Problemas de factorización de matemáticas de secundaria
=a^4 2a? 1-a?
=(a? 1)?-a?
=(a? a 1)(a?-a 1)
(2)2a? -7ab6b?
=(2a-3b)(a-2b)
(3)3x? xy-2y?
=(3x-2y)(x y)
(4)10a? ¿b? 11ab-6
=(2ab 3)(5ab-2)
(5)7a? x-28a (la quinta potencia de x)
=7a? (x-4a?)
(6)x? -10x? 16x
=x(x?-10x 16)
=x(x-2)(x-8)
(7)(x? 3 veces)? -2(x? 3x)-8
=(x? 3x 2)(x? 3x-4)
=(x 1)(x 2)(x 4) (x-1)
(8)(x-y)? 4xy-1
=x? -2xyy? 4xy-1
=x? 2xyy? -1
=(x y)? -1
=(x y 1)(x y-1)
9.x^2 -4xy 4y^2 -x 2y -2
= (x-2y)^2 - (x-2y) -2
=(x-2y 1)(x-2y-2)
10.x? ¿hacha? ¿bx? ¿cx? abx bcx acx ab
=x? ¿cx? abx abc bx? hacha bcx? acx
=x? (x c) ab(x c) bx(x c) ax(x c)
=(x c)[x? bx ab ax]
=(x c)[x(x b) a(x b)]
=(x a)(x b)(x c)
11 .¿incógnita? -¿Sí? -y-1/2
=x? -(y? y 1/4)
=x? -(año 1/2)?
=(x y 1/2)(x-y-1/2)
12.x elevado a la cuarta potencia 3x? ¿6x? -4
=x^4x? ¿2 veces? ¿2 veces? 4(x?-1)
=x? (x1) ¿2x? (x 1) (4x-4)(x 1)
=(x 1)(x? 2x? 4x-4)
13.x? -3x? 4
=x? 1-3(x?-1)
=(x 1)(x?-x 1)-(3x-3)(x 1)
=(x 1) (x?-4x 4)
=(x 1)(x-2)?
14.32a[(x^2 2x)^2]-2a
=2a[16(x^2 2x)^2-1]
=2a(4x^2 8x 1)(4x^2 8x-1)
15.16 8(x^2 4x) (x^2 4x)^2
=(4 x^2 4x)^2
=(x^2 4x 4)^2
=(x 2)^4
16.3x^ny 9x ^(n-1)y^2 x^(n 1)/4
=x^(n-1)(3xy 9y^2 x^2/4)
=x^(n-1)(x^2/4 3xy 9y^2)
=x^(n-1)(x/2 3y)^2<
/p>
=(1/4)[x^(n-1)](x 6y)^2
17.a^4 a? 3a-5
=a? *(a? a) 3a-5
=3a? 3a-5
=3(a? a)-5
18.1 x x(x 1) x(x 1)^2 x(x 1)^3
=(1 x) x(x 1) x(x 1)^2 x(x 1)^3
=(1 x)(1 x) x(x 1)^2 x(x 1)^3
=(1 x)? (1x)x(x1)^3
=(1x)? (1 x)
=(1 x)^4
19.(x-y)(2x-2y-3)-2
=(x-y) [2(x-y)-3]-2
=2(x-y) ^2-3(x-y)-2
=[(x-y)-2][2(x-y) ) 1]
=(x-y-2)(2x-2y 1).
x2-3xy-10 y2 x 9y-2 =(x-5y 2)(x 2y-1).
x2-y2 5x 3y 4 =(x y 1)(x-y 4).
xy y2 x-y-2=(y 1)(x y-2).
6x 2-7xy-3 y2-xz 7yz-2z 2 =(2x-3y z)(3x y-2z).
