Part A
Answers:
- Number of terms = 2
- Type = Binomial
- Variables = p and q
- Numerical coefficients = 4 and 7
- Degree = 3
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Explanation:
The two terms are separated by a plus sign. Since we have two terms, we have a binomial.
- bi = 2
- nomial = names or terms
The variables are p and q, acting as placeholders for unknown numbers.
The coefficients are the numbers to the left of the variables, which are the 4 and 7.
The degree of multivariable polynomials is found by adding up the exponents for each term, then picking the largest sum. In each case, we get a sum of 3 for each monomial. The degree of the entire polynomial is therefore 3.
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Part B
Answer: t^3 - 20t + 26
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Explanation:
We have an expression of the form
(6t^3-3t+5) - x = (5t^3 + 17t - 21)
which rearranges to
-x = (5t^3 + 17t - 21) - (6t^3-3t+5)
-x = 5t^3 + 17t - 21 - 6t^3 + 3t - 5
-x = (5t^3 - 6t^3) + (17t+3t) + (-21-5)
-x = -t^3 + 20t - 26
x = -(-t^3 + 20t - 26)
x = t^3 - 20t + 26
