2/7
Suppose 5*o = 3*o - 8. Let j be (-9)/o + 1/(-4). Factor 4*n**2 - 10*n**4 - 14*n**3 + j*n**3 + 22*n**4 - 4*n**5.
-4*n**2*(n - 1)**3
Let o(p) = -3*p - 45. Let f be o(-16). Let u(m) be the first derivative of -4 + 0*m - 1/3*m**4 - 1/9*m**6 - 7/15*m**5 + 4/9*m**f + 0*m**2. Factor u(s).
-s**2*(s + 2)**2*(2*s - 1)/3
Let i(s) be the third derivative of 1/147*s**7 - 1/1176*s**8 + 0 + 0*s**3 - 1/42*s**4 + 1/30*s**5 + 0*s - 7*s**2 - 3/140*s**6. Suppose i(f) = 0. What is f?
0, 1, 2
Let p be (-60)/270 - (-10)/18. Let k(r) be the first derivative of 0*r - 2 + 8/9*r**3 - p*r**4 - 2/3*r**2. Factor k(b).
-4*b*(b - 1)**2/3
Let k be 34/10 - 126/315. Factor 0 - 2/5*o - 4/5*o**2 - 2/5*o**k.
-2*o*(o + 1)**2/5
Let l(z) be the third derivative of 1/630*z**7 + 38*z**2 - 1/6*z**3 + 0*z + 0 - 1/30*z**5 - 1/9*z**4 + 0*z**6. Factor l(y).
(y - 3)*(y + 1)**3/3
Solve 5/2*o**2 + 0*o - 1/4*o**4 + 0 - 3/4*o**3 = 0 for o.
-5, 0, 2
Let y(a) = -a**2 + 3*a + 2. Let u be y(3). Suppose 0 - u = -w. Suppose 4*t - 6*t**4 - 3*t**5 + 6*t**w + 0*t**5 - t = 0. Calculate t.
-1, 0, 1
Let c be -12*(3 - (-65)/(-20)). Factor 19*d**2 + 8*d - 7*d**3 + 43*d**c + 4*d**5 - 47*d**2 - 20*d**4.
4*d*(d - 2)*(d - 1)**3
Suppose -35*b + 115 = 10. Let d(w) be the second derivative of -1/6*w**b + 1/120*w**6 + 4*w - 1/16*w**4 + 1/2*w**2 + 0 + 1/40*w**5. Factor d(g).
(g - 1)**2*(g + 2)**2/4
Let h(v) be the first derivative of 4/9*v**3 + 1/6*v**4 + 12 - 5/3*v**2 - 4*v. Factor h(r).
2*(r - 2)*(r + 1)*(r + 3)/3
What is l in -978/13*l**2 + 232/13*l + 120/13 + 16/13*l**4 + 60/13*l**3 = 0?
-10, -1/4, 1/2, 6
Factor 3600*s + 120*s**2 + 36000 + 4/3*s**3.
4*(s + 30)**3/3
Find m, given that 2/3*m**2 + 14/3*m + 8 = 0.
-4, -3
Suppose -35*r + 19 = -51. Factor -1/2 + 1/3*u + 1/6*u**r.
(u - 1)*(u + 3)/6
Let l = -56 - -68. Let z be 8/l*24/28. Let 10/7*y + 4/7 + 2/7*y**2 - z*y**3 = 0. What is y?
-1, -1/2, 2
Let c be ((-305)/(-65) - 4)*1. Let h = 97/65 - c. Factor -2/5*f**2 + 6/5 - h*f.
-2*(f - 1)*(f + 3)/5
Solve -12*p**2 + 26/5*p**3 + 0 - 144/5*p + 16/5*p**4 + 2/5*p**5 = 0 for p.
-4, -3, 0, 2
Suppose -13*b + 5*b + 16 = 0. Let g(k) be the first derivative of 1/5*k**5 + 0*k**b + 0*k + 1/3*k**3 + 1/2*k**4 - 5. Factor g(i).
i**2*(i + 1)**2
Let w = -25 - -26. Suppose 4*b + 5*v = 1, -3*b - 2 = 5*v + w. Factor 9/7*t**2 + 15/7*t + 6/7 - 3/7*t**b - 3/7*t**3.
-3*(t - 2)*(t + 1)**3/7
Factor -50*k**2 - 3*k**3 - 7 + 12*k**2 + 27*k + 20*k**2 + 49.
-3*(k - 2)*(k + 1)*(k + 7)
Let c be 15/18 + (-3 - 114/(-36)). Let g be -2 + 60/28*c + 0. Factor -g*k**3 - 5/7*k**2 - 8/7*k - 4/7.
