Evaluate the following polynomial expression using Hornerβs rule. Assume the value of x is 3.
π(π₯)=10π₯τ° +6π₯τ° +3π₯τ° β6π₯τ° +8π₯+15
Show all the intermediate steps.
Problem is π(π₯) = 10x5Β + 6x4+ 3x3Β β 6x2Β + 8π₯ + 15
At x= 3
Or "x_o=3"
So
This is of this type
f(x) = a0Β + a1x + a2x2Β + a3x3Β + a4x4Β + a5x5
Can be arranged as follows
at "x_o"
f(x0) = a0Β + x0(a1Β + x0(a2Β + x0(a3Β + x0(a4Β + a5x0))))
So
At k= 5
b5= a5=10
At k=4
b4=a4+xob5= 6+3Γ10=36
At k=3
b3=a3+xob4=3+3Γ36=111
At k=2
b2=a2+xob3=-6+3Γ111=327
At k=1
b1=a1+xob2=8+3Γ327=989
At k=0
b0=a0+xob1=15+3Γ989=2982
Therefore
"\\boxed{f(3)=2982}answer"
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