Respuesta :
[tex]x^2+\dfrac{3}{2}x-1=x^2-\dfrac{1}{2}x+2x-1=x\left(x-\dfrac{1}{2}\right)+2\left(x-\dfrac{1}{2}\right)\\\\=\left(x-\dfrac{1}{2}\right)(x+2)\\\\Answer:\ x-\dfrac{1}{2}[/tex]
Answer:
[tex](x -\frac{1}{2})[/tex].
Step-by-step explanation:
Given : [tex]x^{2} +\frac{3x}{2} -1[/tex].
To find : Which of the following expressions is a factor of the polynomial.
Solution : We have given
[tex]x^{2} +\frac{3x}{2} -1[/tex].
On factoring
[tex]x^{2} -\frac{1x}{2} + 2x -1[/tex].
Taking common x from first two terms and 2 from last two terms.
[tex]x(x -\frac{1}{2})+ 2 (x -\frac{1}{2})[/tex].
On grouping
[tex](x -\frac{1}{2}) (x + 2)[/tex].
Therefore, [tex](x -\frac{1}{2})[/tex].