For the following polynomial Px 2x4 3x2 3x 4 Evaluate P3

For the following polynomial P(x) = 2x^4 - 3x^2 + 3x - 4, Evaluate P(3) by using Horner\'s method.

Solution

P(x) = 2x⁴ - 3x² + 3x - 4

= x( 2x³ - 3x¹ + 3) - 4

= x ( x (( 2x² - 3x )+ 3)) - 4

= x ( x (x( 2x - 3 )+ 3)) - 4

  = x ( x (x(x( 2) - 3 )+ 3)) - 4

Also,we can use synthetic method

2 0 -3 3 -4

3

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2

Now multiply the number on the bottom and total as follows.

2 0 -3 3 -4

3 6 18 45 144

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2 6 15 48 140

We have f(3)=32. Let\'s run a check

f(3)=2*8139+3*34=.140