Toán Lớp 8: 3A. Phân tích đa thức thành nhân tử a) $x^{2}-5x+6$ b) $3x^{2}+9x-30$ c) $3x^{2}-5x-2$ d) $x^{3}-7x-6$ e) $x^{4}+2x^{3}+6x-9$ f) $x^{2}

Question

Toán Lớp 8:  3A. Phân tích đa thức thành nhân tử a) $x^{2}-5x+6$ b) $3x^{2}+9x-30$ c) $3x^{2}-5x-2$ d) $x^{3}-7x-6$ e) $x^{4}+2x^{3}+6x-9$ f) $x^{2}-7xy+10y^{2}$

tuyethutanhthu · Answer

a)x^2-5x+6   =x^2-2x-3x+6   =(x^2-2x)-(3x-6)   =x(x-2)-3(x-2)   =(x-3)(x-2)   __   b)3x^2+9x-30   =3(x^2+3x-10)   =3(x^2+5x-2x-10)   =3[(x^2+5x)-(2x+10)]   =3[x(x+5)-2(x+5)]   =3(x-2)(x+5)   __   c)3x^2-5x-2   =3x^2+x-6x-2   =(3x^2+x)-(6x+2)   =x(3x+1)-2(3x+1)   =(3x+1)(x-2)   __   d)x^3-7x-6   =x^3+3x^2-3x^2+2x-9x-6   =(x^3+3x^2+2x)-(3x^2+9x+6)   =x(x^2+3x+2)-3(x^2+3x+2)   =(x^2+3x+2)(x-3)   =(x^2+x+2x+2)(x-3)   =[(x^2+x)+(2x+2)](x-3)   =[x(x+1)+2(x+1)](x-3)   =(x+1)(x+2)(x-3)   e)x^4+2x^3+6x-9   =x^4+3x^3-x^3+3x^2-3x^2+9x-3x-9   =(x^4+3x^3+3x^2+9x)-(x^3+3x^2+3x+9)   =x(x^3+3x^2+3x+9)-(x^3+3x^2+3x+9)   =(x^3+3x^2+3x+9)(x-1)   =[(x^3+3x^2)+(3x+9)](x-1)   =[x^2(x+3)+3(x+3)](x-1)   =(x^2+3)(x+3)(x-1)   f)x^2-7xy+10y^2   =x^2-2x-5x+10y^2   =(x^2-2xy)-(5xy-10y^2)   =x(x-2y)-5y(x-2y)   =(x-5y)(x-2y)

lyly98 · Answer

Giải đáp + Lời giải và giải thích chi tiết:    B&agrave;i 3:   a, x^2 - 5x + 6   = x^2 - 2x - 3x + 6   = x(x - 2) - 3(x - 2)   = (x - 3)(x - 2)   b, 3x^2 + 9x - 30    = 3(x^2 + 3x - 10)    = 3(x^2 + 5x - 2x - 10)    = 3[ x(x + 5) - 2(x + 5)]    = 3(x - 2)(x + 5)   c, 3x^2 - 5x - 2    = 3x^2 + x - 6x - 2    = x(3x + 1) - 2(3x + 1)    = (x - 2)(3x + 1)   d, x^3 - 7x - 6    = x^3 + 3x^2 + 2x - 3x^2 - 9x - 6    = (x^3 + 3x^2 + 2x) - (3x^2 + 9x + 6)    = x(x^2 + 3x + 2) - 3(x^2 + 3x + 2)    = (x - 3)(x^2 + 3x + 2)    = (x - 3)(x^2 + 2x + x + 2)    = (x - 3)[ x(x + 2) + (x + 2)]    = (x - 3)(x + 1)(x + 2)   e, x^4 + 2x^3 + 6x - 9    = x^4 + 3x^3 + 3x^2 + 9x - x^3 - 3x^2 - 3x - 9    = (x^4 + 3x^3 + 3x^2 + 9x) - (x^3 +3x^2 + 3x + 9)    = x(x^3 + 3x^2 + 3x + 9) - (x^3 + 3x^2 + 3x + 9)    = (x - 1)(x^3 + 3x^2 + 3x + 9)    = (x - 1)[ x^2(x + 3) + 3(x + 3)]    = (x - 1)(x^2 + 3)(x + 3)   f, x^2 - 7xy + 10y^2    = x^2 - 2xy - 5xy + 10y^2    = x(x - 2y) - 5y(x - 2y)    = (x - 5y)(x - 2y)