Polynomials and Properties of Exponents Review Practice
Connections Academy 8th Grade
Please only use this to check your answers.
Equations with / are fractions and the ^ are for exponents.
1. Write and simplify the polynomial represented by the model.
A. -2x^2 + 2x + 3
B. 2x^2 - 2x - 3 ***
C. 3x^2 - 2x - 3
D. 2x^2 - 2x + 3
2. Simplify the polynomial.
3x^2 + 5x - 5x^2 - 4x + 5 - 2
A. -8x^2 - 9x + 3
B. 2x^2 + x + 3
C. -2x^2 - 9x + 3
D. -2x^2 + x + 3 ***
3. (8x - 2y)+(3x - 4y)
A. 11x + 8y
B. 4x - y
C. 11x - 6y ***
D. 5x + 2y
4. (5x^2 - 4x - 1)-(-4x^2 - 4)
A. -9x^2 - 8x - 1
B. 9x^2 - 4x + 3 ***
C. x^2 - 4x - 3
D. 9x^2 + 4x - 3
5. The distance from Newtown to Oldtown on the highway is (6x^2 + 2x - 2) miles. Using the back roads, the distance is (5x^2 - 8x - 6) miles. How many miles shorter is the second route?
A. 11x^2 + 10x - 8
B. -x^2 - 6x + 4
C. x^2 + 10x + 4 ***
D. x^2 - 6x - 8
6. 7^5 x 7^6
A. 49^30
B. 7^ 30
C. 49^11
D. 7^11 ***
7. 6^a x 6^v
A. 6^a + v ***
B. 6^av
C. 36^av
D. 36^a + v
8. 2^8/2^7
A. 2^1 ***
B. 2^8/7
C. 2^56
D. 2^15
9. x^56/x^24
A. x^80
B. x^23
C. x^32 ***
D. none of these
10. Multiply. Write the result in scientific notation.
(9 x 10^4)(8 x 10^6)
A. 7.2 x 10^25
B. 1.7 x 10^11
C. 7.2 x 10^11 ***
D. 1.7 x 10^25
11. Find the area of the rectangle.
A. 15x + 1
B. 56x^2 + 8x ***
C. 56x + 8
D. 15x^2 + 9x
12. (-8x) x 3x^2
A. -5x^3
B. -24x^2
C. -24x^3 ***
D. -5x^2
13. (-11z)^0
A. z
B. 1 ***
C. -11
D. -1
14. 14^-4
A. 1/14^4 ***
B. -56
C. 1/14
D. 1/14^-4
A. 1/14^4 ***
1. The polynomial represented by the model is B. 2x^2 - 2x - 3.
2. Simplifying the polynomial 3x^2 + 5x - 5x^2 - 4x + 5 - 2 gives us D. -2x^2 + x + 3.
3. (8x - 2y) + (3x - 4y) simplifies to C. 11x - 6y.
4. (5x^2 - 4x - 1) - (-4x^2 - 4) simplifies to B. 9x^2 - 4x + 3.
5. The second route is (5x^2 - 8x - 6) miles long, which is C. x^2 + 10x + 4 miles shorter than the first route.
6. 7^5 x 7^6 simplifies to D. 7^11.
7. 6^a x 6^v simplifies to A. 6^a + v.
8. 2^8/2^7 simplifies to A. 2^1.
9. x^56/x^24 simplifies to C. x^32.
10. Multiplying (9 x 10^4)(8 x 10^6) gives us C. 7.2 x 10^11 in scientific notation.
11. The area of the rectangle is the product of its length and width. Since the length is 8x and the width is 7x, the area is (8x)(7x) = 56x^2 + 8x, which is B. 56x^2 + 8x.
12. (-8x) x 3x^2 simplifies to C. -24x^3.
13. (-11z)^0 is equal to 1, so the answer is B. 1.
14. 14^-4 is equal to 1/14^4, so the answer is A. 1/14^4.