(x + 3) (x - 4) - (x + 2) (x - 6)
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1
ANSWER
As x
2
+x−6=(x+3)(x−2)
Let f(x)=2x
4
+x
3
−ax
2
+bx+a+b−1
We get
f(−3)=2(−3)
4
+(−3)
3
−a(−3)
2
+b(−3)+a+b−1=0
⇒134−8a−2b=0⇒4a+b=67→ (1)
And
f(2)=2(2)
4
+2
3
−a(2)
2
+2b+a+b−1=0
⇒39−3a+3b=0⇒a−b=13→(2)
Solving (1) and (2), we get
a=16,b=3
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