(u) be the third derivative of 2/57*u**3 + 1/76*u**4 + 13*u**2 + 1/570*u**5 + 0*u + r. Find s such that k(s) = 0.
-2, -1
Let r = -29241/658 - -615/14. Let g = r + 189/94. Determine v, given that 0 - g*v + 3/4*v**2 = 0.
0, 2
Let a(x) be the first derivative of 4*x**3/15 - 264*x**2 + 2636*x/5 + 2402. Factor a(t).
4*(t - 659)*(t - 1)/5
Let y(i) = -2*i**3 - 47*i**2 - 24*i - 23. Let q be y(-23). Let t = q + 3/2. Let -12*n**2 - t*n**3 - 24*n + 0 = 0. Calculate n.
-4, 0
Let z(v) be the third derivative of v**7/42 + v**6/3 - v**5/3 - 20*v**4/3 - 1244*v**2. What is w in z(w) = 0?
-8, -2, 0, 2
Suppose 0 = -208*t + 25*t - 0*t. Let m(a) be the second derivative of -2/45*a**6 + 1/63*a**7 - 1/9*a**3 + 0 + 1/9*a**4 + t*a**2 - 12*a + 0*a**5. Solve m(c) = 0.
-1, 0, 1
Suppose 76/5*i**4 + 0*i**2 + 0 + 2/5*i**5 + 96*i**3 + 0*i = 0. Calculate i.
-30, -8, 0
Let r(n) = -2*n**3 - 22*n**2 - 2*n - 26. Let h be r(-11). Let b be (-5*2/h)/(4/52). Suppose -b*o**3 - 47*o**2 - 4 + 34*o = 0. Calculate o.
-2, 2/13, 2/5
Let t = 5754 - 5748. Let i(l) be the third derivative of 0 - 2/21*l**7 + 0*l + 25/24*l**4 - 3/8*l**t - 38*l**2 + 5/2*l**3 - 1/4*l**5. Factor i(q).
-5*(q + 1)**3*(4*q - 3)
Factor -242 + 1382*r**3 - 1853*r**3 + 1160 + 1851*r**2 + 3*r**4 - 2301*r.
3*(r - 153)*(r - 2)*(r - 1)**2
Let b(y) be the first derivative of 3*y**5/5 + 675*y**4 + 202500*y**3 - 2132. Find i, given that b(i) = 0.
-450, 0
Let a be (-28)/49 + (6 - (-9)/84*-32). Factor 0 + 4/3*d**a - 32/3*d.
4*d*(d - 8)/3
Suppose -k + 19*k = -108. Let q(o) = -56*o**3 - 78*o**2 + 90*o + 10. Let s(m) = 5*m**3 + 7*m**2 - 8*m - 1. Let u(x) = k*q(x) - 68*s(x). Solve u(f) = 0 for f.
-2, -1, 1
Factor -257049/2 - 1/2*d**2 - 507*d.
-(d + 507)**2/2
Find h such that -100*h**3 + 341*h + 3569 + 5*h**4 - 200*h + 535*h**2 - 793*h - 2789 - 448*h = 0.
2, 3, 13
Let u(q) = -11*q - 64. Let a be u(-11). Let d = a + -49. Determine s so that 1 + s**2 - d*s + 3*s**3 - 2*s**3 - 13 = 0.
-2, 3
Let r = -47537 + 47537. Let n(a) be the third derivative of -24*a**2 + 0*a**3 + 7/120*a**5 - 1/30*a**6 + 0 + 1/420*a**7 + 0*a + r*a**4. Factor n(d).
d**2*(d - 7)*(d - 1)/2
Suppose 441 + 67 - 3*a**2 - 5*a**2 + 512*a + a**2 + 11*a**2 = 0. Calculate a.
-127, -1
Let s be (-42)/(-2835)*-198*6*4/(-16). Let -4/5*t - s*t**2 + 0 = 0. What is t?
-2/11, 0
Let x = 3888 - 466559/120. Let f(i) be the third derivative of x*i**5 + 0 + 0*i + 8*i**2 + 1/12*i**3 - 1/24*i**4. Factor f(u).
(u - 1)**2/2
Suppose -150 = 25*g - 0*g. Let h be -206*3/90 - (g + -1). Determine v, given that 4/15*v - 2/5*v**2 - h*v**5 + 0 - 2/15*v**3 + 2/5*v**4 = 0.
-1, 0, 1, 2
Let w = 61 + -1. Let o be -9*(-8)/w*35/189. Factor -4/3 - 2/9*v + o*v**2.
2*(v - 3)*(v + 2)/9
Factor -148*y - 1220*y**2 + 302*y + 2430 + 456*y + 7*y**3 - 2*y**3 + 595*y.
