How can i Multiply and Divide Polynomials by Monomials?
X+7=4
To multiply and divide polynomials by monomials, you need to follow certain steps. Let's start with multiplication.
1. Multiplying a polynomial by a monomial:
- Multiply each term of the polynomial by the monomial.
- Use the distributive property to simplify.
- Combine like terms, if any, by adding or subtracting.
For example, let's multiply the polynomial (2x^2 - 3x + 4) by the monomial 5x:
(2x^2 - 3x + 4) * 5x
Multiply each term:
2x^2 * 5x = 10x^3
-3x * 5x = -15x^2
4 * 5x = 20x
Simplify:
10x^3 - 15x^2 + 20x
2. Dividing a polynomial by a monomial:
- Divide each term of the polynomial by the monomial.
- Simplify each division, if possible.
- Combine like terms, if any, by adding or subtracting.
For example, let's divide the polynomial (6x^3 - 9x^2 + 12x) by the monomial 3x:
(6x^3 - 9x^2 + 12x) / 3x
Divide each term:
6x^3 / 3x = 2x^2
-9x^2 / 3x = -3x
12x / 3x = 4
Simplify:
2x^2 - 3x + 4
Remember to carefully simplify each expression, combine like terms, and follow the rules of exponents when dealing with variables raised to powers.