+ 0). Suppose 79*f - 77*f - 8 = w. Let 12*t + 5*t**3 - 29*t**3 + 19*t**4 - 8*t**2 + 12*t**5 - 15*t**f + 4 = 0. What is t?
-1, -1/3, 1
Let n(y) = 2179*y**2 + 2*y - 3. Let h be n(1). Find r such that -77*r - 4*r**2 - r**2 + h - 55*r + 4*r**2 + 3*r**2 = 0.
33
Let m = -5308 - -47818/9. Factor -40/9*u + m*u**2 - 8/9 - 4/3*u**3.
-2*(u - 2)**2*(6*u + 1)/9
Let -5/2*v**2 - 655*v + 3975/2 = 0. Calculate v.
-265, 3
Let g(a) be the first derivative of -155 - 47*a + 24*a**2 - 1/3*a**3. Determine c, given that g(c) = 0.
1, 47
Let a be 46/69 - 26/3. Let m(t) = -t**2 - 5*t + 26. Let u be m(a). Factor -1/4*r**u - 5/4 - 3/2*r.
-(r + 1)*(r + 5)/4
Suppose 15 = 4*c + 3. Suppose c*i - 16 = -1. Determine w so that 3*w + 3 - 9*w + 2*w**2 + 14*w + i = 0.
-2
Let t = 69864 + -69864. Factor 9/4*q**4 + t*q**2 + 0*q**3 + 3/4*q**5 + 0*q + 0.
3*q**4*(q + 3)/4
Let n = 966/361 - 3640/3249. Factor -80/9*t + 8/3 - n*t**2.
-2*(t + 6)*(7*t - 2)/9
Suppose -16*a = -14*a - 6*n + 52, 0 = -a + 2*n - 16. Determine l so that -2*l**3 - 2/3*l**a + 0*l + 0*l**2 + 0 = 0.
-3, 0
Let c be 1968/5904 + (-5)/(-3). Find z, given that -87/8*z - 45/4 + 3/8*z**c = 0.
-1, 30
Factor 164025 - 63585*k + 1/4*k**4 + 23029/4*k**2 + 157/2*k**3.
(k - 5)**2*(k + 162)**2/4
Let n(z) = -z**3 + z**2 - z. Suppose -9*l + 12*l - 17 = 4*b, 3*b = -15. Let x(s) = -5*s**3 + 3*s**2 - 15*s - 5. Let y(a) = l*x(a) + 6*n(a). Factor y(i).
-(i - 5)*(i + 1)**2
Factor 126*l - 204 - 80*l**3 + 200*l**2 + 4*l**4 + 103*l - 128*l**3 - 21*l.
4*(l - 51)*(l - 1)**2*(l + 1)
Let y(m) = -m**3 + 24*m**2 + m - 21. Let k be y(24). Factor 144*d**2 + 986*d**3 + 114*d**2 - 989*d**k.
-3*d**2*(d - 86)
Let v(a) be the first derivative of -a**3/3 + 7*a**2 + 648. Factor v(i).
-i*(i - 14)
Determine l so that 5148*l + l**3 + 4832 + 3827 + 12468 + 5009 + 138*l**2 = 0.
-66, -6
Let -480/7*c**2 + 104/7*c**3 + 2/7*c**5 - 2304/7*c + 0 + 32/7*c**4 = 0. What is c?
-8, -6, 0, 4
Suppose -5*b - 11 = 3*x, 7 = -3*x - 2*b - 1. Let q = x + 6. Let -21*n**4 + 5*n**q + 8*n**3 + 12*n**4 = 0. What is n?
0, 2
Suppose 2*q + 3*x = 5, 2*x - 5 = -5*q + 13. Let c(z) = 8387*z + 58709. Let y be c(-7). Factor 0 - 2/7*h**q + 0*h**2 + 4/7*h**3 - 2/7*h**5 + y*h.
-2*h**3*(h - 1)*(h + 2)/7
Let q(i) = 2*i**4 - i**3 + 2*i + 2. Let x(l) = 6*l**4 + 68*l**3 - 2*l**2 - 66*l + 4. Let o(a) = 2*q(a) - x(a). Solve o(s) = 0.
-35, -1, 0, 1
Let r(q) be the first derivative of q**6/18 + 2*q**5 + 25*q**4/2 - 1240*q**3/9 - 85*q**2/2 + 1734*q - 858. Solve r(i) = 0 for i.
-17, -2, 3
Let l(o) be the third derivative of o**5/240 + 17*o**4/32 - 55*o**3/6 - 1237*o**2. Factor l(m).
(m - 4)*(m + 55)/4
Let n = -278179/70 - -3974. Let u(i) be the second derivative of -10*i + 0 + 1/42*i**4 + 1/21*i**3 - 1/7*i**2 - n*i**5. What is f in u(f) = 0?
