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{:[p(n)=(n^(3)-12n^(2)+47 n-60)],[q(n)=(n+13)(n-4)]:} The functions p and q are defined. One of the functions has a zero at n=5. What is the value of p(5)+q(5) ?

p(n)=(n3−12n2+47n−60)q(n)=(n+13)(n−4) \begin{array}{l} p(n)=\left(n^{3}-12 n^{2}+47 n-60\right) \\ q(n)=(n+13)(n-4) \end{array} \newlineThe functions p p and q q are defined. One of the functions has a zero at n=5 n=5 . What is the value of p(5)+q(5)? p(5)+q(5) ?

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Q. p(n)=(n3−12n2+47n−60)q(n)=(n+13)(n−4) \begin{array}{l} p(n)=\left(n^{3}-12 n^{2}+47 n-60\right) \\ q(n)=(n+13)(n-4) \end{array} \newlineThe functions p p and q q are defined. One of the functions has a zero at n=5 n=5 . What is the value of p(5)+q(5)? p(5)+q(5) ?
  1. Identify zero at n=5n=5: Identify which function has a zero at n=5n=5. To find out if p(n)p(n) or q(n)q(n) has a zero at n=5n=5, we need to substitute nn with 55 in both functions and see if the result equals zero. First, let's check p(5)p(5): p(5)=(53)−12×(52)+47×5−60p(5) = (5^3) - 12\times(5^2) + 47\times5 - 60 p(5)=125−300+235−60p(5) = 125 - 300 + 235 - 60 n=5n=500
  2. Check p(5)p(5): Since we have found that p(5)=0p(5) = 0, we do not need to check q(5)q(5) for being zero because the question only asks for the function that has a zero at n=5n=5, which we have already identified as p(n)p(n). Now we need to calculate q(5)q(5).\newlineq(5)=(5+13)(5−4)q(5) = (5 + 13)(5 - 4)\newlineq(5)=18×1q(5) = 18 \times 1\newlineq(5)=18q(5) = 18
  3. Check q(5)q(5): Calculate p(5)+q(5)p(5) + q(5).\newlineSince we have already found that p(5)=0p(5) = 0, we only need to add q(5)q(5) to it.\newlinep(5)+q(5)=0+18p(5) + q(5) = 0 + 18\newlinep(5)+q(5)=18p(5) + q(5) = 18

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