Operaciones con polinomios

Aquí os dejo unos ejercicios de suma, resta y multiplicación de polinomios.

Siendo:
\(P\left( x\right) =2x^{2}-3x+1\)
\(Q\left( x\right) =5x^{2}+x-3\)
\(R\left( x\right) =4x-3\)
\(S\left( x\right) =x^{3}+2x^{2}-x+3\)

\(\bullet\ P\left( x\right) +Q\left( x\right) =\)

\(P\left( x\right) +Q\left( x\right) =2x^{2}-3x+1+5x^{2}+x-3\)

\(\boxed{P\left( x\right) +Q\left( x\right) = 7x^{2}-2x-2}\)

\(\bullet\ P\left( x\right) +Q\left( x\right) -S\left( x\right)  =\)

\(\ P\left( x\right) +Q\left( x\right) -S\left( x\right)  = 2x^{2}-3x+1+5x^{2}+x-3-x^{3}-2x^{2}+x-3\)

\(\boxed{\ P\left( x\right) +Q\left( x\right) -S\left( x\right)  = -x^{3}+5x^{2}-x-2}\)

\(\bullet\ R\left( x\right)\cdot P\left( x\right) =\)

\(\ R\left( x\right)\cdot P\left( x\right) = \left( 4x-3\right) \left( 2x^{2}-3x+1\right)\)

\(\ R\left( x\right)\cdot P\left( x\right) = 8x^{3}-12x^{2}+4x-6x^{2}+9x-3\)

\(\boxed{\ R\left( x\right)\cdot P\left( x\right) = 8x^{3}-18x^{2}+13x-3}\)

\(\bullet\ R\left( x\right)\cdot Q\left( x\right) =\)

\(R\left( x\right)\cdot Q\left( x\right) = \left( 4x-3\right) \left( 5x^{2}+x-3\right)\)

\(R\left( x\right)\cdot Q\left( x\right) = 20x^{3}+4x^{2}-12x-15x^{2}-3x+9\)

\(\boxed{R\left( x\right)\cdot Q\left( x\right) = 20x^{3}-11x^{2}-15x+9}\)

\(\bullet\ P\left( x\right) \cdot S\left( x\right) =\)

\(P\left( x\right)\cdot S\left( x\right) = \left( 2x^{2}-3x+1\right) \left( x^{3}+2x^{2}-x+3\right)\)

\(P\left( x\right)\cdot S\left( x\right) = 2x^{5}+4x^{4}-2x^{3}+6x^{2}-3x^{4}-6x^{3}+3x^{2}-9x+x^{3}+2x^{2}-x+3\)

\(\boxed{\ P\left( x\right)\cdot S\left( x\right) =2x^{5}+x^{4}-7x^{3}+11x^{2}-10x+3}\)

Si veis alguna errata o tenéis alguna duda dejad un comentario