Question

Faceti va rog exercitile 1si 4 dau 30 puncte ,(Se calculeaza cu descompunerea in factori)

Answer 1

a)3x+3y+mx+my=3(x+y)+m(x+y)=(x+y)(3+m)
b)5x+5y+n²x+n²y=5(x+y)+n²(x+y)=(x+y)(5+n²)
c)4x²+4xy+5xy²+5x²y=4x(x+y)+5xy(y+x)=(x+y)(4x+5xy)
d)x⁴-x³+7x-7=x³(x-1)+7(x-1)=(x-1)(x³+7)
e)5x²+10x+5=5(x²+2x+1)=5(x+1)²
f)25x³-16x=x(25x²-16)=x(5x-4)(5x+4)
g)(a+b-2)²-a²=(a+b-2-a)(a+b-2+a)=(b-2)(2a+b-2)
h)x⁸-y⁸=(x⁴-y⁴)(x⁴+x⁴)=(x²-y²)(x²+y²)(x⁴+x⁴)=(x-y)(x+y)(x²+y²)(x⁴+x⁴)
i)x²+8x+15=x²+5x+3x+15=x(x+5)+3(x+5)=(x+5)(x+3)
j)x²+8x+7=x²+7x+x+7=x(x+7)+(x+7)=(x+7)(x+1)     *la j) am inlocuit pe a² cu x² altfel nu se putea face nimic-probabil e o greseala in carte
k)x²+2x-3=x²+3x-x-3=x(x+3)-(x+3)=(x+3)(x-1)

a)x²-7x=x(x-7)
b)x²+3x=x(x+3)
c)5x⁶+25x²=5x²(x⁴+5)
d)x²(x+5)+x(x+5)²=x(x+5)(x+x+5)=x(x+5)(2x+5)
e)a²b-a²-b+1=a²(b-1)-(b-1)=(b-1)(a²-1)=(b-1)(a-1)(a+1)
f)25xy+5x-5y-1=5x(5y+1)-(5y+1)=(5y+1)(5x-1)
g)49xy-7x+7y-1=7x(7y-1)+(7y-1)=(7y-1)(7x+1)
h)49x²-121=(7x-11)(7x+11)
i)(x-3)²-9x²=(x-3-3x)(x-3+3x)=(-2x-3)(4x-3)
j)(x+3)²-25x²=(x+3-5x)(x+3+5x)=(3-4x)(3+6x)
k)x²+12x+36-y²=(x+6)²-y²=(x+6-y)(x+6+y)
l)x²+11x+18= x²+9x+2x+18= x(x+9)+2(x+9)=(x+9)(x+2)
m)x²-7x+12=x²-3x-4x+12=x(x-3)-4(x-3)=(x-3)(x-4)
n)x²+5x-6=x²+6x-x-6=x(x+6)-(x+6)=(x+6)(x-1)
o)x³+x²-2010x-2010=x²(x+1)-2010(x+1)=(x+1)(x²-2010)