find a and b if 2x+3 is one factors of polynomial p(x)=2x^3+9x^2-x-b
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Step-by-step explanation:
ANSWER
Since 2x+3 is a factor of the polynomial p(x)=2x
3
+9x
2
−x−b
Therefore, by Factor theorem p(−
2
3
)=0
⇒2(−
2
3
)
3
+9(−
2
3
)
2
−(−
2
3
)−b=0
⇒−
4
27
+
4
81
+
2
3
−b=0
⇒
4
−27+81+6
−b=0⇒b=
4
60
=15
∴ b=15
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