what must be subtracted from x3 -3x2+4x-6 to get x2- 2x+1
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Step-by-step explanation:
The given expression is
x^4+2x^3-2x^2+4x+6x
4
+2x
3
−2x
2
+4x+6
The divisor is x^2+2x-3x
2
+2x−3 .
Use long division method to divide the given expression by x^2+2x-3x
2
+2x−3 .
x^4+2x^3-2x^2+4x+6=x^2+1+\frac{2x + 9}{x^2+2x-3}x
4
+2x
3
−2x
2
+4x+6=x
2
+1+
x
2
+2x−3
2x+9
The remainder is 2x+9. It means if we subtract (2x + 9) from given expression, then it is exactly divisible by x^2+2x-3x
2
+2x−3 .
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