Answer:
The quotient is 3x+4
Step-by-step explanation:
Given the dividend and divisor i.e we have to find the quotient if [tex]6x^2+23x+20[/tex] is divided by 5+2x
Given dividend is
[tex]6x^2+23x+20[/tex]
⇒ [tex]6x^2+15x+8x+20[/tex]
⇒ [tex]3x(2x+5)+4(2x+5)[/tex]
⇒ [tex](3x+4)(2x+5)[/tex]
Hence, the given dividend can written in two factors.
Now, [tex]\frac{6x^2+23x+20}{5+2x}=\frac{(3x+4)(2x+5)}{2x+5}=3x+4[/tex]
Hence, the quotient is 3x+4
