Question

The polynomial 6x2 + x − 15 has a factor of 2x − 3. What is the other factor?

3x − 5
3x + 5
4x − 5
4x + 5

Answer 1

6x^2 / 2x = 3x and
-15 / -3 = +5

so the answer is (3x + 5)

Answer 2

Option 2 - 3x+5

Explanation:

Given : Polynomial
`6x^2+x-15` has a factor of 2x-3.

To find : What is the other factor?

Solution :

Expression
`6x^2+x-15=0`

Solve by quadratic formula,

The general form of quadratic equation is
`ax^2+bx+c=0` with solution
`x=(-b\pm√(b^2-4ac))/(2a)`

On comparing with
`6x^2+x-15=0`, a=6 , b=1, c=-15

Substitute in solution,

`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-1\pm√((1)^2-4(6)(-15)))/(2(6))`

`x=(-1\pm√(1+360))/(12)`

`x=(-1\pm√(361))/(12)`

`x=(-1\pm 19)/(12)`

`x=(-1+19)/(2),(-1-19)/(12)`

`x=(18)/(12),(-20)/(12)`

`x=(3)/(2),(-5)/(3)`

So, The two factors are
`(x-(3)/(2)),(x+(5)/(3))`

or
`(2x-3),(3x+5)`

One factor is given i.e. (2x-3) so other factor is (3x+5).

Therefore, Option 2 is correct.