40 = 5*t. Let j(h) = -48*h - 84. Let w be j(-2). Determine r, given that -3*r**2 - r - w + n*r - r**2 - 3*r = 0.
1, 3
Let d(x) be the third derivative of 0*x**6 + 0*x + 0*x**3 - 57*x**2 + 0 + 0*x**4 + 1/15*x**5 - 2/105*x**7. Suppose d(c) = 0. What is c?
-1, 0, 1
Let h(s) = -s**2 - 17*s - 65. Let n be h(-10). Let o be 76/(-72) + n/2. Factor 64/9*d + 0 + 20/3*d**3 + 1/9*d**5 - 112/9*d**2 - o*d**4.
d*(d - 4)**3*(d - 1)/9
Let i(x) be the second derivative of -5*x**4/12 - 875*x**3/6 - 1290*x**2 + 7346*x - 2. Let i(d) = 0. Calculate d.
-172, -3
Let i(p) = 3*p**4 - 3*p**3 - p**2 - p + 1. Let j(o) = 17*o**4 - 29*o**3 - 6*o**2 - 6*o + 6. Let m(c) = 30*i(c) - 5*j(c). Suppose m(u) = 0. Calculate u.
-11, 0
Let i(b) be the first derivative of -b**3/18 - 397*b**2/12 - 197*b - 7403. Factor i(k).
-(k + 3)*(k + 394)/6
Factor 184718 - 3*x**2 + 455614 + 2*x**2 + 4*x**2 - 2772*x.
3*(x - 462)**2
Suppose 3*m + 5 = q - 2, -11 = -2*q + 3*m. Let i be (-9)/6 + 6/q. Let -17*o**3 - 5*o**4 + o**2 - o**5 - 8*o**2 + 8*o**3 + i*o - 2*o = 0. What is o?
-2, -1, 0
Let m(a) be the first derivative of 3*a**4/4 - 23*a**3 + 93*a**2 - 120*a - 1343. Suppose m(d) = 0. What is d?
1, 2, 20
Let p = 1077555629/3448178 - 2/1724089. Find y, given that 1/2*y**4 + 25*y**3 + 312*y**2 - p - 25*y = 0.
-25, -1, 1
Let o(x) = 2*x. Let f be o(2). Suppose 5*v - f + 26 = w, -96 = -2*w - 3*v. Let 92*z**2 + w*z**5 - 96*z**4 + 29*z + 7*z - 106*z**5 + 4 + 28*z**3 = 0. What is z?
-1, -1/4, 1
Let l = 55 + -35. Let x = -16 + l. Factor -8*y**3 + 3*y**4 + 5*y - 5*y - 5*y**x.
-2*y**3*(y + 4)
Let l(m) be the first derivative of 2*m**5/5 - 5*m**4/2 + 6*m**3 - 7*m**2 + 4*m + 22. Factor l(k).
2*(k - 2)*(k - 1)**3
Let p be 8 - 1167*1/(-4). Let c = p + -299. Factor -c*g + 3/4*g**2 + 3/4*g**3 + 0 - 3/4*g**4.
-3*g*(g - 1)**2*(g + 1)/4
Let t(o) = -4*o**2 + 37*o. Let z(q) = 36*q**2 - 332*q. Let g be 4/(1 - 8/7). Let k(i) = g*t(i) - 3*z(i). Let k(l) = 0. Calculate l.
0, 10
Let v = -4405 - -4405. Let n(f) be the first derivative of 17 + 2/3*f**3 + v*f**2 - 8*f. Let n(i) = 0. What is i?
-2, 2
Factor 2/5*n**4 + 0 + 2/5*n**2 + 0*n - 4/5*n**3.
2*n**2*(n - 1)**2/5
What is q in 101*q**3 + 0*q - 1/2*q**4 - 10201/2*q**2 + 0 = 0?
0, 101
Let v be (-22)/(-330) - 0/(-4). Let s(j) be the second derivative of -13*j - 1/5*j**3 + 0*j**2 + 1/50*j**5 + v*j**4 + 0. Solve s(d) = 0 for d.
-3, 0, 1
Suppose -30 = -11*w + 6*w. Suppose 0 = 2*c + w*c - 16. Factor -13*a**c + 15*a**2 + 3 - 11.
2*(a - 2)*(a + 2)
Factor 3*j**2 + 11708 + 11098 - 24336 - 501*j.
3*(j - 170)*(j + 3)
Factor -1/4*c**4 - 3*c**2 + 7*c + 0 - 15/4*c**3.
-c*(c - 1)*(c + 2)*(c + 14)/4
Let c be 8/160*-12 + (-27)/5 + 10. Suppose -15 = -3*b - 0*b + 3*m, -3*b + m + 13 = 0. Factor -10*p + 5 + 2 + c*p + 3*p**2 - b.
