Tính ( x^4 – 6x^3 + 2x^2 – 6x + 1 ) : ( x^2 + 1 ) ( x^3 + x^2 + x + 6 ) : ( x + 2 ) 02/08/2021 Bởi Allison Tính ( x^4 – 6x^3 + 2x^2 – 6x + 1 ) : ( x^2 + 1 ) ( x^3 + x^2 + x + 6 ) : ( x + 2 )
Giải thích các bước giải: $\begin{array}{l} \frac{{{x^4} – 6{x^3} + 2{x^2} – 6x + 1}}{{{x^2} + 1}}\\ = \frac{{{x^2}({x^2} + 1) – 6x({x^2} + 1) + ({x^2} + 1)}}{{{x^2} + 1}}\\ = \frac{{({x^2} + 1)({x^2} – 6x + 1)}}{{{x^2} + 1}}\\ = {x^2} – 6x + 1\\ \frac{{{x^3} + {x^2} + x + 6}}{{x + 2}}\\ = \frac{{{x^2}(x + 2) – x(x + 2) + 3(x + 2)}}{{x + 2}}\\ = \frac{{(x + 2)({x^2} – x + 3)}}{{x + 2}}\\ = {x^2} – x + 3 \end{array}$ Bình luận
Giải thích các bước giải:
$\begin{array}{l} \frac{{{x^4} – 6{x^3} + 2{x^2} – 6x + 1}}{{{x^2} + 1}}\\ = \frac{{{x^2}({x^2} + 1) – 6x({x^2} + 1) + ({x^2} + 1)}}{{{x^2} + 1}}\\ = \frac{{({x^2} + 1)({x^2} – 6x + 1)}}{{{x^2} + 1}}\\ = {x^2} – 6x + 1\\ \frac{{{x^3} + {x^2} + x + 6}}{{x + 2}}\\ = \frac{{{x^2}(x + 2) – x(x + 2) + 3(x + 2)}}{{x + 2}}\\ = \frac{{(x + 2)({x^2} – x + 3)}}{{x + 2}}\\ = {x^2} – x + 3 \end{array}$