# 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).

Use the appropriate Lagrange interpolating polynomials to find the cubic polynomial whose graph passes through the given points. $\left(1,2\right),\left(2,1\right),\left(3,3\right),\left(6,1\right)\left(1,2\right),\left(2,1\right),\left(3,3\right),\left(6,1\right)$.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

jlo2niT

Step 1
With , the Langrange interpolating polynomials give
${p}_{1}\left(x\right)=\frac{\left(x-{x}_{2}\right)\left(x-{x}_{3}\right)\left(x-{x}_{4}\right)}{\left({x}_{1}-{x}_{2}\right)\left({x}_{1}-{x}_{3}\right)\left({x}_{1}-{x}_{4}\right)}$
$=\frac{\left(x-2\right)\left(x-3\right)\left(x-6\right)}{\left(1-2\right)\left(1-3\right)\left(1-6\right)}$
$=\frac{\left({x}^{2}-5x+6\right)\left(x-6\right)}{\left(-1\right)\left(-2\right)\left(-5\right)}$
$=-\frac{{x}^{3}-6{x}^{2}-5{x}^{2}+30x+6x-36}{10}$