3*(p - 1)**2
Let k(z) be the first derivative of z**6/3 + 10*z**5 + 84*z**4 + 96*z**3 + 1629. Factor k(j).
2*j**2*(j + 1)*(j + 12)**2
Let v = 187276/11 - 374541/22. Suppose 0*j**3 + 0 - v*j**5 - 2*j**2 + 3/2*j**4 + 0*j = 0. Calculate j.
-1, 0, 2
Suppose 0 = 2*v + 4*c, 0 = 2*v + 5*c - 5 + 3. Let z be v + ((-622)/(-90) - (-10)/(-90)). Factor -z*t**2 + 0 - 4/5*t + 8/5*t**3.
2*t*(t - 2)*(4*t + 1)/5
Let g(h) be the first derivative of -5/3*h**3 + 0*h + 0*h**2 - 23 + 1/720*h**6 - 7/48*h**4 - 1/40*h**5. Let k(z) be the third derivative of g(z). Factor k(l).
(l - 7)*(l + 1)/2
Suppose -5*g - 5*v = -35, v = 4 + 1. Let j = 477 + -2383/5. Factor 8/5 + g*l + j*l**2.
2*(l + 1)*(l + 4)/5
Let h(s) be the third derivative of 121*s**7/42 - 143*s**6/3 + 861*s**5/4 + 715*s**4/3 - 6760*s**3/3 + s**2 - 3490*s. Find b such that h(b) = 0.
-1, 1, 52/11
What is w in 66*w**2 - 133*w**2 - 10 + 95*w - 45*w**3 + 27*w**2 = 0?
-2, 1/9, 1
Find g, given that -214*g**3 + 162*g + 268*g - 4*g**4 - 38*g**3 - 240*g**2 - 231*g + 297*g = 0.
-62, -2, 0, 1
Let b(w) be the third derivative of 7*w**5/20 - 79*w**4/4 - 165*w**3/2 + 39*w**2 + 86. Factor b(c).
3*(c + 1)*(7*c - 165)
Suppose 4*j = -1533 - 547. Let q = 522 + j. What is m in -4/3*m**3 - 1/3*m**4 + 0 - 4/3*m**q + 0*m = 0?
-2, 0
Let j = 4/12833 + 12813/64165. Find w, given that w + 0 + j*w**2 = 0.
-5, 0
Suppose 4*l - 44 = 128. Suppose l = 4*p + 3. Solve 5*x**2 - 9*x**2 + p*x - 6 - 2 + 2*x**2 = 0 for x.
1, 4
Let z be (-12)/(-338 - -329 - (-20 + 2)/3). Let -24/5*g + z*g**2 - 2/5*g**3 - 144/5 = 0. Calculate g.
-2, 6
Let a(r) be the third derivative of 7*r**6/2340 + r**5/195 - r**4/52 + 46*r**3/3 - 64*r**2. Let o(h) be the first derivative of a(h). Solve o(q) = 0.
-1, 3/7
Let b = -266 - -270. Factor 68 - 8 - 12*a - 23 + 0*a**2 - 21 - b*a**2.
-4*(a - 1)*(a + 4)
Let x be 12*((-4)/10 - (-27)/30). Determine g, given that 15*g**5 - 18*g**4 - 241*g**2 - 8*g**3 + 253*g**2 + x*g**3 - 7*g**3 = 0.
-4/5, 0, 1
Let w(c) be the first derivative of c**7/9660 - 9*c**5/460 + 9*c**4/46 + 7*c**3/3 + 4*c - 25. Let q(m) be the third derivative of w(m). Factor q(l).
2*(l - 3)**2*(l + 6)/23
Let o(t) be the first derivative of -13*t**6/40 + 19*t**5/5 + 3*t**4/2 + 6*t**2 + 61. Let h(m) be the second derivative of o(m). Let h(z) = 0. What is z?
-2/13, 0, 6
Let j(m) be the third derivative of m**10/252000 + m**9/25200 + m**8/8400 + m**5/30 + 13*m**3/3 + 6*m**2. Let r(n) be the third derivative of j(n). Factor r(v).
3*v**2*(v + 2)**2/5
Let n = 49 - 55. Let f be n/27 + (-6)/(-27). Factor f*u**2 + 9 + 4*u**2 - 9*u - 7.
(u - 2)*(4*u - 1)
Let z(g) be the second derivative of g**8/16800 + g**7/2100 - g**6/450 - 241*g**4/12 + 237*g. Let b(y) be the third derivative of z(y). Factor b(f).
2*f*(f - 1)*(f + 4)/5
Let n = 74926 - 74926. Solve 4*m**2 + 0 + 2/3*m**3 + n*m = 0 for m.
