+1206 Find h(x), with terms in order of decreasing degree, if \(3x^4+2x-1+h(x)=5x^2-6x-1.\)
+128475 Not too bad.....
We need to figure this
3x^4 + 2x + 1
+ h(x)
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5x^2 - 6x - 1
Note that the first term of h(x) must have been -3x^4 since there is no fourth power term in the final result
The second term must have been 5x^2
The third term must have been 2x + ax = - 6x ....so ax = -8x
And the last term must have been -1 + k = -1 ⇒ k = 0
So h(x) must have been -3x^4 + 5x^2 - 8x
Check :
3x^4 + 0x^2 + 2x - 1
-3x^4 + 5x^2 - 8x + 0
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5x^2 - 6x - 1
