# Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. (1,2),(2,1),(3,3),(6,1)(1,2),(2,1),(3,3),(6,1).

Annette Arroyo 2020-11-09 Answered
Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. $\left(1,2\right),\left(2,1\right),\left(3,3\right),\left(6,1\right)\left(1,2\right),\left(2,1\right),\left(3,3\right),\left(6,1\right)$.
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Step 1
With , the Langrange interpolating polynomials give
${p}_{1}\left(x\right)=\frac{\left(x-{x}_{2}\right)\left(x-{x}_{3}\right)\left(x-{x}_{4}\right)}{\left({x}_{1}-{x}_{2}\right)\left({x}_{1}-{x}_{3}\right)\left({x}_{1}-{x}_{4}\right)}$
$=\frac{\left(x-2\right)\left(x-3\right)\left(x-6\right)}{\left(1-2\right)\left(1-3\right)\left(1-6\right)}$
$=\frac{\left({x}^{2}-5x+6\right)\left(x-6\right)}{\left(-1\right)\left(-2\right)\left(-5\right)}$
$=-\frac{{x}^{3}-6{x}^{2}-5{x}^{2}+30x+6x-36}{10}$