Question #189623

Evaluate the following polynomial expression using Horner’s rule. Assume the value of x is 3.

𝑃(π‘₯)=10π‘₯τ°€ +6π‘₯τ° +3π‘₯τ°‚ βˆ’6π‘₯τ°ƒ +8π‘₯+15

Show all the intermediate steps.


1
Expert's answer
2021-05-07T14:23:26-0400


Problem is 𝑃(π‘₯) = 10x5 + 6x4+ 3x3 βˆ’ 6x2 + 8π‘₯ + 15

At x= 3

Or xo=3x_o=3


So

This is of this type


f(x) = a0 + a1x + a2x2 + a3x3 + a4x4 + a5x5


Can be arranged as follows

at xox_o

f(x0) = a0 + x0(a1 + x0(a2 + x0(a3 + x0(a4 + a5x0))))


So

At k= 5

b5= a5=10


At k=4

b4=a4+xob5= 6+3Γ—10=36


At k=3

b3=a3+xob4=3+3Γ—36=111


At k=2

b2=a2+xob3=-6+3Γ—111=327


At k=1

b1=a1+xob2=8+3Γ—327=989


At k=0

b0=a0+xob1=15+3Γ—989=2982


Therefore

f(3)=2982answer\boxed{f(3)=2982}answer





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