Respuesta :
Answer:
Option 2 - 3x+5
Step-by-step explanation:
Given : Polynomial [tex]6x^2+x-15[/tex] has a factor of 2x-3.
To find : What is the other factor?
Solution :
Expression[tex]6x^2+x-15=0[/tex]
Solve by quadratic formula,
The general form of quadratic equation is [tex]ax^2+bx+c=0[/tex] with solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
On comparing with [tex]6x^2+x-15=0[/tex], a=6 , b=1, c=-15
Substitute in solution,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-1\pm\sqrt{(1)^2-4(6)(-15)}}{2(6)}[/tex]
[tex]x=\frac{-1\pm\sqrt{1+360}}{12}[/tex]
[tex]x=\frac{-1\pm\sqrt{361}}{12}[/tex]
[tex]x=\frac{-1\pm 19}{12}[/tex]
[tex]x=\frac{-1+19}{2},\frac{-1-19}{12}[/tex]
[tex]x=\frac{18}{12},\frac{-20}{12}[/tex]
[tex]x=\frac{3}{2},\frac{-5}{3}[/tex]
So, The two factors are [tex](x-\frac{3}{2}),(x+\frac{5}{3})[/tex]
or [tex](2x-3),(3x+5)[/tex]
One factor is given i.e. (2x-3) so other factor is (3x+5).
Therefore, Option 2 is correct.
