I am supposed to be learning how to divide polynomials by monomials but im stuck please help. (4x³ + 10x² + 3a) ÷ 2x²
just divide term by term, using the distributive property:
(4x³ + 10x² + 3a) ÷ 2x²
= 4x³÷2x² + 10x²÷2x² + 3a÷2x²
= 2x + 5 + 3a÷2x²
4 x^3/2x^2 = 2x
10 x^2 /2 x^2 = 5
3 a/2x^2 = (3/2) a/x^2
{which is 1.5a x^-2}
now add (distributive property)
2x + 5 + 1.5 a x^-2
To divide a polynomial by a monomial, such as in the expression (4x³ + 10x² + 3a) ÷ 2x², you can follow these steps:
Step 1: Identify the terms
In the given polynomial (4x³ + 10x² + 3a), there are three terms: 4x³, 10x², and 3a.
Step 2: Divide each term by the monomial
Divide each term of the polynomial by 2x² individually:
- For the term 4x³: (4x³) ÷ (2x²) = 2x³
- For the term 10x²: (10x²) ÷ (2x²) = 5x²
- The term 3a does not have any x² term, so when divided by 2x², it remains as (3a) ÷ (2x²)
Step 3: Simplify the expression
The simplified result of the division is: 2x³ + 5x² + (3a ÷ 2x²)
So, the final result of (4x³ + 10x² + 3a) ÷ 2x² is 2x³ + 5x² + (3a ÷ 2x²).