EJERCICIOS DE FACTORIZACIÓN

ACTIVIDAD Nº 1

Problema 01:

Factoriza:x6y3 – x4y5 + x2y7

2a4b – 4ab4 – 6a4b4

x2y – y – zy7abc – 35abc2

15xyz3 – 5xy3z + 25x3yz6a8 + 12a6 – 18a4 + 24a2

Problema 02:

Factoriza:(x + 4)y – (x + 4)znx – 2ny – mx + 2myx2 + xy + zx + zyax – bx + ay – by abc + ab + c + 1x5 + ax3 + 2a2 + 2ax2

Problema 03:

Factoriza: x + y + 3xz + 3yz n + 2m2 + 1 + 2m2n 3axy + 3axz + y + z ax + bx – cx + ay + by – cy w2x5 + 3w2 – t3x5 – 3t3

5a2x + 3a2y – 5b3x – 3b3y

Problema 04:

Factoriza:(m + n – 1)x2 + (m + n – 1)x – (m +

n – 1)(a2 + b2)3a + (a2 + b2)5c + (a2 + b2)2

(m2 + n)(x - y) – (m2 + n)(2x + 5y) (x + y)3 – (x + y)4z (x + y)(a + b) + (x + y)(m + n)

Problema 05:

Factoriza: (a + b)m2 + (a + b)n (x + y)a3 + (x + y)b2

(a + 2b)x4 + (2b + a)y3

(m2 + n2)x2 + (m2 + n2)y2

(a + b + 1)2 – (a + b + 1)(x – 2) + (a + b + 1)

Problema 06:

Factoriza:ax + az + bx + bzmx – m – x + 1xy – zy + xt + ztx5 + x3 + x2 + 1ab + bc + xa + xc

ACTIVIDAD Nº 2

Problema 01:

Factoriza:x + y + 3xz + 3yzn + 2m2 + 1 + 2m2n3axy + 3axz + y + zz + 3axy + y + 3axza2 – 3 + a2n – 3n

Problema 02:

Factoriza: ya + yb 25x2 – 50x 3m2 + 6m 2ab – 2ay + 3bx – 3xy x9y4 – x4y6

mx + xy –mz – yz x6 – 4x4 – x2

Problema 03:

Factoriza: (x – 4)y – (x – 4)zx(x + 7) + y(x + 7) – z(x + 7)x4(2a + 5b) + x(2a + 5b) – (2a + 5b)a(p – q) + b(p – q) + c(p – q)mz + m2 + zy + myaz + bz + cz + ay + by + cy

Problema 04:

Factoriza: m3 – mn + mp – np m3 + m2 + m + 1 m2 + mn + mp + np – m – n + x(m +n) x(3m – 2b) – 3m + 2b (c + 1)(b + 1) + (a + b)(c + 1) 3b(2x + 3) + 2x + 3

Problema 05:

Factoriza: (x – 2)y – (x – 2)z x(x + 5) + y(x + 5) – z(x + 5) x4(2a – 5b) + x(2a – 5b) – (2a – 5b) a(p + q) + b(p + q) + c(p + q) mx + m2 + xy + my ax + x2 + ab + bx ax + bx + cx + ay + by + cy

Problema 06:

Factoriza: x2 + y2 – 5y(x2 + y2) 1 – x – 2y(1 – x) x3 – x2 + x – 1 5y5 – 15y2z + y3 – 3z a5 – a4 + a – 1 3xy – 3xz + 3x – y + z – 1 2a2x + 2ax + 2x – a2 – a – 1

ACTIVIDAD Nº 3

Problema 01:

Factoriza:(x – y)a + (x – y)b(a + b)m2 + (a + b)n(x + y)a3 + (x + y)b2

(a+ 2b)x4 + (2b + a)y3

(m2 + n2)x2 + (m2 + n2)y2

Problema 02:

Factoriza: (a + b + c)x + (a + b + c)y (m3 + n4)a4 – (m3 + n4)b3

(x + y)3 – (x + y)4z (m2 + n) (x – y) – (m2 + n) (2x +

5y) (x4 – a)3y2 – (x4 – a)(y – 1)

Problema 03:

Factoriza:x2 + xy + zx + zyax – bx + ay – bymnp + mn + c + 1x5 + ax3 + 2a2 + 2ax2

x2y + xy + zx + z

Problema 04:

Factoriza: 2a8b7 – 4a6b9 – 8a5b10

15a4b5 + 30a8b7 – 10a6b4

m4x – m5y + m3

m7 + 2m10 – m8x xn + 5 + xn + 8 + xn + 4

nx – 2ny – mx + 2my

Problema 05:

Factoriza:2x3y + 3y2x4a2b3 + 4a3b2 + 8abyx8 + yx6

x8y2 – 2x7y5

7x6y9 – 5x7y5