5.2 Homework Problems: Introduction to Polynomials & Addition and Subtraction

1. Identify each expression as a monomial or polynomial

a. 3x⁴

b. 4xy³

c. 14a⁷ – 2a – 6

d. 7x + 3

e. 4m³7y²

f. [latex]\frac{1}{2}[/latex]x³ – [latex]\frac{2}{5}[/latex]x

2. Simplify the polynomial by combining like terms. Write the polynomial in descending order and state the degree and the leading coefficient

a. 6a⁵ + 2a² -7a³ – 3a²

b. 7x³ + 3x² – 2x + x – 5x³ + 1

c. 2x + 4x² + 6x + 9x³

3. Evaluate the given polynomials

a. p(x) = x² + 14x – 3 for p(-1)

b. g(x) = 3x³ – 9x² – 10x – 11 for g(3)

c. q(a) = 2a⁴ + 3a² – 8a for q(-1)

d. f(x) = 3x+5 for f(a+2)

e. h(x) = 5x – 10 for h(2a+7)

4. Simplify the following polynomials using addition and subtraction

a. (2x² – x – 1) + (x² + x + 1) = _____________________________________

b. (-4x² + 2x – 1) + (3x² – x + 2 ) + (x – 8) = _________________________________

c. (4x² + x – 1) + (6x – 5) – ( 3x² – 4x + 2) = ___________________________________

d. (x² + 2x – 1) + (3x² – x + 2) + (2x³ – 4x – 8) = ___________________________________

e. (2x² – x – 10) – (– x² + 3x – 2) = ___________________________________

f. (– 3x⁴ + 2x³ – 7x² + 6x + 12) – (x⁴ + 9x³ + 4x² + x – 1) = _________________________

g. (3x⁴ – 2x³ – 8x – 1) – (5x³ – 3x² – 3x – 10) = ___________________________________

h. 5x + 2(x – 3) – (3x +7) = ___________________________________

i. (x² – 1) + 2[4 + (3 – x)] = __________________________________

j. Subtract 3x² – 4 x + 2 from the sum of 4x² + x – 1 and 6x – 5

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