Adding and Subtracting Polynomials Quiz
Questions: 16 · 10 minutes
1. Simplify (-2p² + 7p - 5) - (3p² - 4p + 2).
p² + 3p - 3
-5p² + 3p - 7
-5p² + 11p - 7
-5p² + 11p - 3
2. After simplifying (3x⁴ + x²) - (3x⁴ - 2x³ + 5), what is the degree of the result?
4
3
1
2
3. When (z³ + 5z - 4) is subtracted from z³ - 2z + 9, which polynomial remains?
2z³ + 3z + 5, a cubic expression with a positive linear term
7z + 13, a linear expression with a positive coefficient
-7z + 5, a linear expression with five as its constant
-7z + 13, because the cubic terms cancel during subtraction
4. Which term is like -7m³ and can therefore be combined with it?
2m³, which has the same variable raised to the third power
2m, which has the same variable raised to the first power
2m², which has the same variable raised to the second power
2n³, which has a different variable raised to the third power
5. Nora claims that (½x² + 3x) + (1½x² - x) simplifies to 2x² + 2x. Which assessment is accurate?
The x² coefficient should be 1 because the fractional coefficients must be subtracted.
The linear term should be 4x because the negative sign before x can be ignored in addition.
Nora is correct because the x² coefficients total 2 and the linear coefficients total 2.
The expression cannot be simplified because fractional coefficients are not like terms.
6. Simplify (3x² + 5x - 2) + (2x² - x + 7).
5x² + 4x - 9
5x² + 6x + 5
6x² + 4x + 5
5x² + 4x + 5
7. A student is about to simplify (5x² - 2x + 1) - (2x² + 3x - 4). Which procedure should the student use?
Subtract only the leading terms and add all remaining terms.
Combine every term because all terms belong to polynomials.
Change every sign in the first polynomial before combining terms.
Distribute the subtraction sign to every term in the second polynomial, then combine like terms.
8. A triangular frame has side lengths x + 2, 2x - 1, and 3x + 4. Which calculation gives its perimeter?
6x + 5, obtained by adding all three side expressions
6x + 7, obtained when the negative constant is treated as positive
5x + 5, obtained after omitting one x-term
6x² + 5, obtained by multiplying rather than adding variable terms
9. An original display uses 8x² + 3x + 10 tiles, while a redesigned display uses 5x² - 2x + 6 tiles. Which expression shows how many more tiles the original model uses?
3x² + x + 4, found without changing the sign of the redesigned linear term
13x² + x + 16, found by adding the two display models
3x² + 5x + 4, found by subtracting the redesigned model from the original
3x² - 5x + 4, found by reversing the order of the linear coefficients
10. If (kx² + 3x) + (2x² - x) = 7x² + 2x, what is the value of k?
5
9
2
7
11. A polynomial added to 2y² + 3y - 4 produces 5y² - y + 8. What is the missing polynomial?
3y² + 2y + 4
3y² - 4y + 12
7y² + 2y + 4
3y² - 2y - 12
12. A shop models first-week revenue by R(n) = 4n² + 2n - 6 and second-week revenue by S(n) = n² - 3n + 8. Which expression represents R(n) - S(n)?
3n² + 5n - 14, after subtracting every term of S(n)
5n² - n + 2, after adding the two weekly models
3n² - n + 2, with the subtraction signs left undistributed
3n² - 5n - 14, with the linear terms combined using the wrong sign
13. A student subtracts 3x² - 2x + 6 from x² + 4x - 1. Which result is correct?
-2x² + 2x + 5, with positive two as the linear coefficient
-2x² + 6x - 7, with six as the linear coefficient
-2x² + 2x - 7, with negative seven but an unchanged linear sign
2x² + 6x - 7, with a positive leading coefficient
14. Simplify (6a² - 3a + 4) - (2a² + a - 5).
4a² - 2a - 1
4a² - 4a + 9
8a² - 4a - 1
4a² - 4a - 1
15. Simplify (4t³ - 2t + 1) + (-t³ + 5t² - 3).
3t³ + 3t² - 2
3t³ + 5t² - 4t - 2
5t³ + 5t² - 2t - 2
3t³ + 5t² - 2t - 2
16. Let P(x) = 2x² - x + 3 and Q(x) = -x² + 4x - 1. What is the value of P(x) + Q(x) when x = 2?
14
8
12
20