 Suppose 5*z = -18 - 7, 0 = -3*a + 2*z + m. Factor 0*h**5 - 6*h**5 + 6*h**4 + 3*h**3 + 2*h**5 + a*h**5.
3*h**3*(h + 1)**2
Let t = -52/15 + 11/3. Let h(j) = -j**2 + 38*j - 237. Let v be h(8). Determine d so that -3/5*d + 3/5*d**v - 1/5*d**4 + t*d**2 + 0 = 0.
-1, 0, 1, 3
Let q(v) be the third derivative of v**8/840 - 19*v**7/35 + 149*v**6/2 - 5875*v**5/3 + 93375*v**4/4 - 151875*v**3 + 1727*v**2. Find i, given that q(i) = 0.
5, 135
Let q be 6/(-4)*(-24 - -15)*-42. Let a be q/(-252) - 18/8. Determine w so that 9/2*w**3 + 0*w + 0 + a*w**2 - 6*w**4 + 3/2*w**5 = 0.
0, 1, 3
Let h(p) be the first derivative of -5*p**3/3 + 3265*p**2/2 - 6510*p - 6387. Suppose h(n) = 0. What is n?
2, 651
Let j be 69/92 + 53*1/4. Suppose -136*n**2 + 92*n**3 + 2*n**4 + j*n**4 - 53*n + 81*n = 0. What is n?
-7, 0, 1/4, 1
Let k(b) be the first derivative of -26/5*b**3 - 22*b**2 + 147 - 121/5*b - 1/25*b**5 + b**4. Factor k(w).
-(w - 11)**2*(w + 1)**2/5
Suppose 0*w**2 - 30 - 995*w + 963*w + w**2 + 6*w**2 - 9*w**2 = 0. Calculate w.
-15, -1
Let p(g) be the first derivative of -76 + 484*g**3 + 2/5*g**5 + 1682*g - 28*g**4 + 1624*g**2. Let p(s) = 0. What is s?
-1, 29
Let z(d) be the second derivative of d**5/30 - d**4/9 - 5*d**3/9 + 2*d**2 + 1379*d. Suppose z(w) = 0. What is w?
-2, 1, 3
Let p(t) = t**3 + 373*t**2 + 5711*t - 354. Let c be p(-357). What is v in 98/9*v**5 + 14/3*v**4 + 0*v + 8/9*v**2 + 0 - 16/3*v**c = 0?
-1, 0, 2/7
Let v(l) be the first derivative of l**5/180 + l**4/36 - 2*l**3/27 - 100*l - 91. Let z(p) be the first derivative of v(p). Factor z(g).
g*(g - 1)*(g + 4)/9
Let c be (-5 - (10 + -4 + -4)) + 9. Let d be 160/(-12)*(-162)/4. Let 228*w**3 + 497*w**3 + 175*w**3 - d*w**c - 500*w**4 + 108*w = 0. What is w?
0, 3/5
Suppose -5*a - 5*s + 63 + 537 = 0, 245 = 2*a + s. Suppose 139*c = a*c. Suppose 1/4*x**2 - 1/4*x + c = 0. Calculate x.
0, 1
Let l(n) be the second derivative of -71*n**4/30 + 139*n**3/15 + 6*n**2/5 - 2727*n - 2. Factor l(a).
-2*(a - 2)*(71*a + 3)/5
Suppose -21*s = -10*s - 33. Factor 600*h - h**4 - 600*h + 2*h**s.
-h**3*(h - 2)
Let w(q) be the first derivative of q**5/5 - 5*q**4/4 - 374*q**3/3 + 8391. Find f such that w(f) = 0.
-17, 0, 22
Find m such that -57/2*m**2 - 1313/2*m - 23 = 0.
-23, -2/57
Let s(y) be the second derivative of 0*y**2 + 1/30*y**6 + 197*y + y**3 - 7/12*y**4 + 0*y**5 + 0. Suppose s(u) = 0. Calculate u.
-3, 0, 1, 2
Find c such that 9*c**2 - 3/5*c**4 + 0*c + 0 + 6/5*c**3 = 0.
-3, 0, 5
Factor 2*q**2 - 160/7*q + 1/7*q**3 + 352/7.
(q - 4)**2*(q + 22)/7
Let p(y) be the first derivative of 2*y**5/15 - 47*y**4/6 + 392*y**3/9 + 196*y**2 - 3540. Solve p(n) = 0 for n.
-2, 0, 7, 42
Let k be (-10)/60 - (-78)/36. Suppose f = 1, -3 = j + k*f - 7*f. Solve 1/5*y**j + 0 - 4/5*y = 0.
