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Álgebra Leyes de exponentes A) 15
NIVEL BÁSICO
C)
D) 35
Sheet Music 1.
B) 30
Si x ≠ 0 y n ∈ N, reduzca la siguiente expresión.
E)
NIVEL INTERMEDIO
2
7 − 2) veces ( x ⋅ x ⋅ … ⋅ x x10−2 ⋅ ⋅ x ⋅… ⋅x x ⋅ x ⋅ … ⋅ x x ( +18) veces veces n
n
n
n
A) x2
B) x–1
D) x3 2.
6.
64 9
C) x
y
2⋅3
+
4⋅3
−
2
y
=
481
−
x
13
B)
6
C)
23
D) 6
B) 12/5
D) 2
7.
C) 8 E) 3
E)
Si se cumple que x
Si 2 x – 2 x – 3=14,
Unlock full access with a A) free2trial.
halle E = x −2 x 2 + 9
D) 12 Download With Free Trial
A) 5
B) 4
D) 7
C) 3 E) 6
8.
Master your semester with Scribd Determine el valor reducido de la siguiente 4. & The New York Times expresión. x
−
=
6,
B) 3
C) 5 E)
¿Qué valor debe estar en el recuad
para que la siguiente igualdad se ver
UNMSM 2013 - II
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x 6 6
determine el valor de x x . You're Reading a Preview
3.
64
8
x −1
A) 24/5
1
1
−
calcule x–1.
A)
y
Si 2 equivale a 3 , calcule el equivalente de x + 3
2( x 5)
E) 1
x
2
Si se cumple que
a
−c − b
−1
⋅
= 1;
a ≠1
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Álgebra 10.
of 12
Ex_4B_pol+frac.alg Algebra Basica
Reduzca la expresión
Sheet Music
m+ n
E = 2 n
a
a
+
a
a
; a>0
m− n
13. E + E + E + ... + E
=
3
x
3
x
2
x
=x
4 −1 a y
10
EE ... E
=
a
7 (3
b−1
10 veces
b+1
9
III. E =a2
−
)
2 (3
2b
)
=
b
3
halle la suma de a+ b.
A) I y III
B) solo I
D) todas
C) I y II
A) 4
E) solo III
B) 6
D) 3
NIVEL AVANZADO 14.
Determine el valor aproximado d
You're Reading a Preview 11.
C)
2
Si x es un número positivo, tal qu
na
n veces
II.
1
D) 6
e indique las proposiciones correctas. I.
B)
n
3 m+ 2 n
+
3 m
m
A)
3 3
Unlock full access with a free trial. Determine el valor de x si se cumple que J = 1 27 3 x −
−
(0, 01)
=
0, 0001
Download With Free Trial
6+
6+
A) 1 A) 1
B) 2
D) 8
3
3
3
3
6 + ...
−
2 2 2
B) 2
D) 3
C) 4 E) 6
Master your semester with Scribd Simplifique siguiente expresión. & The12.New Yorkla Times Special offer for students: Only $4.99/month. 1
3
2 n
−
n−1
21
Si t t – t=1, determine el equivale Read Free Foron 30this Days Sign up to vote title de K .
15.
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K
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=
t t t
( t + 1)( t +1)
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Álgebra Productos notables NIVEL BÁSICO
NIVEL INTERMEDIO
Sheet Music
1.
Sean x e y dos números, de modo que x
+
xy
y
=
4 3
=
2 3
−
+
6.
E =24 · (52+1)(54+1)(58+1)+1
2
3
A) 625
Calcule el valor de 2 x 2 + 2 y2 . A) 3
B) 2
•
4
•
+
4 y
x
+
y
=
xy si
se sabe que
=
Determine el valor de 3
x
+ 3
3
B) 5
2
a
+
a
A) b3 D) a3
=
3
2
+
y
2
si se sa
xy
7
x
4
B) 2 + 3 7
C) 9 E) 100
−
6
b
⋅
3
a
2
−
B) b2
D) 7 − 3 3 7
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C)
3
E)
3
8.a Preview Halle el valor de (a – b)6 si se sabe qu You're Reading (a – b)2 – (a – b)= –1
Unlock full access with a free trial. a
4
−
b
6
A) Trial –1 Download With Free D) 3 2
C) b5 E) a2
Master your semester with Scribd Si a > 0, simplifique la siguiente expresión. 4. x & The(aNew a x – a – xTimes +a – x)(York )(a4 x+1+a– 4 x) A) a6 x+a– 6 x
y
A) 7
= 10
Simplifique la expresión P. P
7.
x
4
A) 8 D) 13 3.