5*(y - 243)*(y - 2)*(y + 1)
Suppose -15*k + 206 - 86 = 0. Suppose -2*c**4 - 88*c + 161*c**2 + k*c**4 - 51*c**2 - 52*c**3 + 24 + 0*c**4 = 0. What is c?
2/3, 1, 6
Let u(y) be the second derivative of 7 - 1/3*y**4 + 14*y**2 - 4*y**3 - 6*y. Solve u(g) = 0.
-7, 1
Factor 32 - 75*g - 128 - 212*g + 3*g**2.
(g - 96)*(3*g + 1)
Let t be (-4)/((-32)/174)*4. Solve -24*r**2 + 28*r**3 - 5*r**4 + 87 - 7*r**3 - t + 4*r = 0 for r.
0, 1/5, 2
Let t(r) be the first derivative of 5*r**4 + 44*r**3 + 3801. Find b such that t(b) = 0.
-33/5, 0
Factor 4/5*x**4 + 0 - 104/5*x**2 - 21/5*x**3 - 16*x + 1/5*x**5.
x*(x - 5)*(x + 1)*(x + 4)**2/5
Let k = 1460532/5 + -292106. Solve 0 + k*t**3 + 128/5*t + 32/5*t**2 = 0.
-8, 0
Factor 155*o**4 + 1444*o**3 - 151*o**4 + 1467*o**2 - 27*o**2.
4*o**2*(o + 1)*(o + 360)
Suppose 5*q = 4*t + 80, t = 5*q + 3*t - 50. Suppose -14*v + 40 = -q*v. Factor 38*w**5 + 10*w**2 + 3*w + v*w**4 - 33*w**5 - 3*w + 25*w**3.
5*w**2*(w + 1)**2*(w + 2)
Suppose 0 = 228*d + 237 - 298 - 851. Find g such that -67/4*g**2 - 1 + 93/8*g**3 + 15/2*g - 5/2*g**d = 0.
1/4, 2/5, 2
Suppose -115*s + 124*s = 36. Suppose x**3 - x**s - 26*x**2 + 20*x**2 + 4*x - 8*x + 10*x**2 = 0. What is x?
-2, 0, 1, 2
Let z = 9212337/116 + -79416. Let j = z - -16/29. Determine w so that -7/4*w - 1/4*w**3 + j*w**2 + 3/4 = 0.
1, 3
Factor -3*g**4 - 458866733217885 + 70903603556015 - 154615359253758 - 47928*g**3 - 287136648*g**2 - 220823868720260 - 764549181408*g.
-3*(g + 3994)**4
Let o(m) = -34*m - 26*m + 61*m. Let n(s) = 6*s**2 + 4*s + 4*s - 2*s**2. Let k(r) = -n(r) + 4*o(r). Factor k(j).
-4*j*(j + 1)
Let j be (43 + (-13392)/310)*50/(-2). Determine o so that -16/11*o**3 + 2/11*o**j + 0*o - 24/11*o**2 + 2/11*o**4 + 0 = 0.
-2, 0, 3
Let -15199 + w**3 - 4790 + 2125*w + 1239 - 80*w**2 = 0. What is w?
25, 30
Suppose -171*o - 961*o = -501 - 4027. Suppose -3 = -3*k + 2*k. Let 0*j + 2/5*j**o - 1/5*j**k - 1/5*j**5 + 0 + 0*j**2 = 0. What is j?
0, 1
Let c be 61/21 + 16/168. Determine v so that 5*v**c - 2683*v**2 + 1358*v**2 + 1345*v**2 + 20*v = 0.
-2, 0
Let o = -502709/27 + 18619. Let g(c) be the third derivative of 1/945*c**7 + 0 - 1/90*c**5 + 1/270*c**6 + 0*c - 17*c**2 - 2/27*c**4 - o*c**3. Factor g(y).
2*(y - 2)*(y + 1)**2*(y + 2)/9
Let f(k) be the third derivative of k**5/48 - 5215*k**4/48 + 5439245*k**3/24 + 8960*k**2. Let f(x) = 0. What is x?
1043
Let b(o) be the third derivative of 7/6*o**3 + 1/720*o**6 + 0*o**5 - o**2 + 0*o**4 + 0 + 0*o. Let x(p) be the first derivative of b(p). Factor x(v).
v**2/2
Factor -3926/3*b - 1/3*b**2 - 3853369/3.
-(b + 1963)**2/3
Suppose -2*c = 5*d - 117 - 123, 0 = 2*c + 10. Let t = d - 47. What is u in 20/3*u + 4/3*u**2 - 4/3*u**t + 4 = 0?
-1, 3
Determine l so that -73/5*l**2 - 10571/5 - 1643/5*l - 1/5*l**3 = 0.
