Given the functions j(x) = x2 − 9 and k(x) = −x + 7, which operation results in a 3rd degree polynomial?
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We want to multiply the monomial by the monomial
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Remember that to multiply monomials we need to use the laws of exponents; in this case, the law for multiplying powers with the same base. The rule says that, when you multiply powers of the same base, you just need to add the exponents: ,
. Also, is worth pointing out that the exponent of a variable with no exponent is 1:
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Remember that we also need to multiply their coefficients , which are the numbers that multiply the variables; again, variables with no numbers have a coefficient of 1, so . Multiply coefficients is easy, you just need to multiply them as you usually do with everyday numbers.
Let's apply all of that to our multiplication:
We can conclude that 2x times x squared is 2x cubed.
