# 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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 Question 190673This question is from textbook : 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 YouThis question is from textbook Answer by jim_thompson5910(28717)   (Show Source): You can put this solution on YOUR website!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:. --------------------------------------------------- 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.