Question

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

Answer 1

`\large \boxed{\sf \ \ \ (x+2)(x-(1)/(2)) \ \ \ }`

Explanation:

Hello,

let's solve

`x^2+(3)/(2)x-1=0\\\\<=> 2x^2+3x-2=0 \ \text{multiply by 2}\\\\\\`

`\Delta=b^2-4ac=9+4*2*2=9+16=25`

There are two solutions

`x_1=(-3-√(25))/(4)\\\\x_1=(-3-5)/(4)\\\\x_1=(-8)/(4)\\\\\boxed{x_1=-2}`

And

`x_2=(-3+√(25))/(4)\\\\x_2=(-3+5)/(4)\\\\x_2=(2)/(4)\\\\\boxed{x_2=(1)/(2)}`

So we can write

`x^2+(3)/(2)x-1\\\\=(x-x_1)(x-x_2)\\\\=(x+2)(x-(1)/(2))`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you