What is the coefficient of in the expansion above?
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A way to determine the coefficient of x 4 is by expanding the innermost algebraic expression, which is x ( x + 2 ) + 3 = x 2 + 2 x + 3 Note that there are 6 preceding x 's of the expression above. From the previous statement, we are now certain that the highest degree of the polynomial is 8 . It now implies that its expansion would start with x 6 ( x 2 + 2 x + 3 ) = x 8 + 2 x 7 + 3 x 6 and so on, until reaching 9 . Therefore, the succeeding terms decrease in its degree. Hence by counting, we arrive at an answer of 5 .