Find the value of b for which 2x+3 is a factor of 2x^3+9x^2-x-b
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Let p(x)=2x^3+9x^2-x-b
And g(x)=2x+3
So ,zero of polynomial= 2x+3=0
2x =-3
X =-3/2
By remainder theoram = p(x)=2x^3+9x^2-x-b
P(-3/2) = 2(-3/2)^3+9(-3/2)^2-(-3/2)-b
=2(-27/8)+9(6/4)+3/2-b
=-57/8+72/4+3/2-b
=LCM of 8,4, 3 ,1= 8
=-57/8+72×2/4×2+3×4/2×4-b×8/1×8
=-57/8+ 144/8+12/8-8b/8
=-57+144+12-8b/8
=99-8b/8
-99=-8b/8
-99=b
{8/8 is cut}
And g(x)=2x+3
So ,zero of polynomial= 2x+3=0
2x =-3
X =-3/2
By remainder theoram = p(x)=2x^3+9x^2-x-b
P(-3/2) = 2(-3/2)^3+9(-3/2)^2-(-3/2)-b
=2(-27/8)+9(6/4)+3/2-b
=-57/8+72/4+3/2-b
=LCM of 8,4, 3 ,1= 8
=-57/8+72×2/4×2+3×4/2×4-b×8/1×8
=-57/8+ 144/8+12/8-8b/8
=-57+144+12-8b/8
=99-8b/8
-99=-8b/8
-99=b
{8/8 is cut}
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