-31, -11
Let u(w) be the first derivative of -2/25*w**5 + 2/15*w**3 + 0*w + 1/30*w**6 + 32 - 1/20*w**4 + 0*w**2. Let u(g) = 0. What is g?
-1, 0, 1, 2
Factor 0 + 2/3*r**5 + 3468*r**2 + 0*r + 1870*r**3 + 208/3*r**4.
2*r**2*(r + 2)*(r + 51)**2/3
Let m be (6/4)/(50/100). Suppose -2*n = -m*n + c + 7, 5*n = 4*c + 30. What is h in 3/2*h**n - 6*h + 9/2 = 0?
1, 3
Let j(c) be the first derivative of 4*c**3/3 - 48*c**2 + 576*c - 1046. Factor j(k).
4*(k - 12)**2
Let y(r) be the third derivative of -r**6/200 - 3*r**5/20 + 9*r**4/20 + 16*r**3/5 - 10*r**2 - 3*r. Factor y(s).
-3*(s - 2)*(s + 1)*(s + 16)/5
Let b(y) be the third derivative of -1/24*y**6 + 21*y**2 + 0 + 11/48*y**4 - 1/672*y**8 - 2*y + 1/2*y**3 - 1/70*y**7 + 0*y**5. Find z, given that b(z) = 0.
-3, -2, -1, 1
Suppose 5*k - 66 = 9. Factor 20 - 20 - f**2 - 4*f**2 + 10*f + k.
-5*(f - 3)*(f + 1)
Let h = 188622 - 2074832/11. Let b(i) = i. Let z be b(2). Find c such that -h*c**z + 4/11 + 6/11*c = 0.
-2/5, 1
Suppose -4*f - 2*c = -8, 0 = 2*f - 3*c - 0*c - 4. Let s be 7 + (-75)/10 + f/3. Factor -s*y**2 + 1/2*y + 2/3.
-(y - 4)*(y + 1)/6
Let u(q) = -9*q**3 + 20*q**2 + 56*q + 60. Let h(b) = -2*b**3 + b**2. Let r(f) = 20*h(f) - 4*u(f). Find l such that r(l) = 0.
-10, -3, -2
Suppose 0 = -n + 3*k + 600, 3*k + 2 = 4*k. Find d such that 9 + 2*d**2 - n*d + 594*d + d**2 = 0.
1, 3
Let o(t) be the third derivative of -t**6/420 + 809*t**5/210 - 1615*t**4/84 + 269*t**3/7 + 10830*t**2. Factor o(p).
-2*(p - 807)*(p - 1)**2/7
Suppose -4*o + 48 = -4*v, 3161*o + 72 = 4*v + 3167*o. Factor 4/5*q**2 - 2/5*q**3 + v - 2/5*q.
-2*q*(q - 1)**2/5
Let m(k) be the second derivative of -5 + 0*k**2 + 0*k**3 - 14*k + 1/10*k**6 + 0*k**4 + 9/4*k**5. Suppose m(z) = 0. Calculate z.
-15, 0
Let r = 176267/264405 - -1/88135. Find v such that 0 - 2/3*v**3 + 0*v + r*v**2 = 0.
0, 1
Let s be 3 + -1 + 4 + (-78)/13. Let t be ((-4)/3 + 0)*-3. Solve -15/2*g**t + 0*g**2 - 35/2*g**3 + s + 10*g = 0 for g.
-2, -1, 0, 2/3
Let h be (-2)/6 - (-9 + (-4730)/15). Suppose -3*t = 3*s - 9, 5*t - 2*s = -3*s + 19. Find l, given that 22 + 75 - h*l + 146 - 36*l**3 + 3*l**t + 162*l**2 = 0.
3
Let b(y) be the first derivative of -y**8/2520 + y**7/1890 + y**6/1620 - 2*y**3/3 + y + 42. Let d(r) be the third derivative of b(r). Factor d(p).
-2*p**2*(p - 1)*(3*p + 1)/9
Let d be 3/(-54)*-3 - 3051/(-162). Suppose 5*f + 4*w = 30, -d*f + 21*f - 4*w = -16. Factor 2/5 - 2/5*t**f + 0*t.
-2*(t - 1)*(t + 1)/5
Let l be (-70)/(-65) - 2604/2418. Factor 5*t**3 + 0 + 25/2*t**2 + 1/2*t**4 + l*t.
t**2*(t + 5)**2/2
Suppose 6*q = -5*w + q + 30, 13 = -2*w + 3*q. Let a be -4 + w + 5 - 1 - -1. Factor 25*v + 661 - 5*v**a - 661.
-5*v*(v - 5)
Let z(o) = o + 1. Suppose -2*j + j - 1 = -u, u - 1 = 2*j. Let v(s) = -u - 2*s - s**3 + 8*s 