E) 125
y x
C) 5
D) 1
E) 4
Calcule el valor de
B) 25
C) 2
D) 3 2.
Calcule el valor de 16 E si se sabe que
9.
Si
x
2
y
−
B) 1
C) 2 E) 3
y
2 =
3( x − y);
x≠
0 e
y≠
x
4 yForon x this Read Free Sign up to title xvote Days y30 = x + Not halle Useful y useful H
y anytime. x Cancel
0
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Ex_4B_pol+frac.alg Algebra Basica
Álgebra NIVEL AVANZADO
Search document
A)
3
Sheet Music 11.
D)
¿Que valor se obtiene al simplificar la expresión M ?
B) 1
2 1 2
M =( x+ y+ z)2+( x – y+ z)2+(– x+ y+ z)2+
( x+ y – z)2 – 4( x2+ y2+ z2)
14.
Dados los números 2
A = ( 3 3 )
A) 1
2
3
+1
y B = ( 3 2 )
+
3
C) 0 D) x+ y+ z
A) –1
E) 2( x2+ y2+ z2) Dado que 4 n
−
B) 0 1
n 4
=
C) 1
1,
calcule el valor de 22 n +
D) 3 1 2 n
E) 5
.
2
15. Si a+ b=1; ab=1 You're Reading a Preview
A) 5 B) 4 C) 3 D) 5 E) 3 13.
3
2 calcule el valor de 1 + + 1 A
B) –1
12.
+
halle el valor reducido de E .
Unlock full access with a free trial. E
=
a
2048
Download With Free Trial 2
2
2
2
B) –1
halle el valor de E .
C) 0
Special offer for students: Only $4.99/month.
b
2048
1 +
2048
a
1 +
2048
b
A) – 2
Si (2 x – y – z) – (2 x – y+ z) =2[(y–2 x) + z ]
Master your − z 2 2 x − y with Scribd 2 x semester + E = − 2 2 z z y & The New York Times
+
D) 1 Free Read Foron 30this Days Sign up to vote title 2 E)Useful Not useful Cancel anytime.
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Álgebra Polinomios 5.
NIVEL BÁSICO
Ex_4B_pol+frac.alg Algebra Basica
polinomio
Sheet Music .
N( x )
Si los monomios A( x; y; z ) 9 x 5 a =
B( x;y;z )
=
Calcule el valor de m+n+ p si se sa
−
−
ax 2a y6
−
( n n − 4 ) x 2 + ( 3 m − 2) x + m − n
es idénticamente nulo.
2 b 2 b 3 1 / c
y
=
z
b 4
z
A) 2
B) 8
D) 14
son semejantes, halle el valor de
C) 4 E) 12
A( x; y; z) – B( x; y; z).
NIVEL INTERMEDIO
A) 7 x6 y4 z3 B) x9 y3 z4
6.
C) 6 x6 y3 z4
Si la expresión polinomial P( x)= nx n – 4 – 2 x n – 3+ x7 – n+1
4 3 6
D) 5 x y z
es un trinomio, calcule el valor de P
E) 7 x4 y3 z4
A) 1 .
Dada la expresión matemática f ( x )
=
A) 4
C) 11 E) –
You're Reading a Preview
).
Si el polinomio 7. Unlock full access with a free trial. 12
2 +1
P( x;y ) = 5 x n + 2 xy n−5 + ( n − 12) y2 C) 2 Download With Free Trial se reduce a dos términos, indique E) 0 P( n; 0).
B) 1
D) 2 2 .
D) – 3
2 x2 − x − 2 2 + 1
halle el valor de f (
B) – 7
Si se cumple que a3= b3,
Master your semester b with Scribd a & The A)New YorkB) Times 2 1 C) –1 indique el menor valor de
a
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D) 1/2
b
+
A) 0
.
E) – 2
B) 50
D) 100 Read Free Foron 30this Days Sign up to vote title
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C) 60 E) 80
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8.
Si P( x)=ax – x0; ax0 ≠ 0,
además, P
x , entonces ¿a qué
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Álgebra 10.
of 12
Ex_4B_pol+frac.alg Algebra Basica
Sheet Music
Si P(
10 5 x +x
13.
15 )=x ,
Dado el polinomio cúbico P( x)= x
halle el valor de P(–1).
