Answer:
[tex]3x - 11[/tex]
Step-by-step explanation:
Given
[tex]\frac{3x^2 + 4x + 5}{x + 5}[/tex]
Required
Determine the quotient
First, we check if the divisor (x + 5) can divide the dividend (3x^2 + 4x + 5) without having a reminder
Equate the denominator to 0.
[tex]x + 5 = 0[/tex]
[tex]x = -5[/tex]
Substitute -5 for x in the numerator
[tex]3x^2 + 4x + 5 = 3*(-5)^2 + 4 * (-5) + 5[/tex]
[tex]3x^2 + 4x + 5 = 60[/tex]
This means that it has a reminder of 60
To get the quotient, we subtract 60 from the numerator and evaluate
[tex]\frac{3x^2 + 4x + 5}{x + 5}[/tex] becomes
[tex]\frac{3x^2 + 4x + 5 - 60}{x + 5}[/tex]
[tex]\frac{3x^2 + 4x - 55}{x + 5}[/tex]
Expand the numerator
[tex]\frac{3x^2 + 15x - 11x - 55}{x + 5}[/tex]
Factorize:
[tex]\frac{3x(x + 5) - 11(x + 5)}{x + 5}[/tex]
Factor out x + 5
[tex]\frac{(3x- 11)(x + 5)}{x + 5}[/tex]
Cancel out x + 5
[tex]3x - 11[/tex]
Hence, the quotient is [tex]3x - 11[/tex]
