = -1+1+21-45 = -24}}}
No, (x+1) is not a factor of f(x), so (x+1) does not represent a dimension of the prism.<br>
(2) {{{x^3+x^2-21x-45 = (x-5)(x^2+6x+9) = (x-5)(x+3)^2}}}<br>
(3) {{{(x+3)^2 = 289}}}
{{{x+3 = 17}}}
{{{x = 14}}}<br>
The dimensions are (x+3) by (x+3) by (x-5) = 17x17x9.