Multiplying a Monomial by a Polynomial A polynomial is a combination of constants and variables raised to different powers. Multiplying a monomial by a poly...
Multiplying a Monomial by a Polynomial
A polynomial is a combination of constants and variables raised to different powers. Multiplying a monomial by a polynomial involves combining the coefficients and exponents of like terms.
Step 1: Identify the degrees of the monomial and the polynomial.
The degree of a monomial is the highest exponent of the variable.
The degree of a polynomial is the highest exponent of all the variables involved.
Step 2: Multiply the coefficients of like terms.
Coefficients are numbers in front of variables raised to specific powers.
When multiplying coefficients, they are added together.
Step 3: Combine like terms.
Like terms are terms with the same variable and exponent.
These terms can be added together to form a new term in the polynomial.
Example:
Multiply (x + 2) by x^2 + 3x - 1.
Step 1:
Monomial: x + 2
Polynomial: x^2 + 3x - 1
Step 2:
Coefficients: 1, 3, -1
Multiply coefficients: 1 * 1 = 1, 3 * 2 = 6, -1 * 1 = -1
Step 3:
Therefore, (x + 2) * (x^2 + 3x - 1) = x^3 + 6x^2 - x + 2x^2 + 6x - 2