Question

1.Descompuneti urmatoarele expresii in produs de factori primi ireductibili:
a) 3x³+6x²+3x=
b) 4x(x+1)-3(x+1)=
c) (x+1)²-9=
d) 4x²-(x-1)²=
e)x²+6x+8=
f) x²-9x+14=
g) x³+3x³-4x-12=
h) x³+2x²-9x-18=
i) x²-6x-16=
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Answer 1

a)
$3x ^{3} + 6x ^{2} + 3x = 3x \times (x ^{2} + 2x + 1) = 3x \times (x + 1) ^{2}$
b)
$4x(x + 1) - 3(x + 1) = (x + 1) \times (4x - 3)$
c)
$(x + 1) ^{2} - 9 = (x + 1 - 3) \times (x + 1 + 3) = (x - 2) \times (x + 4)$
d)
$4x ^{2} - (x - 1)^{2} = (2x - (x - )) \times (2x + (x - 1)) = (2x - x + 1) \times (2x + x - 1) = (x + 1) \times (3x - 1)$
e)
$x ^{2} + 6x + 8 = x ^{2} + 4x + 2x + 8 = x \times (x + 4) + 2(x + 4) = (x + 4) \times (x + 2)$
f)
$x ^{2} - 9x + 14 = x ^{2} - 2x - 7x + 14 = x \times (x - 2) - 7(x - 2) = (x - 2) \times (x - 7)$
g)
${x}^{3} + 3x ^{3} - 4x - 12 = 4x ^{3} - 4x - 12 = 4( {x}^{2} - x - 3)$
h)
${x}^{3} + {2x}^{2} - 9x - 18 = {x}^{2} \times (x + 2) - 9(x + 2) = (x + 2) \times ( {x}^{2} - 9) = (x + 2) \times (x - 3) \times (x + 3)$
i)
${x}^{2} - 6x - 16 = {x}^{2} + 2x - 8x - 16 = x (x + 2) - 8(x + 2) = (x + 2) \times (x - 8)$