Degree of a Product
Degree of a product is a Grade 7 algebra skill from Yoshiwara Intermediate Algebra teaching that the degree of a product of polynomials equals the sum of their individual degrees. For example, multiplying a degree-2 polynomial by a degree-3 polynomial yields a degree-5 polynomial.
Key Concepts
Property The degree of a product of non zero polynomials is the sum of the degrees of the factors. That is: If $P(x)$ has degree $m$ and $Q(x)$ has degree $n$, then their product $P(x)Q(x)$ has degree $m + n$.
Examples If you multiply a polynomial of degree 3 by a polynomial of degree 4, the resulting polynomial will have a degree of $3 + 4 = 7$. Let $P(x) = 3x^5 + x$ and $Q(x) = 2x^2 1$. The degree of $P(x)Q(x)$ is $5 + 2 = 7$. The lead term of the product $(4x^2 + 3x)(2x^3 5)$ is found by multiplying the lead terms of each factor: $(4x^2)(2x^3) = 8x^5$. The degree is 5.
Explanation When you multiply polynomials, their degrees add up. To find the degree of the resulting polynomial, just sum the degrees of the original polynomials you are multiplying together. This is a quick way to know the final outcome without full calculation.
Common Questions
What is the degree of a product of polynomials?
The degree of the product equals the sum of the degrees of the factors. For example, (degree 2) times (degree 3) = degree 5.
What is the degree of (x^2 + 1)(x^3 - 2x)?
The product has degree 2 + 3 = 5.
Does this rule apply to polynomials with more than two factors?
Yes. For a product of k polynomials, the degree of the result equals the sum of all k degrees.
Why does degree add when multiplying polynomials?
When you multiply the leading terms, you add their exponents. The highest degree term in the product comes from multiplying the highest degree terms of each factor.