3
– 3 x2+3 x –1
Halle el equivalente de J . −27
A) 2
B) 0
( P( ) ) x J =
P(1 / 3)
C) 1
D) –1
E) 4
3 P ( x −1)
NIVEL AVANZADO
A)
+3
8
; x ≠ 1
P( x +1)
x − 1
B)
2
( x − 1)2 2
D) ( x –1)3 11.
y x − 1 + y + 1 x x y − 1 x + 1 y
Si P( x;y ) = Evalúe P 4
(
9 + 2;
3 −4 4
)
14.
que
.
P( x )
=
n
[( n + 1) x − 1]
−
n(x
n
−
1) +
A) 1
Si la suma de coeficientes exce
B) –1
término independiente, ¿cuál e P( n)?
C) 2
You're Reading a Preview A) 2
D) – 2 E) 2 2 12.
Sea P( x) un polinomio de grado p
B) 7
Unlock full access with a free trial.
D) 15
Download With Free Trial Dado el polinomio P( x)= x3 –1, halle el equiva15. El polinomio
lente de J . J
=
+ 3x ( x ))
P P
(
3
P( x)=(7 x P( x )
+1
Master A) your semester with Scribd 3 x & The New York Times B) x3+1 3 Special offer forC) students: x –1 Only $4.99/month. 9
D)
2
– 3) n – 3(2 x –1) n+1+
( n2 x3 – 9)5(2 x+3) n –13+(5 x
tiene como término independien Read Free For 30this Days Sign to vote title n. ces,up halle el on valor de
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A) 13
B) 18
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Álgebra División algebraica A) –1 D) – 3
NIVEL BÁSICO Sheet Music 1.
Luego de efectuar la división de polinomios x 4
+
NIVEL INTERMEDIO
, se obtuvo por cociente q( x). 6.
Evalúe q(10).
Al dividir
B) 91
x
4
+
2x
3
x
C) 99 E) 100 2
−
4x
+
2x − 3
2
x 2 + x − 1
+
A) 23 D) 20
7.
Determine el valor de a+b. A) 7 D) 3
B) 6
x
+
x
+
x
10
+ ... +
x
2
+
Si la división
x +1
x
4
+
2
admite cociente q( x) y residuo R( x), calcule el valor de q(1) ÷ R(1). A) 4your semester B) 6 C) 1/2 Scribd Master with D) –1 E) – 1/2 & The New York Times Al dividir
5
+
ax
3
x
2
2
−
bx
+
x +1
+
4x −
B) 6
ax + 3 b
se obtiene un cociente
+
x +1
es exacta.
A) 1 D) 2 9.
C) 8 E) 11
valor de a+b si la división
Download With Free Trial x
80 Special offer for students: Only $4.99/month. 5 x − mx + 4
2 x
A) 5 D) 9 You're Reading a Preview Unlock full access with a free trial. 8. Calcule el
x − 1
4.
C) 21 E) 19
Halle el valor de a+ b. C) 5 E) 2
Si la división algebraica 11
B) 22 x+1
ax + b
se obtiene un resto de la forma R( x)=3 x+1.
12
Calcule el resto de la siguiente divisió ( x + 2) ( x − 4 ) ( x − 1) ( x + 5)
A) 101 D) 1000
3.
C) 1 E) 2
x2 + 1
x 2 + x + 1
2.
B) 3
C) 0 E) –
B) –1
Read Free For 30this Days Sign up toelvote on title ab si se sabe Determine valor de q Useful es Not useful sión exacta. Cancel anytime. ax
3
+
3 bx 2
2
+
5x − 2
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Ex_4B_pol+frac.alg Algebra Basica
Álgebra 13.
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NIVEL AVANZADO
P( x)= mx3+ nx2+7 x+2
Sheet Music
entre d ( x)=2 x2 – 3 x+1
11.
su residuo es R( x)=6 x+3.
En el siguiente esquema de una división de polinomios en x por Horner, halle el resto. a
a
b
b
a
b
c
c
b
b
b
c
Halle el valor de n / m. A) 3 B) – 3 C) – 2 D) 2 E) –1
a
c 2
c b
Al dividir
c
( b+2c)(a+c2)
14.
Si el polinomio P( x) se divide
cociente es x2+2 x+1 y el residuo A) R( x)=7 x –11
P( x) se divide por ( x – 4), el residu
B) R( x)=11 x – 7
es el valor e r ?
C) R( x)=7 x+11
A) 25 D) – 20 You're Reading a Preview
D) R( x)=6 x –12 E) R( x)=6 x+12 12.
Unlock full access with a free trial.
