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Ruffini's Rule Polynomial Division

The document provides a series of problems involving dividing polynomials using Ruffini's rule, finding polynomials given certain quotients, and factoring polynomials. It contains 13 problems involving dividing polynomials using Ruffini's rule, finding polynomials that satisfy given quotients, determining values of k that make a quotient exact, finding remaining roots and factoring a polynomial given some known roots.

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Daniel Porretti
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25 views1 page

Ruffini's Rule Polynomial Division

The document provides a series of problems involving dividing polynomials using Ruffini's rule, finding polynomials given certain quotients, and factoring polynomials. It contains 13 problems involving dividing polynomials using Ruffini's rule, finding polynomials that satisfy given quotients, determining values of k that make a quotient exact, finding remaining roots and factoring a polynomial given some known roots.

Uploaded by

Daniel Porretti
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Matemática III Ruffini-20/D

FISICANET fisicanet@interlap.com.ar

Leer atentamente antes de proceder


1) Dividir aplicando regla de Ruffini:
a) (-2.x3 + x4 - 1):(x + 2) =
b) (a.x4 - a5):(x - a) =
c) [(1 + i).x4 - i.x3 + x - 9.(3 - i)]:(x + 3 - i) =
d) (3.x3 - 6.x + 1):(3.x - 9) =
e) (4.z3 + z2):[z + (1 + i)] =
f) (i.x4 - 2.x2 + i):(x + i) =
g) (-a.x3 + a3.x - 1):(x - a) =
h) (3.x4 + x3/2 - 29.x2/6 + 16.x/15 - 3/15):(x + 1/3) =
i) (x5 - 2.x3 - x2 + 3):(x - 3) =
j) (3.x8/2 - 7.x6/4 + 9.x4/4 + x - 3):(x - 1) =
k) (2.a4 + 11.a/2 + 3 - a2/2):(a + 3/2) =
l) 3.x3 - 32.x2/15 - 24.x/5 + 10):(x - 0,6) =
m) (3.y4 + 2.y3/5 - 27.y2/25 + 9.y/10 + 1):(y + 0,2) =
2) Hallar el polinomio P(x) tal que:
a) P(x)/(x + a) = x3 - a.x2 + a2.x - a3
b) (x5 - 32)/P(x) = x4 + 2.x3 + 4.x2 + 8.x + 16
c) P(x)/(x + 3) = x3 - 3.x2 + 9.x - 27
d) P(x)/(x - 3) = x3 + 3.x2 + 9.x + 27
3) Dada la expresión:

x 5  x 4 - 7.x 3  x 2  k.x
S(x) 
x2 - 1
a) Hallar aplicando sucesivamente la regla de Ruffini el valor de k para que el cociente sea exacto.
b) Decir para que valores no esta definido S(x).
c) Factorear S(x).
4) Obtener las restantes raíces y factorear el polinomio: P(x) = x 5 - 3.x4 - x3 + 11.x2 - 12.x + 4, sabiendo
que 2 y -2 son raíces.

Ricardo Santiago Netto

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