-(k + 1)*(k + 2)**2/7
Find r such that -45/7*r**2 + 72/7*r + 6/7*r**3 + 48/7 = 0.
-1/2, 4
Let k = 22531/3 + -7505. Let k - 28/3*r**2 + 20/3*r**3 - 32/3*r = 0. What is r?
-1, 2/5, 2
Let n(h) be the third derivative of h**6/320 - 9*h**4/64 - 2*h**2 + 39*h. Find u, given that n(u) = 0.
-3, 0, 3
Let m be ((-2)/(-12))/((-3731)/156 - -25). Find z such that 2/13*z**2 + 4/13*z + m = 0.
-1
Suppose 5*t = 15*u - 14*u + 24, 0 = t + u. What is x in 0*x**3 - 8/3*x**2 + 16/3 + 0*x + 1/3*x**t = 0?
-2, 2
Suppose -4*y - 5*o + 20 = 0, -3*y - 22*o + 21*o = -4. Factor 98/13*u + y - 28/13*u**2 + 2/13*u**3.
2*u*(u - 7)**2/13
Let a(n) = n**2 + 15*n + 1. Let g be a(-10). Let s be (-21)/g - 22/(-14). Let 0*t**2 - 10*t + s*t + t**3 + 9*t + 2*t**2 = 0. What is t?
-1, 0
Let m(w) be the second derivative of -w**5/20 - w**4/6 + w**3/2 - w + 1. Find y such that m(y) = 0.
-3, 0, 1
Let v(a) = -11*a**3 - 13*a**2 + 29*a + 31. Let l(b) = -2*b**3 - 2*b**2 + 5*b + 5. Let i(z) = -34*l(z) + 6*v(z). Determine j, given that i(j) = 0.
-1, 2, 4
Let j(v) be the first derivative of v**9/1512 - v**8/420 + v**6/90 - v**5/60 + 10*v**3 + 28. Let w(t) be the third derivative of j(t). Factor w(k).
2*k*(k - 1)**3*(k + 1)
Determine f so that 744/5*f + 492/5 + 51*f**2 + 3/5*f**3 = 0.
-82, -2, -1
Let m(p) be the third derivative of p**5/20 + p**4/4 - 40*p**3 - 235*p**2. What is v in m(v) = 0?
-10, 8
Let z be 257/(-3)*((-33)/(-56))/11. Let m = z + 39/8. What is f in 0 + 3/7*f**3 + 0*f**2 + m*f**4 - 1/7*f = 0?
-1, 0, 1/2
Factor 17/4*y**2 + 1/4*y**3 + 20*y + 16.
(y + 1)*(y + 8)**2/4
Suppose 2/15*r**3 + 2/5 - 2/15*r - 2/5*r**2 = 0. Calculate r.
-1, 1, 3
Let y(q) = -q - 11. Let s be y(-13). Determine p so that -43*p**2 - 45*p**s + 84*p**2 - 53 + 64*p - 203 = 0.
8
Let s(b) be the second derivative of -b**8/2352 - b**7/490 - b**6/280 - b**5/420 + 6*b**2 + 2*b. Let c(y) be the first derivative of s(y). Solve c(o) = 0.
-1, 0
Let b = -1259/232 - -190/29. Find k, given that -3/4 - 3/8*k + b*k**2 = 0.
-2/3, 1
Let p(s) be the second derivative of s**5/40 - 3*s**4/16 + s**3/2 + 23*s**2/2 - 4*s. Let u(i) be the first derivative of p(i). Find j such that u(j) = 0.
1, 2
Suppose 2*m + o = 7, o = 5*m - 10 + 3. Determine g, given that -111/7*g**3 + 192/7*g**m + 48/7 - 3/7*g**5 - 156/7*g + 30/7*g**4 = 0.
1, 2, 4
Let w(d) be the second derivative of d**5/300 - d**4/60 - 9*d**2/2 + 13*d. Let c(l) be the first derivative of w(l). Factor c(n).
n*(n - 2)/5
Factor -55*i**2 + 39*i**2 - 115*i + 74*i**2 + 5*i**3 + 52*i**2.
5*i*(i - 1)*(i + 23)
Let m = 242678 - 1221904/5. Let g = m - -1710. Factor -g*w**2 + 24/5*w + 2*w**3 + 16/5.
2*(w - 2)**2*(5*w + 2)/5
Let b(z) be the first derivative of -z**7/2100 - z**6/300 - z**5/100 - z**4/60 - 15*z**3 - 29. Let l(g) be the third derivative of b(g). What is x in l(x) = 0?
-1
Let u(i) be the second derivative of -i**3 + 0*i**4 - 1/210*i**7 + 0 + 0*i**5 + 1/45*i**6 + i + 0*i**2. Let d(g) be the second derivative of u(g). Factor d(j).
