The correct answer is:
x²+2x+3.
Explanation:
[tex]\frac{5x^3+10x^2+15x}{5x}[/tex]
We need to divide each term of the numerator by the denominator. For the first term:
[tex]\frac{5x^3}{5x}[/tex]
Dividing the coefficients, we have 5/5 = 1.
When dividing the variables, we use the quotient rule: when dividing powers that have the same base, subtract the exponents. This gives us:
x³/x = x³/x¹ = x³⁻¹ = x²
For the first monomial, this gives us 1x² = x².
The second term:
[tex]\frac{10x^2}{5x}[/tex]
Dividing the coefficients, we have 10/5 = 2.
Dividing the variables, we again use the product rule:
x²/x = x²/x¹ = x²⁻¹ = x¹ = x
Together this gives us 2x.
The third term:
[tex]\frac{15x}{5x}[/tex]
Dividing the coefficients, we have
15/5 = 3.
Dividing the variables, we have x/x; when you divide something by itself, the answer is 1. This gives us:
3*1 = 3.
Together our quotient is x²+2x+3.
