(3x^4 + 10 – 19x +11x^3 – 5x^2):(3x-2+x^2) .Gúp mình vs mai mk thi rồi 18/11/2021 Bởi Gianna (3x^4 + 10 – 19x +11x^3 – 5x^2):(3x-2+x^2) .Gúp mình vs mai mk thi rồi
Đáp án: \(3{x^2} + 2x – 5\) Giải thích các bước giải: \(\begin{array}{l}\dfrac{{3{x^4} + 10 – 19x + 11{x^3} – 5{x^2}}}{{3x – 2 + {x^2}}}\\ = \dfrac{{3{x^4} + 11{x^3} – 5{x^2} – 19x + 10}}{{{x^2} + 3x – 2}}\\ = \dfrac{{3{x^4} + 9{x^3} – 6{x^2} + 2{x^3} + 6{x^2} – 4x – 5{x^2} – 15x + 10}}{{{x^2} + 3x – 2}}\\ = \dfrac{{3{x^2}\left( {{x^2} + 3x – 2} \right) + 2x\left( {{x^2} + 3x – 2} \right) – 5\left( {{x^2} + 3x – 2} \right)}}{{{x^2} + 3x – 2}}\\ = \dfrac{{\left( {{x^2} + 3x – 2} \right)\left( {3{x^2} + 2x – 5} \right)}}{{{x^2} + 3x – 2}}\\ = 3{x^2} + 2x – 5\end{array}\) Bình luận
Đáp án:
\(3{x^2} + 2x – 5\)
Giải thích các bước giải:
\(\begin{array}{l}
\dfrac{{3{x^4} + 10 – 19x + 11{x^3} – 5{x^2}}}{{3x – 2 + {x^2}}}\\
= \dfrac{{3{x^4} + 11{x^3} – 5{x^2} – 19x + 10}}{{{x^2} + 3x – 2}}\\
= \dfrac{{3{x^4} + 9{x^3} – 6{x^2} + 2{x^3} + 6{x^2} – 4x – 5{x^2} – 15x + 10}}{{{x^2} + 3x – 2}}\\
= \dfrac{{3{x^2}\left( {{x^2} + 3x – 2} \right) + 2x\left( {{x^2} + 3x – 2} \right) – 5\left( {{x^2} + 3x – 2} \right)}}{{{x^2} + 3x – 2}}\\
= \dfrac{{\left( {{x^2} + 3x – 2} \right)\left( {3{x^2} + 2x – 5} \right)}}{{{x^2} + 3x – 2}}\\
= 3{x^2} + 2x – 5
\end{array}\)