1. Write and simplify the polynomial represented by the model.
The algebra tiles listed are: 3 white boxes (x^2), 2 black rectangles (x), 3 white ones, 1 black box (x^2), and 6 black ones.
A.) -2x²+2x+3
B.) 2x²-2x-3
C.) 3x²-2x-3
D.) 2x²-2x+3
D) 2x²-2x+3 (combining the 3 white boxes and 1 black box gives 4x², and combining the 2 black rectangles and 6 black ones gives -8x, simplifying to 2x²-2x+3)
2. Simplify the polynomial.
3x²+5x-5x² - 4x + 5 − 2 -
A.) -8x²-9x+3
B.) 2x²+x+3
C.) -2x²-9x+3
D.) -2x²+x+3
C) -2x²-9x+3 (combining like terms, -5x² and 3x² gives -2x², -4x and 5x gives -9x, and combining the constant terms gives 3)
Add or subtract.
(8x-2y)+(3x-4y)
A.) 11x+8y
B.) 4x-y
C.) 11x-6y
D.) 5x+2y
A) 11x+8y (adding the like terms, 8x and 3x gives 11x, and -2y and -4y gives -6y, resulting in 11x-6y)
Add or subtract.
(5x² - 4x-1)-(-4x²-4)
A.) -9x²-8x-1
B.) 9x²-4x+3
C.) x²-4x-3
D.) 9x²+4x-3
D) 9x²+4x-3 (distributing the negative in the second term of the expression being subtracted gives 4x²+4x, which simplifies to -9x²+9x-3)
The distance from Newtown to Oldtown on the highway is (6x² + 2x − 2) miles. Using the back roads, the distance is (5x² - 8x-6) miles. How many miles shorter is the second route?
A.) 11x²+10x-8
B.) -x²-6x+4
C.) x²+10x+4
D.) x²-6x-8
B) -x²-6x+4 (subtracting the second expression from the first gives (6x² + 2x − 2) - (5x² - 8x-6) = x²+10x-8, which is the simplified expression for the distance difference. To find the difference in distance, we only need the coefficient of the x² term which is -1)
7^5 * 7^6
A.) 49^30
B.) 7^30
C.) 49^11
D.) 7^11
B) 7^30 (when multiplying exponential expressions with the same base, we add the exponents, giving 7^(5+6) which simplifies to 7^11)
6^a * 6^v
A.) 6^a+v
B.) 6^av
C.) 36^av
D.) 36^a+v
A) 6^a+v (when multiplying exponential expressions with the same base, we add the exponents, giving 6^(a+v))
8. 28 27
(1 point)
A.) 2^1
B.) 2^8/7
C.) 2^56
D.) 2^15
B) 2^8/7 (using the rule that says x^(a/b) is equivalent to the bth root of x^a, we can rewrite the expression as the 8/7th root of (2^7)^4, which simplifies to the 8/7th root of 2^28, and therefore, 2^(8/7))
x^56/x^24
A.) x^80
B.) x^23
C.) x^32
D.) none of these
C) x^32 (when dividing exponential expressions with the same base, we subtract the exponents, giving x^(56-24) which simplifies to x^32)
(9.104) (8.106)
A.) 7.2.1025
B.) 1.7.1011
C.) 7.2.1011
D.) 1.7.1025
B) 1.7.1011 (multiplying the two numbers and expressing the answer in scientific notation gives (9.104) (8.106) = 7.2 * 10^11, which is equivalent to 1.7.1011)
Find the area of the rectangle:
length: 7x + 1
hight: 8x
A.) 15x+1
B.) 56x²+8x
C.) 56x+8
D.) 15x²+9x
B) 56x²+8x (the area of a rectangle is given by multiplying its length by its height, which gives (7x+1)(8x) = 56x²+8x)
12. (-8x) 3x²
A.) -5x^3
B.) -24x^2
C.) -24x^3
D.) -5x^2