Question

[Harold Joseph]

Tìm x

a)2x³ + 3x² + 2x + 3 = 0

b)x(2x - 1 ) (1- 2x) = 0

mình học dạng phân tích đa thức thành nhân tử nha

giúp mình nha :))))))))

Answer 1

[Lightning Farron]

a)\(2x^3+3x^2+2x+3=0\)

\(\Leftrightarrow2x^3+2x+3x^2+3=0\)

\(\Leftrightarrow2x\left(x^2+1\right)+3\left(x^2+1\right)=0\)

\(\Leftrightarrow\left(2x+3\right)\left(x^2+1\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}2x+3=0\\x^2+1=0\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}2x=-3\\x^2+1>0\left(loai\right)\end{array}\right.\)

\(\Leftrightarrow x=-\frac{3}{2}\)

b)\(x\left(2x-1\right)\left(1-2x\right)=0\)

\(\Leftrightarrow-x\left(2x-1\right)\left(2x-1\right)=0\)

\(\Leftrightarrow-x\left(2x-1\right)^2=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}-x=0\\\left(2x-1\right)^2=0\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\2x=1\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=\frac{1}{2}\end{array}\right.\)

Answer 2

[Phương An]

\(2x^3+3x^2+2x+3=0\)

\(2x\left(x^2+1\right)+3\left(x^2+1\right)=0\)

\(\left(2x+3\right)\left(x^2+1\right)=0\)

\(2x+3=0\left(x^2+1\ge1>0\right)\)

\(2x=-3\)

\(x=-\frac{3}{2}\)

\(x\left(2x-1\right)\left(1-2x\right)=0\)

\(\left[\begin{array}{nghiempt}x=0\\2x-1=0\\1-2x=0\end{array}\right.\)

\(\left[\begin{array}{nghiempt}x=0\\2x=1\\2x=1\end{array}\right.\)

\(\left[\begin{array}{nghiempt}x=0\\x=\frac{1}{2}\end{array}\right.\)