Question

Pзаложите на множители 1)х^2-5х+6 2)х^2+6х+8 3)m^2-7mn+12n^2 4)a^2-7ab+10b^2

Answer 1

1) x²-5x+6=(x-2)(x-3)
D= 25-4*1*6=25-24=1
x₁=$\frac{5-1}{2} = \frac{4}{2} =2$
x₂=$\frac{5+1}{2} = \frac{6}{2} =3$
2)x²+6x+8=(x+4)(x+2)
D= 36-4*1*8=36-32=4
x₁=$\frac{-6-2}{2} =- \frac{8}{2} =-4$
x₂=$\frac{-6+2}{2} =- \frac{4}{2} =-2$
3)m²+7mn+12n²=m²+4mn+3mn+12n²=m(m+4n)+3n(m+4n)=(m+4n)(m+3n)
4)a²-7ab+10b²=a²-5ab-2ab+10b²=a(a-5b)-2b(a-5b)=(a-5b)(a-2b)