+744 What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?
+1001
(x3 + x2 + x + 1)(x4 - 8x3 + 17x2 - 23x + 14)
Every term in the first expression will be multiplied with every term in the second expression.
Which term(s) times which term(s) will result in x with no exponent....
(x3 + x2 + x + 1)(x4 - 8x3 + 17x2 - 23x + 14) gives us 14x
(x3 + x2 + x + 1)(x4 - 8x3 + 17x2 - 23x + 14) gives us 23x
Add them together 37x
So the coefficient the problem is asking for is 37.
.
+1001
Dang, I made a careless mistake. I wonder how many of you caught it.
I overlooked the minus in front of 23x. Too late to edit my mistake, grrr.
The lines should look like this:
(x3 + x2 + x + 1)(x4 – 8x3 + 17x2 – 23x + 14) gives us 14x
(x3 + x2 + x + 1)(x4 – 8x3 + 17x2 – 23x + 14) gives us –23x
Add them together –9x
So the coefficient the problem is asking for is –9.
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