-1, 1
Let h = -414011 - -2070057/5. Suppose -h*r**3 + 14/5*r**2 - 30 + 2*r = 0. What is r?
-3, 5
Let 1868*c**4 - 579955*c + 75855*c - 1398868*c**2 - 4*c**5 + 1436*c**4 + 393508*c**2 - 472*c**4 - 498424*c**3 = 0. Calculate c.
-1, 0, 355
Suppose 3*i + 386 = 26. Let s = -36 - i. What is w in s*w**2 - 336*w - 113*w - 4*w**3 + 1372 + 46*w - 185*w = 0?
7
Let z be ((2 + 15/(-6))*(-5)/(-2))/((-36255)/4834). Factor 0 - 1/6*b + z*b**2.
b*(b - 1)/6
Factor -122/9*d + 2/9*d**2 - 124/9.
2*(d - 62)*(d + 1)/9
Let h(i) be the third derivative of 12*i**2 + 1/42*i**7 + 0 - 1/12*i**5 + 0*i**3 + 5/12*i**4 - 3*i - 1/12*i**6. Factor h(m).
5*m*(m - 2)*(m - 1)*(m + 1)
Let m = 205819/6 + -34303. Let z(b) be the first derivative of 39 - 2/5*b**5 + 2*b**2 - m*b**6 + 8/3*b**3 + 0*b + 3/4*b**4. Factor z(d).
-d*(d - 2)*(d + 1)**2*(d + 2)
Suppose -13161 - 13189 = 19*r - 26388. Let 2/3*y**r + 294 + 28*y = 0. What is y?
-21
Let m(g) be the first derivative of -g**6/3 + 44*g**5/5 - 59*g**4 + 88*g**3/3 + 535*g**2 + 700*g + 3982. Find q, given that m(q) = 0.
-1, 5, 14
Let f = -1399 - -4208/3. Let q(a) be the first derivative of f*a**3 + 2/3*a**6 - 13/5*a**5 + 7/4*a**4 + 3 - 11/2*a**2 + 2*a. Determine t so that q(t) = 0.
-1, 1/4, 1, 2
Let j(p) be the second derivative of p**6/2 - 21*p**5/10 - 113*p**4/4 + 49*p**3 + 36*p**2 + 5*p + 248. What is l in j(l) = 0?
-4, -1/5, 1, 6
Find m, given that 22330/9*m**2 - 1240/9 + 8*m**4 + 344*m + 2488*m**3 = 0.
-310, -2/3, -1/2, 1/6
Let y(o) be the third derivative of o**8/24 + 13*o**7/21 + 11*o**6/60 - 737*o**5/30 - 35*o**4/2 + o**2 + 161*o + 6. Suppose y(i) = 0. Calculate i.
-7, -5, -2/7, 0, 3
Let a(p) be the third derivative of p**7/105 + 2*p**6/3 - 433*p**5/30 + 98*p**4/3 + 5183*p**2. Let a(r) = 0. Calculate r.
-49, 0, 1, 8
Suppose 5*p = 3*m + 103, -p + 16*m + 3 = 17*m. What is i in -16/3*i**3 + 13/3 - 40/3*i + 1/3*i**4 + p*i**2 = 0?
1, 13
Factor 51*l - 5*l**3 - 3*l - 8*l**2 + 14*l**3 - 13*l**3 + 12*l + 144.
-4*(l - 4)*(l + 3)**2
Suppose 2*u + 1/2*u**2 - 117/2 = 0. Calculate u.
-13, 9
Let v(m) = 29737*m - 208129. Let r be v(7). Factor -r*i**2 - 1083/2 + 1311/4*i + 3/4*i**3.
3*(i - 19)**2*(i - 2)/4
Let j(r) be the first derivative of 5*r**6/6 - 15*r**5 - 85*r**4/2 + 13801. Suppose j(a) = 0. Calculate a.
-2, 0, 17
Suppose -16*z + 704 = -2256. Factor 30*m + 89*m**4 - z*m**4 - 9*m**2 + 91*m**4 + 34*m**2 - 10*m**3.
-5*m*(m - 2)*(m + 1)*(m + 3)
Let o(y) be the second derivative of -27 + 0*y**2 + 1/18*y**4 + 1/9*y**3 + 2*y. Factor o(q).
2*q*(q + 1)/3
Let b(x) = -7*x + 137. Let a be b(19). Suppose 0 = a*j - m - 8, -50 + 46 = -2*j - m. Solve -4/7*d**3 + 12/7*d**j + 0 - 8/7*d = 0 for d.