-6, 0
Factor -68/11*t**2 + 2/11*t**3 + 130/11*t - 64/11.
2*(t - 32)*(t - 1)**2/11
Suppose 5 = w, 9 = -2*x + 5*w - 8. Determine u, given that -12/5*u**3 - 16*u - 2/5*u**x + 0 + 72/5*u**2 = 0.
-10, 0, 2
Let m(y) be the second derivative of -y**6/30 - 9*y**5/4 - 225*y**4/4 - 1125*y**3/2 + y + 576. Find v, given that m(v) = 0.
-15, 0
Let t(i) be the first derivative of -i**3/3 - 13*i**2/2 + 68*i + 606. Factor t(d).
-(d - 4)*(d + 17)
Let d be 25 + -19 + -27 + 1351/35. Let -36/5*b**3 - 32/5*b**4 - 96/5 + d*b**2 - 4/5*b**5 + 16*b = 0. Calculate b.
-6, -2, 1
Let k(s) = s**3 - 1740*s**2 + 3471*s - 1744. Let d(y) = y**3 + y**2 - 8*y. Let i(u) = 6*d(u) - 3*k(u). Suppose i(p) = 0. What is p?
-1744, 1
Let d be (-4 - 168/(-18)) + (-2)/6. Let m(n) = 4*n**2 + 10*n - 6. Let b be m(d). Factor 17*i + 0*i**2 - 3*i**2 + 7*i**2 + 31*i + b.
4*(i + 6)**2
Suppose 0 = -5*h + 20, -3*t - 5*h + 34 = -466. Solve 2*p**2 - 79 - 79 + t - 4*p = 0.
1
Let 82/5 + 1/5*d**2 - 43/5*d = 0. Calculate d.
2, 41
Let q(y) be the third derivative of -1331/8*y**4 + 0*y**3 - 1/70*y**7 + 0 - 2*y - 18*y**2 - 363/20*y**5 - 33/40*y**6. Factor q(a).
-3*a*(a + 11)**3
Let r(f) = -3*f**3 + 1241*f**2 + 1242*f - 2466. Let y(v) = 12*v**3 - 4968*v**2 - 4968*v + 9861. Let q(d) = -9*r(d) - 2*y(d). Factor q(j).
3*(j - 412)*(j - 1)*(j + 2)
Let s be ((-9)/(-6))/((-4)/(40/(-3))). Determine j, given that 32*j - 14*j**2 - 2 + 2 - s - 3 = 0.
2/7, 2
Suppose c = 4*v - 49, 0 = 4*c - v - 27 + 193. Let a = c - -46. Suppose 148*l**4 + 9*l**3 - 3*l**a - 2*l**2 - l**2 - 6*l - 145*l**4 = 0. What is l?
-1, 0, 1, 2
Determine p, given that -6181128/11 - 7032/11*p - 2/11*p**2 = 0.
-1758
Let l(n) be the first derivative of 4*n**3/3 - 156*n**2 - 8316*n + 5898. Factor l(p).
4*(p - 99)*(p + 21)
Let n(r) be the third derivative of 12*r**2 + 0*r**4 + 0*r - 2 + 1/126*r**7 - 17/720*r**6 - 1/2016*r**8 + 0*r**3 + 1/45*r**5. Let n(w) = 0. What is w?
0, 1, 8
Let x(i) = 7*i**4 - 15*i**3 - 12*i**2 - 7*i + 3. Let s(c) = -1 + 12*c**4 + c**2 + 2 - c - 12*c**4 - c**3 + c**4. Let w(l) = -6*s(l) + 2*x(l). Factor w(j).
2*j*(j - 4)*(2*j + 1)**2
Solve -1/4*l**5 - 21/2*l - 29/4*l**2 + 5/4*l**4 + 0 + 19/4*l**3 = 0.
-3, -1, 0, 2, 7
Let u be -5 - -5 - (-7 + 4). Suppose 151*c**2 + 142*c**2 + 151*c**2 - 3*c**u - 15*c - 426*c**2 = 0. What is c?
0, 1, 5
Let w(d) be the third derivative of 3/20*d**6 - 32/3*d**3 - 7*d**2 + 0 + 89/6*d**4 + 0*d - 31/6*d**5. Factor w(z).
2*(z - 16)*(z - 1)*(9*z - 2)
Suppose -4*u + 10 = -42. Determine t, given that -2*t**2 + u*t - 24 + 20*t - 4*t - 2*t**2 - 9*t = 0.
2, 3
Suppose -56 = -13*v + 12*v. Factor -46 + 7 - 2*f**2 - 21 + 6*f**2 + v*f.
4*(f - 1)*(f + 15)
Suppose -f + z = -199, f = -4*z + 7*z + 207. Let