Show:
Polynomials
Finding Roots
Exponents
Linear Equations
Radicals
100
Find the sum of (5a^2 - 3) + (8a^2-1).
Steps: 1. (5a^2 - 3) + (8a^2 - 1) 2. 5a^2 - 3 + 8a^2 - 1 Answer: 13a^2 - 4
100
Find the roots of the equation (x+2)(x+6).
Answer: x=-2, -6
100
Simplify the expression 4^2 * 4^6.
Answer: 4^8
100
Write the equation so that y is a function of x 2x+y=7.
Answer: y=7 - 2x
100
Simplify √32 (square root of 32).
Steps: 1.√16*2 2. √16 * √2 Answer: 4√2
200
Find the sum of (4m^2 - m + 2) + (-3m^2 + 10m + 7).
Steps: 1. (4m^2 - m + 2) + (-3m^2 + 10m + 7) 2. 4m^2 - m + 2 - 3m^2 + 10m + 7 Answer: m^2 + 9m + 9
200
Find the roots of the equation (3x+6)(5x+10).
Steps: 1. 3x + 6=0 1. 5x + 10=0 2. 3x = -6 2. 5x = -10 3. x = -2 3. x = -2 Answer: x=-2
200
Solve for x when 7^x * 7^2 / 7^4 = 7^6.
Steps: 1. 7^x * 7^2 / 7^4 = 7^6 2. 7^x * 7^2 = 7^10 3. 7^x = 7^8 Answer: x=8
200
Solve the equation 7=5/6c - 8.
Steps: 1. 7=5/6c - 8 2. 15=5/6c 3. 90= 5c Answer: c = 18
200
Simplify √9x^3 (square root of 9x cubed).
Steps: 1. √9 * x^2 * X 2. √9 √x^2 √x Answer: 3x√x
300
Find the product of (y - 5) (2y + 3).
Steps: 1. (y - 5) (2y + 3) 2. 2y^2 + 3y - 10y -15 Answer: 2y^2 - 7y - 15
300
Find the roots of the equation (5x-3)(8x+5).
Steps: 1. 5x - 3=0 1. 8x + 5=0 2. 5x = 3 2. 8x = -5 3. x = 3/5 3. x = -5/8 The answer is x=3/5, -5/8
300
Simplify the expression using only positive exponents 5m^-3 n^-4.
Answer: 5/m^3 n^4
300
Solve the equation -32 = 8/7(3w-1).
Steps: 1. -32 = 8/7(3w-1) 2. -32 = 24/7w - 8/7 3. -216/7 = 24/7w Answer: w=-9
300
Which expression is equivalent to √9x/16. A. √3x/4 B. 3√x/4 C. 3√x/16 D. 3x/4
Answer: B
400
Factor the monomial x^3 + x^2 + 2x + 2.
Answer: (x + 1) (x^2 +2)
400
Find the roots of the equation x^2+10x+25.
Find the roots of the equation x^2+10x+25 Steps: 1. (x+5) Answer: x=-5
400
Simplify the expression 12x^8 y^-7 / (4x^-2 y ^-6)^2.
Answer: 3x^12 y^5 / 4
400
Solve the equation 40 + 14j = 2(-4j - 13).
Steps: 1. 40 + 14j = 2(-4j - 13) 2. 40 + 14j = -8j - 26 3. 66 + 14j = -8j 4. 66 = -22j Answer: j=-3
400
Simplify the expression 3√7 - 5√14 + 2 √28.
Steps: 1. Answer: 7√7 - 5√14
500
Factor the polynomial 9t^3 + 18t - t^2 - 2.
Answer: (9t - 1) (t^2 + 2)
500
Find the roots of the equation x^2+3x+10.
Steps: 1.(-3+or- square root of 9-40)/2 2.(-3+or- square root of -31)/2 Answer: x=(-3- square root of -31)/2, (-3+ square root of -31)/2
500
Write the number in scientific notation 0.0001685.
Answer: 1.685 * 10^-4
500
Solve the proportion 6r/10 = 36/15.
Steps: 1. 6r/10 = 36/15 2. 360 = 90r 3. r = 4 Answer: 4
500
Simplify the expression √512rs^6 * √t^3.
Steps: 1. √512rs^6 * √t^3 2. √256rs^6 * √2 * √t^3 3. 16s^3√2r * t√t Answer:16s^3 t√2rt