Simplify completely the quantity 5 times x to the third power plus 10 times x to the 2nd power plus 15 times x all over 5 times x. x2 + 10x2 + 15x 2x + 6 x2 + 2x + 3 x4 + 2x3 + 3x2

The correct answer is:

x²+2x+3.

Explanation:



We need to divide each term of the numerator by the denominator.  For the first term:


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:


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:


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.