Solve for (B) with detais. Also is there any way to know thwe numbers of multipl

Question

Solve for (B) with detais. Also is there any way to know thwe numbers of multiplications and the nuber of addition opreations without solving it. such as n+1/n= somthing. either way solve B only neatly and clearly

Nested Multiplication (a) Rewrite the following polynomials in nested form: P2(x) -3x4 +4x3 +5x25x1 b) Explain how to evaluate the following polynomial for a given input x, using as few op- erations as possible. State the number of multiplications and additions required by the method you suggest

Explanation / Answer

Write P4(x) as

P4(x) = a0 + x5 * ( a5 + x5 * (a10 + x5 * (a15)))

Clearly we need 3 multiplication and 3 additions to evelaute this expression

and to calculate x5 = x2 * x2 * x ,

we need 3 multiplications ( two in the calculation and one in finding x2 = x*x )

So total is 3+3 = 6 multiplications and 3 additions.

and P5(x) as

P5(x) = x7 *  ( a7 + x5 * (a12 + x5 * ( a17 + x5 * ( a22))))

Clearly we need 4 multiplication and 3 additions in calculating above expression and

x2 = x*x (1 multiplication)

x3 = x*x2 (1+1= 2 multiplication )

x5 = x3 * x2 ( 2+1 = 3 multiplication)

x7 = x5 * x2 = (3+1 = 4 multiplication)

we need x5 and x7 , we will need 4 multiplications.

Total is 4+4 = 8 multiplications and 3 additions

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