0, 1, 2
Suppose 25 = -5*f, -2*h + 8*f - 11*f + 235 = 0. Let s = -373/3 + h. Let -4/3*d + 4/3*d**3 + s*d**4 - 2/3 + 0*d**2 = 0. Calculate d.
-1, 1
Let p be (-6 + 0)/6 + 64/66. Let a = p + 41/264. Find m such that 3/4*m**3 + 1/2*m**2 + 0 + 1/2*m**4 + a*m**5 + 1/8*m = 0.
-1, 0
Let o(i) be the third derivative of -i**5/60 + 407*i**4/12 - 165649*i**3/6 + 5*i**2 + 3*i + 6. Factor o(l).
-(l - 407)**2
Let a(l) be the first derivative of -l**3/3 + 525*l**2/2 + 2093. Factor a(s).
-s*(s - 525)
Let z(o) be the third derivative of -o**8/131040 + o**7/5460 - o**6/585 - 9*o**5/20 - 91*o**2. Let m(l) be the third derivative of z(l). Factor m(d).
-2*(d - 4)*(d - 2)/13
Suppose -20 = 19*g - 23*g. Determine b so that -g*b**3 + 69*b - 30 - 73*b - 61*b - 40*b**2 = 0.
-6, -1
Let z be ((-2)/(-3))/((-7)/(-126)). Suppose -10*r + 32*r - 18 + z*r**4 + 6 - 228*r**3 + 208*r**3 - 2*r**5 = 0. Calculate r.
-1, 1, 2, 3
Let a(g) be the first derivative of g**6/3 + 23*g**5/5 + 8*g**4 - 190*g**3/3 + 91*g**2 - 49*g + 593. Find f, given that a(f) = 0.
-7, 1/2, 1
Let w(p) be the third derivative of -9/8*p**4 - 3/10*p**6 + 1/21*p**7 - 4*p - 1/336*p**8 + 0*p**3 - 6*p**2 + 0 + 9/10*p**5. Factor w(h).
-h*(h - 3)**3*(h - 1)
Let z(b) be the first derivative of 2*b**3/3 - 87*b**2 + 340*b + 388. Solve z(u) = 0 for u.
2, 85
Let v(t) = t**3 - 6*t**2 - 5*t - 1. Let m be v(7). Suppose 4*g = 21 - m. Factor -4*n**g - 2*n + 118*n**5 + 8*n**4 - 126*n**5 - n**3 + 7*n**3.
-2*n*(n - 1)**2*(2*n + 1)**2
Let s be -1 - (-195415)/945 - ((-15466)/(-1026) - 15). What is u in -1600/7 - 4/7*u**3 - s*u + 156/7*u**2 = 0?
-1, 20
Suppose 0*y + 4*r = 4*y + 100, -4*r = -2*y - 52. Let i = y + 184/7. Let 2/7*v**3 + 4/7*v**2 - i - 8/7*v = 0. What is v?
-2, 2
Solve -44*o**4 + 31*o**3 + 126*o**3 + 235*o**3 - 720 + 317*o - 1244*o**2 + 1315*o = 0 for o.
10/11, 2, 3
Let b(x) be the first derivative of 113*x - 20*x**3 - 22*x**3 - 105*x - 50*x**2 + 6*x**3 - 35. Find q, given that b(q) = 0.
-1, 2/27
Let t(j) be the third derivative of -43/2*j**4 + 0 + 9/80*j**6 + 0*j - 249/40*j**5 - 284*j**2 - 29*j**3. Solve t(m) = 0 for m.
-2/3, 29
Suppose 110*u**3 + 2278*u - 504 + 378*u**2 + 22*u**3 - 2286*u + 162*u**4 - 160*u**4 = 0. What is u?
-63, -2, 1
Let d = 11 + -9. Let u = 3125/2 - 1562. Factor 7/2*z - u*z**3 - 3 + 0*z**d.
-(z - 2)*(z - 1)*(z + 3)/2
Suppose -52/11 - 30/11*i - 2/11*i**2 = 0. What is i?
-13, -2
Find z such that -16/9*z**5 - 608920/3*z + 4168/3*z**4 + 3659762/9*z**2 + 33800 - 817444/3*z**3 = 0.
1/2, 390
Factor 45*u**5 + 11599*u + 21*u**2 - 46*u**5 - u**4 - 11635*u + 17*u**3.
-u*(u - 4)*(u - 1)*(u + 3)**2
Let h(w) be the third derivative of w**6/40 + w**5/5 - 7*w**4/8 - 5*w**3 + 853*w**2. Factor h(q).
3*(q - 2)*(q + 1)*(q + 5)
Let d = 84739/15 + -16946/3. Let u be (120/25 - 4)*1. Solve u - d*x**2 - 4/5*x + 1/5*x**4 + 2/5*x**3 = 0 for x.
-2, 1
Let d(x) be the third derivat