Question

разложи многочлены на множители 7 класс

Answer 1

Ответ:

$1)\ \ a^3-5a^2-2a+10=a^2(a-5)-2(a-5)=(a-5)(a^2-2)=\\\\=(a-5)(a-\sqrt2)(a+\sqrt2)\\\\\\2)\ \ 4x^4-2x^3-20x+10=2x^3(2x-1)-10(2x-1)=(2x-1)(2x^3-10)=\\\\=2\, (2x-1)(x^3-5)=2\, (2x-1)(x-\sqrt[3]5)(x^2+\sqrt[3]5x+\sqrt[3]{25})\\\\\\3)\ \ b^5+4b^4-b^3-4a^2=b^3(b^2-1)+4(b^4-a^2)=\\\\=b^3(b-1)(b+1)+4(b^2-a)(b^2+a)\\\\\star \ \ b^5+4b^4-b^3-4=b^3(b^2-1)-4(b^4-1)=b^3(b^2-1)-4(b^2-1)(b^2+1)=\\\\=(b^2-1)(b^3-4(b^2+1)=(b-1)(b+1)(b^3-4b^2-4)\ \ \star$

$\star \ \ b^5+4b^4-b^3-4b^2=b^3(b^2-1)+4b^2(b^2-1)=(b^2-1)(b^3+4b^2)=\\\\=b^2\, (b-1)(b+1)(b+4)\ \ \star$

$4)\ \ 8y^7+16y^6-5y^5-10y^4=8y^6\, (y+2)-5y^4(y+2)=\\\\=(y+2)(8y^6-5y^4)=y^4\, (y+1)(8y^2-5)=\\\\=y^4(y+1)(2\sqrt2y-\sqrt5)(2\sqrt2y+\sqrt5)$