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# Algebra

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What is the coefficient of \$x\$ in \$(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)\$?

Jul 14, 2024

#1
+971
0

(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.

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Jul 14, 2024
#2
+971
0

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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Bosco  Jul 15, 2024
edited by Bosco  Jul 15, 2024