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

Answer: B

Explanation:

Answer 2

`(3x+5)`

Explanation:

The given polynomial expression is:
`6x^2+x-15`

We compare to
`ax^2+bx+c` and have a=6,b=1,c=-15

The product
`ac=6* -15=-90`

Two factors of -90 that sums to 1 are -9 and 10

We split the middle term to get:

`6x^2+10x-9x-15`

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

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

Therefore the other factor is:

`(3x+5)`