a^2 2b^2 3c^2 3ab 4ac 5bc =(a b c)(a 2 b 3c)
x^2-8x 7 =(x-1)(x -7)
X^2 8X 7= (x 1)(x 7)
x^2-10x-11 =(x-11)(x 1) p>
x^2 10X-11=, (x 11)(x-1)
X^ 3x-18 = (x 6)(x-3)
x^2 11x 18 =(x 2)(x 9)
x^2-11x 18 =(x-2)(x-9)
x^ 2 17x -18 =(x 18)(x-1)
x^2-17x-18 =(x-18)(x 1)
xy 6-2x- 3y= (x-3)(y-2)
x2(x-y) y2(y-x)=(x y)(x-y)^2
2x2-(a-2b) x- ab=(2x-a)(x b)
a4-9a2b2=a^2(a 3b)(a-3b)
x3 3x2-4=(x- 1) (x 2)^2
ab(x2-y2) xy(a2-B2)=(ay bx)(ax-by)
(x y)(a-b-c) (x-y )(b c-a)= 2y(a-b-c)
a2-a-b2-b=(a b)(a-b-1)
(3a-b)2-4 (3a -b)(a 3b) 4(a 3b)2=[3a-b-2(a 3b)]^2=(a-7b)^2
(x 1)2( x 2 )-(x 1)(x 2)2 =-(x 1)(x 2)
abc ab-4a=a(bc b-4)
16x 2- 81 =(4x 9)(4x-9)
9x2-30x 25=(3x-5)^2
x2-7x-30=(x-10) (x 3)
x2-25=(x 5)(x-5)
x2 4x 3=(x 1)(x 3)
4x 2 -12x 5 =(2x-1)(2x-5)
3ax2-6ax=3ax(x-2)
x(x 2)-x=x( x 1 )
x2-4x-ax 4a=(x-4)(x-a)
25x2-49=(5x-9)(5x 9)
36x2-60x 25=(6x-5)^2
4x2 12x 9=(2x 3)^2
x2-9x 18=(x-3)(x -6 )
2x2-5x-3=(x-3)(2x 1)
12 x2-50x 8 = 2(6x-1)(x-4)
(x 2)(x-3) (x 2)(x 4)=(x 2)(2x-1)
2ax 2-3x 2ax-3 =(x 1) (2ax-3)
9x2-66x 121=(3x-11)^2
8-2x2=2(2 x)(2-x)
9x2-30x 25=(3x-5)^2
-20x2 9x 20=(-4x 5)(5x 4)
12 x2-29x 15 = (4x -3)(3x-5)
36x2 39x 9=3(3x 1)(4x 3)
21x 2-31x-22 =(21x 11)(x -2 )
>9x4-35x2-4=(9x^2 1)(x 2)(x-2)
(2x 1)(x 1) (2x 1)(x-3)= 2(x -1)(2x 1)
2ax 2-3x 2ax-3 =(x 1)(2ax-3)
x(y 2)-x-y-1 =(x -1)(y 1)
(x2-3x) (x-3)2=(x-3)(2x-3)
9x2-66x 121=(3x -11)^2
8-2x2=2(2-x)(2 x)
x4-1=(x-1)(x 1)(x^2 1)
x2 4x-xy-2y 4=(x 2)(x-y 2)
4x 2-12x 5 =(2x-1)(2x-5)
21x 2-31x-22 =(21x 11)(x-2)
4x 2 4xy y2-4x-2y-3 =(2x y-3)(2x y 1)
9x5-35x3-4x=x(9x^2 1)(x 2)(x-2)
3x2-6x=3x(x-2)
49x2-25=(7x 5)(7x-5)
6x 2-13x 5 =(2x-1)(3x-5)
x2 2-3x =(x-1)(x-2)
12x2-23x-24=(3x-8)(4x 3)
(x 6)(x-6)- (x-6)=(x-6)(x 5)
3(x 2)(x-5)-(x 2)(x-3)= 2(x-6)( x 2)
9x2 42x 49=(3x 7)^2 .
3a3b2c-6a2b2c2 9ab2c3=3ab^2 c(a^2-2ac 3c^2)
xy 6-2x-3y=(x-3)(y-2)
x2(x-y) y2(y-x)=(x y)(x-y)^2
2x2-(a-2b)x-ab=(2x-a)(x b)
x^3 2x^2-16x-32=(x 2)(x 4)(x- 4)
(a-b)a^6 (b-a)b^6=(a-b)^2(a^2 ab b^2)(a b)(a^2-ab b^2)
(x y)(x y 2xy) (xy 1)(xy-1)=(x 1)(y 1)(x y xy-1)
x^8 x^7 1 =(x^2 x 1)(x^6-x^4 x^3-x 1)
x^8 x^6 x^4 x^2 1 =(x^4 x ^3-x 1)(x^4 x^3 x^2 x 1)
x^2-20x 100=(x-10)^2
x^2 -3x 2=(x-1)(x-2)
x^2-2x-15=(x 3)(x-5)
x^2 2x- 15=(x-3)(x 5)
x^2-7x 12=(x-3)(x-4)
x^2-7x-30= (x 3)(x-10)
x^2 2x-3=(x-1)(x 3)
x^2-16x 64=(x-8 )^2
x^2-9x 20=(x-4)(x-5)
x^2-6x 8=(x-2)(x-4 )
x^2-6x-7=(x-7)(x 1)
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