Question

Fatore os polinômios por agrupamento:

A) 5x+ax+5y+ay
B) x ao cubo+2x ao quadrado+7x+14
C) c ao quadrado-c+cx-x
D) ax+bx+ay+by
E) 7a+7c+ma+mc
F) a ao cubo+3a ao quadrado+2a+6
G) x ao cubo-x ao quadrado+5x-5
H) ac+ad+bc+bd
I) 2ax+2a+bx+b
J) 3a+ 9b+2a+6b

Answer 1

Oii, tudo bem??

Bom, vamos lá:

a) 5x + ax + 5y + ay

x . ( 5 + a ) + y . ( 5 + a )

( 5 + a ) . ( x + y )

R = ( 5 + a ) . ( x + y )

b)$x^{3} + 2x^{2}  + 7x + 14$

$x^{2}$ . ( x + 2 ) + 7 . ( x + 2 )

( x + 2 ) . ( $x^{2}$ + 7 )

R = ( x + 2 ) . ( $x^{2}$ + 7 )

c) $c^{2} - c + cx - x$

c . ( c - 1 ) + x . ( c - 1 )

( c - 1 ) . ( c + x )

R = ( c - 1 ) . ( c + x )

D) ax + bx + ay + by

x . ( a + b ) + y . ( a + b )

( a + b ) . ( x - y )

R = ( a + b ) . ( x - y )

E) 7a + 7c + ma + mc

7 . ( a + c ) + m . ( a + c )

( a + c ) . ( 7 + b )

R = ( a + c ) . ( 7 + b )

F) $a^{3}$ +3$a^{2}$ + 2a + 6

$a^{2}$ . ( a + 3 ) + 2 . ( a + 3 )

( a + 3 ) . ( $a^{2}$ + 2 )

R = ( a + 3 ) . ( $a^{2}$ + 2 )

G) $x^{3}  - x^{2}$ + 5x - 5

$x^{2}$ . ( x - 1 ) + 5 . ( x - 1 )

( x - 1 ) . ( $x^{2}$ + 5 )

R = ( x - 1 ) . ( $x^{2}$ + 5 )

H) ac + ad + bc + bd

a . ( c + d ) + b . (c + d )

( c + d ) . ( a + b )

R = ( c + d ) . ( a + b )

I) 2ax + 2a + bx + b

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

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

R = ( x + 1 ) . ( 2a + b )

J) 3a + 9b + 2a + 6b

3 . ( a + 3b ) + 2 . ( a + 3b )

( a + 3b ) . ( 3 + 2 )

R = ( a + 3b ) . ( 3 + 2 )