Question

Which among the following is/are factors of 2$x^2$ - 5x +3 ?

• A. 2x - 3
• B. x - 1
• C. x + 1
• D. (a) and (b) above.

Answer 1

The correct option is D (a) and (b) above.

Assume 2x - 3 = 0, then x = $\frac{3}{2}$
$\therefore$when the given polynomial is divided by 2x -3 ,
the remainder = 2$(\frac{3}{2}{)}^2$ - 5$\left(\frac{3}{2}\right)$+3
= 2$\left(\frac{9}{4}\right)$ - $\frac{15}{2}$ + 3
= $\frac{18}{4}$ - $\frac{15}{2}$ + 3
= $\frac{18-30+12}{4}$
= 0, therefore (2x - 3) is a factor.

Assume x - 1 = 0, then x = 1
$\therefore$when the given polynomial is divided by x - 1,
the remainder = 2$(1{)}^2$ - 5(1) +3
= 2 - 5 + 3 = 0, therefore (x - 1) is a factor.

Assume x + 1 = 0, then x = -1
$\therefore$when the given polynomial is divided by x + 1,
the remainder = 2$(-1{)}^2$ - 5(-1) +3
= 2 +5 +3 = 10 , therefore (x + 1) is not a factor.