Si la división algebraica ( a − 1) x 3
+
B) – 25
El resto de dividir P( x) entre ( Download With Free Trial resto de dividir Q entre ( x – 3) e 15.
( b − 2) x + c − 4
( x)
x − 1
a+ b
es exacta, calcule
valor de
( a − 6)3 + ( b − 1)3 + c3 −1 ( a − 6)( b − 1)c
P( x)=ax3+ bx2+cx+ d y Q( x)= x
Master your semester with Scribd & The New A) 6 York Times B) 3 C) 2 Special offer for students: Only $4.99/month.
D)
1
E)
1
4 + 9 b
sabiendo que
Read Free For 30 Days Sign up 2 to vote on this title 27 A)Useful NotB) useful
D)
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9
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Álgebra Factorización de polinomios NIVEL BÁSICO
NIVEL INTERMEDIO
Sheet Music
1.
Si ( x+1)2 es un factor algebraico del polinomio
6.
Dado el polinomio
P( x)= x4+ mx3+8 x2+ mx+1, determine el valor
P(a; b; c; d )=(a+2 b+5c)(2a+4 b+10
de m.
indique un factor primo.
A) 1
B) 2
D) 4
C) 3
A) a+2 b+c+ d B) 2a+4 b+5c – d
E) 5
C) a+2 b+5c+3 d 2.
Sea P( x; y)= x8 y+3 x7 y+2 x6 y+6 x5 y.
D) a+4 b+10c – 4 d
Determine el número de factores primos
E) a – 4 b – 3c – 2 d
lineales que presenta el polinomio P( x; y). 7.
A) 2
B) 3
D) 5
Si f ( x) es el factor común de los po cuadráticos. P( x)=ax2+(a+ b) x+ b
C) 4 E) 6
Q( x)= bx2 – (a – b) x – a 3.
Determine el valor de f (–1). You're Reading a Preview M (a; x)=(a+ b)2+2(a+ b)(a – b)+(a – b)2 – x2 Unlock full access with A) a free 2 trial. B) 0 Indique la suma de los factores primos. Factorice el siguiente polinomio.
A) 3a
B) 4a
D) ax 4.
C) 5ax
D) –1 Download With Free Trial
E) 2 x
Determine el número de los factores primos
Master semester with Scribd del your polinomio. 5 3 + x2 –1 x)= x – xYork & TheQ(New Times Special offer for students: Only $4.99/month.
A) 1
B) 2
C) 3
C) 5
8.
E) 6
Determine el factor primo g( x) de ma
que representa el siguiente polinomio f ( x)= x4+3 x3 – 5 x2 –13 x+6 2to vote Free Foron 30this Days Sign=up title A) gRead ( x) x +4 x+1
Useful 2
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B) g( x)= xCancel – 3 xanytime. +1 C) g( x)= x2+2 x –1
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Álgebra 10.
Factorice el siguiente polinomio.
13.
Al factorizar el polinomio
P( x)= x4+2 x3+6 x2+5 x+6
q( x)=( x – 2)( x3 – 3 x – 2)–( x –1)2 –
Luego determine la suma de coeficientes del
halle la suma de coeficientes
factor primo de mayor término independiente.
primos.
A) 5
A) 0 D) –1
B) 3
D) –1
C) 2 E) – 3 14.
NIVEL AVANZADO
B) – 5
Si el MCM de los polinomios p( x
y q( x) es x4 – 5 x2+4 y su MCD es suma de raíces del polinomio q
11.
Dados los polinomios f ( x)= x2+ x+1 y p( x)= x5+2 x2+ax+ b, si f ( x) es
A) – 3 D) 2
un factor algebraico de p( x),
B) 1
halle el valor de ab. 15.
A) – 6
B) 6
D) – 8 12.
C) 8
Consideremos el polinomio P( x; y)=2 x2+7 xy+6 y2 – 5 x – 8 y+2
E) 9 además, P(a; b)=11; {a; b} ⊂ Z You're Reading a Preview
Determine el máximo valor de Unlock primos full access with a free trial. Determine el número de factores lineales del polinomio P( x). A) –11 Download With Free Trial P( x)=4( x+1)(2 x+1)( x – 2)(2 x – 3)+4 B) 9 C) – 9 D) 12 A) 0 B) 1 C) 2 E) 11 D) 3 E) 4
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Definición de producto y
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Ex_4B_pol+frac.alg Algebra Basica
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Álgebra Semestral San Marcos II LEYES
DE EXPONENTES
PRODUCTOS NOTABLES
POLINOMIOS
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