-4*j**2*(j - 2)
Let p(g) be the first derivative of 1/4*g**3 + 1/2*g + 13 - 7/8*g**2. Find w, given that p(w) = 0.
1/3, 2
Let z = -8572 - -8574. Factor 10/3*s + 4/3 - z*s**2.
-2*(s - 2)*(3*s + 1)/3
Let b(j) = j**2 - 10*j + 2. Let d be b(0). Let 277/6*c**d - 133/3*c**3 + 38*c + 6 + 49/6*c**4 = 0. Calculate c.
-2/7, 3
Let q(r) be the third derivative of -r**7/70 - 2*r**6/5 - 6*r**5/5 + 40*r**4 - 200*r**3 - 89*r**2. Determine z, given that q(z) = 0.
-10, 2
Let c(g) be the third derivative of g**7/60 - 13*g**6/48 + 41*g**5/40 + 145*g**4/48 - 25*g**3/6 + g**2 - 17*g. Factor c(u).
(u - 5)**2*(u + 1)*(7*u - 2)/2
Determine b, given that -432/7 + 354/7*b**2 + 40/7*b**3 - 6/7*b**4 + 396/7*b = 0.
-3, 2/3, 12
Let y(z) be the first derivative of z**7/42 - z**6/6 + z**5/4 + 5*z**4/6 - 10*z**3/3 + 5*z**2 + 4. Let h(l) be the second derivative of y(l). Factor h(s).
5*(s - 2)**2*(s - 1)*(s + 1)
Let l(v) be the third derivative of 1/15*v**5 - 1/168*v**8 + 0*v**4 + 0*v**7 + 12*v**2 + 0 + 1/20*v**6 + 0*v + 0*v**3. Solve l(p) = 0.
-1, 0, 2
Suppose 14 = 6*p + 2. Suppose 6*c - 68 + p*c - 2*c**2 + 60 = 0. What is c?
2
Let a(s) = -5*s + 42. Let q be a(8). Solve -28*d - 62*d - 8*d**2 + 0*d**3 - 16*d**2 - q*d**3 - 100 = 0 for d.
-5, -2
Let q(v) = v**2 + 82*v - 2160. Let p be q(-103). Factor -6*i**2 + 45/2*i + 1/2*i**p - 25.
(i - 5)**2*(i - 2)/2
Suppose -1435*z = -1443*z + 16 - 0. Factor 2/3*v**z + 0 - 2/3*v.
2*v*(v - 1)/3
Let c(q) be the first derivative of 2*q**5/45 + 5*q**4/2 - 62*q**3/9 + 47*q**2/9 + 201. Factor c(d).
2*d*(d - 1)**2*(d + 47)/9
Let m(z) = z**3 + 7*z**2 + 5. Let l be m(-7). Solve -8*h**3 - 56*h**2 + 0*h**l + 72*h**2 - h**5 - 7*h**4 = 0.
-4, 0, 1
Let r(j) be the first derivative of 7*j**5/20 - 75*j**4/8 - 11*j**3 - 22*j**2 - 30. Let i(l) be the second derivative of r(l). Find h such that i(h) = 0.
-2/7, 11
Let b(o) be the first derivative of o**4/20 - 31*o**3/15 + 112*o**2/5 + 256*o/5 + 106. Factor b(d).
(d - 16)**2*(d + 1)/5
Let q(o) be the third derivative of -o**7/2520 + o**6/240 - o**5/60 + o**4/2 + 3*o**2. Let h(t) be the second derivative of q(t). What is x in h(x) = 0?
1, 2
Let u(h) be the second derivative of -1/6*h**4 - 2/3*h**3 - h**2 + 0 - 12*h. Factor u(v).
-2*(v + 1)**2
Let d(r) be the first derivative of r**5/35 - 11*r**4/28 + 3*r**3/7 + 17*r**2/2 + 14*r + 20. Find y such that d(y) = 0.
-2, -1, 7
Let 1/5*q**4 - 122/5*q**3 + 984*q**2 - 63878/5*q - 68921/5 = 0. What is q?
-1, 41
Let o(k) = 12*k - k**3 - 12*k + k. Let y(s) = -2*s**3 + 4*s**3 - s**2 + s + 4 - 6*s**3. Let t(m) = -20*o(m) + 4*y(m). Solve t(v) = 0 for v.
-2, 1, 2
Let a be (-1)/((-5)/15) - -2. Suppose 0 = -4*u + 39 + a. Solve -u + 12*r**2 + 10*r - 6*r + 3 = 0.
-1, 2/3
Let b(d) = -2*d + 8. Let r(k) = -1. Let l(c) = -b(