1) simplify. 3(sqrt)-1/27
-1/3
(assuming that the “3” here means cube root)
2)multiply. (a+d)(a^2-ad+d^2)
a3 + d3
3)divide and simplify. n^6/n^13
1/n7
4)multiply. (7x+5)(x^2+8x+2)
7x3 + 61x2 + 54x + 10
5) subtract. simplify by collecting radical terms. 4(sqrt)32 -8(sqrt)2
(assuming that the 4 and the 8 are coefficients and not indexes for
the radical signs)
8 2
! 6)find the variation constant and an equation of variation where y varies directly as x and
y=32 when x=4.
k=8
y = 8x
7)rewrite with positive exponents. (7xy)^-8/9
1
(7xy )
!
8
9
8)factor the trinomial. v^3-4v^2-45v
v(v + 5)(v – 9)
9) solve. (x+15)(x-13)(x+4)>0
{ x | -15 < x < -4, x > 13 }
10) factor. r^2+16r+64
(r + 8)(r + 8)
11)multiply and simplify. (16c^2/5c^2-30c+45) * (5c-15/4c)
4c
c "3
! 13)divide. (28b^3+27b^2+22b+47) / (4b+5)
7b2 – 2b + 8 + 7/(4b+5)
14) perform the indicated operations and simplify. w-5/w-7 - w+1/w+7 + w-35/w^2-49
9
w+7
! 15)find the greatest common factor for the group of terms. -18z^4, 3a^5
3a4 or 3z4, depending on whether the a or the z is a typo
If there is no typo, then the GCF is 3
16) multiply and simplify by factoring. 3(sqrt)y^4 3(sqrt)16y^5
2y3(3√2) (2 times y cubed times the cube root of 2)
(assuming that the 3 here means cube root)
17) add. (4s^4-4s^3+5s^2+14s-10) + (s^5+12s^3+3s^2-5s+ + 8s) + (-7s^4+s^2-4s-6)
s5 – 3s + 8s3 + 9s2 + 5s – 8
(assuming that the “8s” in middle is supposed to be “8” )
18)solve. (sqrt) 9x+55 =x+5
x=5
19)identify the degree of each term of the polynomial and the degree of the polynomial. 3x^3+2x^2+8x+3
The degree of the first term is 3
The degree of the second term is 2
The degree of the third term is 1
The degree of the fourth term is 0
The degree of the polynomial is 3
20)solve. 6/x =8/x -1/5
x = 10
21) add. simplify. 6t/t^2-81 + t/t-9
(t2 + 15t) / (t2 – 81)
22) use rational exponents to simplify. 3(sqrt)x^12
x4
23) state the value of the discriminant and then describe the nature of the solutions. 6x^2-2x+6=0 what is the value and type of solution.
Discriminant = 148
Equation has two real number solutions.
(assuming that the coefficient of the x2term is “-6”)
24) subtract. (12x^2+6w+2)-(6w^2+2)
6w2 + 6w
(assuming that the “x^2” should be “w^2”)
25) simplify. 3(sqrt) 512x^8 /y^3
(8x2/y)(3√x2)
(8 times x2 divided by y, times the cube root of x2)
26) rewrite with rational exponent. 4(sqrt)22
221/4
27)convert to decimal notation. 8.93x10^7
89,300,000
28) solve for x. 4x(x-7)-5x(x-6)=-3
x = 3, -1
29) use quadratic formula to solve. 2x^2-x=-6
(1 + i√47)/4, (1 – i√47)/4
30) foil to find product. (7x^4 -6)(x^7 -5)
7x11 – 6x7 – 35x4 + 30
31) simplify. (sqrt)32a^2b
4a√2b
32) write a quadratic equation for the variable x. standard form sx^2+bx+c=0. solution 4,
only solution.
x2- 8x + 16 = 0
33) solve. w^2 -6w -40=0
w = 10, -4
34) find the following. (sqrt) (a+5)^2
|a+5|
35) factor completely. 100s^2 +160st +64t^2
(10s + 8t)(10s + 8t)
36) factor completely. 5x^7 -10x^6 +15x^5
5x5(x2 – 2x + 3)
37) factor completely. 49w^2-100
(7w – 10)(7w + 10)
38) find the x intercept. y=x^2+3x-4
intercepts: (-4, 0), (1, 0)
39) multiply. (-3t)^2 (4t^2)2
144t6
40) multiply y^13 * y^0
y13
41) factor. 10 -7c +c^2
(5 – c)(2 – c)