Toán Lớp 8: Phân tích đa thức thành nhân tử a)(x^2-1)^2-4x^2 b)(3x+1)^2-(x+1)^2 c)x^2-7x+10 d)2x^2+3x-5

Question

Toán Lớp 8:  Phân tích đa thức thành nhân tử   a)(x^2-1)^2-4x^2   b)(3x+1)^2-(x+1)^2   c)x^2-7x+10   d)2x^2+3x-5

truonganhthi · Answer

Ph&acirc;n t&iacute;ch đa thức th&agrave;nh nh&acirc;n tử    a.       ${(x^2-1)^2-4x^2}$        $&hArr;{(x^2)^2&minus;2x^2+1&minus;4x^2}$   $&hArr;{x^ 4 &minus;2x^ 2 +1&minus;4x^ 2}$   $&hArr;{x^ 4 &minus;6x^ 2 +1}$   b.   ${(3x+1)^2-(x+1)^2}$   $&hArr;{9x^ 2 +6x+1&minus;(x+1) ^ 2}$   $&hArr;{9x^ 2 +6x+1&minus;(x^ 2 +2x+1)}$   $&hArr;{9x^ 2 +6x+1&minus;x ^ 2 &minus;2x&minus;1}$   $&hArr;{8x^ 2 +6x+1&minus;2x&minus;1}$   $&hArr;{8x^ 2 +4x+1&minus;1}$   $&hArr;{8x^ 2 +4x}$   c.   ${x^2-7x+10}$   $&hArr;{a+b=&minus;7}$   ${ab=1&times;10=10}$   $&hArr;{&minus;1,&minus;10}$   ${&minus;2,&minus;5}$   $&hArr;{&minus;1&minus;10=&minus;11}$   $&minus;2&minus;5=&minus;7$   $&hArr;{a=&minus;5}$   ${ b=&minus;2}$   $&hArr;{(x^ 2 &minus;5x)+(&minus;2x+10)}$   $&hArr;{x(x&minus;5)&minus;2(x&minus;5)}$   $&hArr;{(x&minus;5)(x&minus;2) }$   d.   $&hArr;{2x^2+3x-5}$   $&hArr;a+b=3$   ${ab=2(&minus;5)=&minus;10}$   $&hArr;{&minus;1,10}$   ${-2,5}$   $&hArr;{&minus;1+10=9}$   ${-2+5=3}$   $&hArr;{a=&minus;2}$   ${b=5}$   $&hArr;{(2x^ 2 &minus;2x)+(5x&minus;5)}$   $&hArr;{2x(x&minus;1)+5(x&minus;1)}$   $&hArr;{(x&minus;1)(2x+5)}$

tonhu12 · Answer

Giải đáp + Lời giải và giải thích chi tiết:    a)   (x&sup2;-1)&sup2;-4x&sup2;   = (x&sup2;-1)&sup2;-(2x)&sup2;   = (x&sup2;-1-2x)(x&sup2;-1+2x)   b)   (3x+1)&sup2;-(x+1)&sup2;   = (3x+1-x-1)(3x+1+x+1)   = 2x(4x+2)   c)   x&sup2;-7x+10   = x&sup2;-2x-5x+10   = (x&sup2;-2x)-(5x-10)   = x(x-2)-5(x-2)   = (x-2)(x-5)   d)   2x&sup2;+3x-5   = 2x&sup2;-2x+5x-5   = (2x&sup2;-2x)+(5x-5)   = 2x(x-1)+5(x-1)   = (x-1)(2x+5)