Question

5.descompuneti în factori a)(x+1)(x+3)²-4(x+1). b) (x+3)(2x+1)²-16(x+3). c)(x-3)(x+2)²-x+3. d)(x-4)(2x+1)²-x+4. e). (x+8)²-25. f). (2x-5)²-36. g). (x-5)²-9x². h). (3x+4)²-(x+5)². i). (2x+1)²-9(x-1)². j). (3x-1)²-4(x+1)². k)). (4x-3)²-9(x+2)²​

Answer 1

Răspuns:

a)

$( x + 1) \times ((x + 3)^{2} - 4) = (x + 1) \times (x + 3 - 2) \times (x + 3 + 2) = (x + 1) \times (x + 1) \times (x + 5) = {(x + 1)}^{2} \times (x + 5)$

b)

$(x + 3) \times ((2x + 1)^{2} - 16) = (x + 3) \times (2x + 1 - 4) \times (2 \times + 1 + 4) = (x + 3) \times (2x - 3) \times (2x + 5)$

c)

$(x + 3) \times {(x + 2)}^{2} - (x - 3) = (x - 3) \times ( {(x + 2)}^{2} - 1) = (x - 3) \times (x + 2 - 1) \times (x + 2 + 1) = (x - 3) \times (x + 1) \times (x + 3)$

d)

$( x - 4) \times {(2x + 1)}^{2} - (x - 4)= (x - 4)( {(2x + 1)}^{2} - 1) = (x - 4) \times (2x + 1 - 1) \times (2x + 1 + 1) = (x - 4) \times 2x \times (2x + 2) = (x - 4)2x \times 2(x + 1) = 2 \times 2x \times (x - 4) \times (x \times 1) = 4x \times (x - 4) \times (x + 1)$

e)

$(x + 8 - 5) \times (x + 8 + 5) = (x + 3) \times (x + 13)$

f)

$(2x - 5 - 6) \times (2x - 5 + 6) = (2x - 1) \times (2x + 1)$

G)

$(x - 5 - 3x) \times (x - 5 + 3x) = ( - 2x - 5) \times (4x - 5)$

h)

$(3x + 4 - (x + 5)) \times (3x + 4 + (x + 5)) = (3x + 4 - x - 5) \times (3x + 4 + x + 5) = (2x - 1) \times (4x + 9)$

i)

$(2x + 1 - 3(x - 1)) \times (2x + 1 + 3(x - 1)) = (2x + 1 - 3x + 3) \times (2x + 1 + 3x - 3) = ( - x + 4) \times (5x - 2)$

j)

$(3x - 1 - 2(x + 1)) \times (3x - 1 + 2(x + 1)) = (3x - 1 - 2x - 2) \times (3x - 1 + 2x + 2) = (x - 3) \times (5x + 1)$

k)

$(4x - 3 - 3(x + 2)) \times (4x - 3 + 3(x + 2)) = (4x - 3 - 3x - 6) \times (4x - 3 + 3x + 6) = (x - 9) \times (7x + 3)$