Question

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

X-1/2
X-2
X-1
X+3/2

Answer 1

`x^2+(3)/(2)x-1=x^2-(1)/(2)x+2x-1=x\left(x-(1)/(2)\right)+2\left(x-(1)/(2)\right)\\\\=\left(x-(1)/(2)\right)(x+2)\\\\Answer:\ x-(1)/(2)`

Answer 2

`(x -(1)/(2))`.

Explanation:

Given :
`x^(2) +(3x)/(2) -1`.

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

Solution : We have given

`x^(2) +(3x)/(2) -1`.

On factoring

`x^(2) -(1x)/(2) + 2x -1`.

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

`x(x -(1)/(2))+ 2 (x -(1)/(2))`.

On grouping

`(x -(1)/(2)) (x + 2)`.

Therefore,
`(x -(1)/(2))`.