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Algebra Operations with Polynomials

1. For each polynomial listed below, determine
i the degree of the polynomial
ii the coefficient of the leading term
iii the constant term

a. P(x) = x + 1
b. Q(x) = 3x + 2
c. R(x) = x2 + 2x + 1
d. W(x) = 4x2 + x + 3
e. Z(x) = 3x3 + 2x2 + x

Questions 2 through 8 below refer to the polynomials P(x), Q(x), R(x), and Z(x) of question #1.

2. What is the value of P(1), that is, P(x) above evaluated at x = 1?
3. What is the value of Z(1), that is, Z(x) evaluated at x = 1?
4. What is the value of Z(2)?

5. What is the polynomial resulting from the polynomial addition P(x) + Q(x)?
6. What is the polynomial resulting from the polynomial subtraction Q(x) - P(x)?
7. What is the polynomial resulting from the polynomial multiplication P(x) * Q(x)?
8. What is the polynomial resulting from the polynomial division R(x) / P(x)?

9. Simplify

a. (5x4)3
b. (-3x2)3

10. Simplify. Write answers without negative exponents

a. (-2x-2y)-3
b. (-3x-3y)2

Attachments

Solution Summary

This solution shows the step for adding, multiplying and subtraction polynomial and rising monomials to several exponents in an attached Word document.

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