we can factorize the equation (x+r1)(x+r2)(x+r3), where r1,r2 and r3 are root of equation

so 3 multiplication

so 3 multiplication

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gatecse
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in Numerical Methods
Sep 15, 2014

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29 votes

Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input $x$ is:

- 3
- 4
- 6
- 9

0

0

**apply the Horner's Rules **

**P(x)= a0 + a1x + a2x^2 + a3x^3**

**P(x)= a0 +(( a1+a2x + a3x^2) x ) // 1 multipication taking the x common**

**P(x)= a0 +(( a1+(a2 + a3x ) x ) x // 2 multipication in x in inner bracket**

**P(x)= a0 +( ( a1+(a2 + a3x ) x ) x ) // 3 multipication entire bracket**

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