SOLUTION: If a fourth degree polynomial is multiplied by a third degree polynomial, what is the degree of the product? Explain your reasoning and provise examples. Thank You

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The product of a fourth degree polynomial and a third degree polynomial is a 7th degree polynomial (just add the two degrees). Why is this the case? Remember, when you multiply variables with common bases, you add the exponents. Since the degree of a polynomial is just the largest exponent, you're really just adding the degrees when you multiply



Example: Let's multiply the fourth degree binomial and the third degree binomial :



Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


Multiply the First terms:.


Multiply the Outer terms:.


Multiply the Inner terms:.


Multiply the Last terms:.


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So we have the terms: , , ,


Now add every term listed above to make a single expression.


Now combine like terms.


So FOILs to .


In other words, .


Notice how the degree of the final answer is 7. So this confirms the original claim.