Adding and Subtracting Polynomials

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Show your work for each problem.

1.
Which terms are like terms?
1. a) $3x^2$ and $5x^2$
2. b) $2x$ and $2y$
3. c) $x^3$ and $x^2$
4. d) $3x^2$ and $3x$
2.
Combine the like terms: $4x^2 + 7x^2 = \square\, x^2$ . What number goes in the box?
3.
Combine the like terms: $9x - 4x = \square\, x$ . What number goes in the box?
4.
What is the result of $(2x + 5) + (3x + 4)$ ?
1. a) $6x + 9$
2. b) $5x^2 + 9$
3. c) $5x + 1$
4. d) $5x + 9$
5.
Add: $(3x^2 + 2x) + (x^2 + 5x)$
6.
What is $(5x^2 - 3x + 2) - (2x^2 + x - 4)$ ?
1. a) $3x^2 - 4x - 2$
2. b) $7x^2 - 2x - 2$
3. c) $3x^2 - 2x - 2$
4. d) $3x^2 - 4x + 6$
7.
Add: $(x^2 + 4x - 3) + (2x^2 - x + 7)$ . What is the constant term of the result?
8.
Subtract: $(4x^2 + 5x - 1) - (x^2 - 3x + 2)$
9.
Add: $(x^3 + 2x) + (4x^2 - x + 5)$ . What is the coefficient of $x$ in the result?
10.
Simplify: $(6x^2 - 4x + 3) - (2x^2 - 4x - 5)$
11.
A rectangle has length $(3x + 5)$ and width $(x + 2)$ . If the length is increased by $(x - 1)$ , what is the new length?
1. a) $3x + 4$
2. b) $4x + 4$
3. c) $4x + 6$
4. d) $2x + 6$
12.
Subtract: $(3x^2 - 2x + 1) - (-x^2 + 4x - 3)$ . What is the coefficient of $x$ in the result?
13.
Simplify: $(2x^3 - x^2 + 3x) + (x^3 + 4x^2 - x + 2) - (x^3 - 2x + 1)$
14.
If $P(x) = 5x^2 - 3x + 7$ and $Q(x) = 2x^2 + x - 4$ , what is $P(x) - 2Q(x)$ ?
1. a) $x^2 - x + 15$
2. b) $x^2 - 5x - 1$
3. c) $x^2 - 5x + 15$
4. d) $9x^2 - 5x - 1$
15.
Find the polynomial that must be added to $(2x^2 - 5x + 3)$ to get $(5x^2 + x - 4)$ .
16.
Work out: $-(3x^2 - 2x + 4) + (x^2 + 5x - 1) - (2x^2 - x)$ . What is the coefficient of $x^2$ in the result?