Toán Lớp 8: Phân tích đa thức thanh nhân tử X^2-10x-27 3x^2-6x-1 3x^2-9x-2 X^2-x-1

Question

Toán Lớp 8:  Phân tích đa thức thanh nhân tử X^2-10x-27 3x^2-6x-1 3x^2-9x-2 X^2-x-1

ngoclanquynh · Answer

Giải đáp:   $a)(x-5-2 sqrt{13})(x-5+2 sqrt{13})   b)( sqrt{3}x- sqrt{3}-2)( sqrt{3}x- sqrt{3}+2)   c)3 left(x- dfrac{9+ sqrt{105}}{6} right) left(x- dfrac{9- sqrt{105}}{6} right)   d) left(x- dfrac{1+ sqrt{5}}{2} right) left(x- dfrac{1- sqrt{5}}{2} right).$   Lời giải và giải thích chi tiết:   $a)x^2-10x-27   =x^2-10x+25-52   =(x-5)^2-( sqrt{52})^2   =(x-5- sqrt{52})(x-5+ sqrt{52})   =(x-5- sqrt{4.13})(x-5+ sqrt{4.13})   =(x-5-2 sqrt{13})(x-5+2 sqrt{13})   b)3x^2-6x-1   =3x^2-6x+3-4   =3(x^2-2x+1)-4   =3(x-1)^2-2^2   =( sqrt{3}x- sqrt{3})^2-2^2   =( sqrt{3}x- sqrt{3}-2)( sqrt{3}x- sqrt{3}+2)   c)3x^2-9x-2   =3 left(x^2-3x- dfrac{2}{3} right)   =3 left(x^2-2. dfrac{3}{2}.x+ dfrac{9}{4}- dfrac{35}{12} right)   =3 left( left(x- dfrac{3}{2} right)^2- sqrt{ dfrac{35}{12}}^2 right)   =3 left(x- dfrac{3}{2}- sqrt{ dfrac{35}{12}} right) left(x- dfrac{3}{2}+ sqrt{ dfrac{35}{12}} right)   =3 left(x- dfrac{3}{2}- dfrac{ sqrt{35}. sqrt{12}}{12} right) left(x- dfrac{3}{2}+ dfrac{ sqrt{35}. sqrt{12}}{12} right)   =3 left(x- dfrac{3}{2}- dfrac{ sqrt{420}}{12} right) left(x- dfrac{3}{2}+ dfrac{ sqrt{420}}{12} right)   =3 left(x- dfrac{3}{2}- dfrac{ sqrt{4.105}}{12} right) left(x- dfrac{3}{2}+ dfrac{ sqrt{4.105}}{12} right)   =3 left(x- dfrac{3}{2}- dfrac{ sqrt{105}}{6} right) left(x- dfrac{3}{2}+ dfrac{ sqrt{105}}{6} right)   =3 left(x- dfrac{9+ sqrt{105}}{6} right) left(x- dfrac{9- sqrt{105}}{6} right)   d)x^2-x-1   =x^2-x+ dfrac{1}{4}- dfrac{5}{4}   = left(x- dfrac{1}{2} right)^2- sqrt{ dfrac{5}{4}}^2   = left(x- dfrac{1}{2}- sqrt{ dfrac{5}{4}} right) left(x- dfrac{1}{2}+ sqrt{ dfrac{5}{4}} right)   = left(x- dfrac{1}{2}- dfrac{ sqrt{5}}{2} right) left(x- dfrac{1}{2}+ dfrac{ sqrt{5}}{2} right)   = left(x- dfrac{1+ sqrt{5}}{2} right) left(x- dfrac{1- sqrt{5}}{2} right).$