<PRE><B>Question 995921</B>
.
if x+1 is a factor of x^3+3x^2+kx+4, find the value of k.
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If &amp;nbsp;x+1&amp;nbsp; is a factor of &amp;nbsp;{{{x^3+3x^2+kx+4}}}, &amp;nbsp;then &amp;nbsp;x = -1 &amp;nbsp;is the root of this polynomial.


It means that if we substitute &amp;nbsp;-1&amp;nbsp; instead of &amp;nbsp;x&amp;nbsp; into the polynomial, &amp;nbsp;we get &amp;nbsp;0:


{{{(-1)^3 + 3(-1)^2 + k*(-1) + 4}}} = {{{0}}}, &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;or


-1 + 3 - k + 4 = 0.


It is the equation to determine &amp;nbsp;k, &amp;nbsp;and it gives


k = -1 + 3 + 4 = 6.


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