Divide 4ϰ² + 2ϰ³ + 5ϰ - 6 by 2ϰ² + 1 + 3ϰ and verify the division algorithm (CLASS 10 / MATHS)
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Step-by-step explanation:
Here, the dividend is x
3
+4x
2
−5x+6, the divisor is x+1, the quotient is x
2
+3x−8 and the remainder is 14, therefore,
x
3
+4x
2
−5x+6=[(x+1)(x
2
+3x−8)]+14
⇒x
3
+4x
2
−5x+6=[x(x
2
+3x−8)+1(x
2
+3x−8)]+14
⇒x
3
+4x
2
−5x+6=x
3
+3x
2
−8x+x
2
+3x−8+14
⇒x
3
+4x
2
−5x+6=x
3
+3x
2
+x
2
−8x+3x−8+14
⇒x
3
+4x
2
−5x+6=x
3
+4x
2
−5x+6
Hence, the division algorithm is verified.
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