Question

Which of the following expressions is a factor of the polynomial x^2 + 3/2x -1

Answer 1

Answer:

$(x -\frac{1}{2})$.

Step-by-step explanation:

Given  : $x^{2} +\frac{3x}{2} -1$.

To find : Which of the following expressions is a factor of the polynomial.

Solution : We have given

$x^{2} +\frac{3x}{2} -1$.

On factoring

$x^{2} -\frac{1x}{2} + 2x -1$.

Taking common x from first two terms and 2 from last two terms.

$x(x -\frac{1}{2})+ 2 (x -\frac{1}{2})$.

On grouping

$(x -\frac{1}{2}) (x + 2)$.

Therefore, $(x -\frac{1}{2})$.

Answer 2

$x^2+\dfrac{3}{2}x-1=x^2-\dfrac{1}{2}x+2x-1=x\left(x-\dfrac{1}{2}\right)+2\left(x-\dfrac{1}{2}\right)\\\\=\left(x-\dfrac{1}{2}\right)(x+2)\\\\Answer:\ x-\dfrac{1}{2}$