Question

2. Fatore os seguintes polinômios:

a)a²+ab+ax+bx

b)ax-x+ab-b

c)a⁵+a³+2a²+2

d)bx²-2by+5x²-10y

e)2b²+2-b²k-k

f)5y³-4y²+10y-8

g)a¹²+a⁸-a⁴-1

h)2an+n-2am-m

i)1/2+1/2x+xy+y​

Answer 1

1Resposta:

Explicação passo a passo:

a)a²+ab+ax+bx=

a(a+b) + x(a+b)=

  (a+b)(a+x)

b)ax-x+ab-b=

  x(a-1) +b(a-1)

   (a-1)(x+b)

c)a⁵+a³+2a²+2=

a³(a²+1)+2(a²+1)

(a²+1)(a³+2)

d)bx²-2by+5x²-10y=

  b(x²-2y)+5(x²-2y)=

   (x²-2y)(b+5)

e)2b²+2-b²k-k=

2(b²+1)-k(b²+1)

(b²+1)(2-k)

f)5y³-4y²+10y-8=

  y²(5y-4)+2(5y-4)

     (5y-4)(y²+2)

g)a¹²+a⁸-a⁴-1 =

a⁸(a⁴+1)-(a⁴+1)=

(a⁴+1)(a⁸-1)

h)2an+n-2am-m

n(2a+1)-m(2a+1)

(2a+1)(n-m)

i)1/2+1/2x+xy+y​

1/2(1+x) +y(x+1)

    (x+1)(1/2+y)