0, 4
Determine o so that 5*o**3 + o**3 + 9*o**5 + 8*o**3 + 32*o**5 - 203*o**4 - 24*o**3 = 0.
-2/41, 0, 5
Let j(p) be the second derivative of p**5/80 - p**4/32 - 5*p**3/2 - 219*p**2/2 - 256*p. Let o(w) be the first derivative of j(w). Find v such that o(v) = 0.
-4, 5
Let t(v) be the third derivative of 19/1155*v**7 + 27/110*v**5 + 0*v**4 + 3/20*v**6 + 0 + 1/1848*v**8 + 0*v**3 - v + 71*v**2. Factor t(i).
2*i**2*(i + 1)*(i + 9)**2/11
Let m = -460481 + 6002176/13. Let o = 1225 - m. Suppose 10/13*k - o*k**3 + 12/13 - 4/13*k**2 = 0. Calculate k.
-3, -1, 2
Let q(v) be the third derivative of v**6/360 - 19*v**5/45 + 23*v**4/24 + 25*v**3 - 2354*v**2. Factor q(w).
(w - 75)*(w - 3)*(w + 2)/3
Let j(y) = -8*y**2 + 23*y - 14. Let c(v) be the first derivative of v**4/4 - v**3/3 - v - 32. Let n(s) = -c(s) - j(s). Factor n(t).
-(t - 5)*(t - 3)*(t - 1)
Let v(t) be the first derivative of -t**6/3 + 94*t**5/5 - 217*t**4/2 + 198*t**3 - 126*t**2 + 767. Determine i, given that v(i) = 0.
0, 1, 3, 42
Factor -1/6*a**3 + 7448/3 + 140/3*a - 37/6*a**2.
-(a - 19)*(a + 28)**2/6
Suppose -6*w - 4 = -10. Let l(z) = 72*z**3 + z**2 - z + 1. Let t be l(w). Suppose -t*h**3 + 20*h**4 + 28*h + 45*h**3 - 2 - 6 - 12*h**2 = 0. What is h?
-1, 2/5, 1
Let x = 29470/19 + -2500808/1615. Let t = -30/17 + x. Factor t - 2/5*i + 2/5*i**3 - 4/5*i**2.
2*(i - 2)*(i - 1)*(i + 1)/5
Suppose 3*s - 126 = -4*h, -4*s + h + 175 = 4*h. Factor 116*k**3 + 39*k - 239*k**3 + 35*k**2 + 45 + 118*k**3 + s*k.
-5*(k - 9)*(k + 1)**2
Let y(v) = v**2 - 3095*v + 63. Let m(f) = f**2 - 1547*f + 27. Let q(w) = 7*m(w) - 3*y(w). Solve q(s) = 0 for s.
0, 386
Suppose 44 = 7*s - 4*s + 5*g, -2*s - 3*g + 28 = 0. Let z(y) be the first derivative of -9*y**3 - 27*y + 10*y**2 - y**2 + 4 + s*y**3. Let z(c) = 0. What is c?
3
Let i(v) = 16187*v - 97120. Let p be i(6). Factor -2/3*n**p + 6 + 0*n.
-2*(n - 3)*(n + 3)/3
Let u(g) = -231*g - 1386. Let m be u(-6). Let o(z) be the third derivative of 0 + 2/3*z**3 + 1/8*z**4 + m*z - 1/60*z**5 + 8*z**2. What is d in o(d) = 0?
-1, 4
Let q(y) be the third derivative of y**8/336 + y**7/14 - 139*y**6/120 + 317*y**5/60 - 47*y**4/4 + 44*y**3/3 + y**2 - 129. Let q(z) = 0. Calculate z.
-22, 1, 4
Let r = 33 + -45. Let s = 18 + r. What is q in -5*q**2 + 2 + 6*q**3 - 12*q**3 + 5*q**3 - 8*q - s = 0?
-2, -1
Let v = -19758 - -19762. Let f(i) be the first derivative of 2/25*i**5 + 0*i - 2/5*i**2 + 1/5*i**v - 20 - 2/15*i**3. Find w such that f(w) = 0.
-2, -1, 0, 1
Let q = 2788 - 128237/46. Let l = q - -6/23. Suppose -1/2*s**4 - s**3 + l + s + 0*s**2 = 0. Calculate s.
-1, 1
Let r(d) be the first derivative of -2*d**3/3 - 52*d**2 - 3860. What is x in r(x) = 0?
-52, 0
Let p(u) = u**3 - 5*u**2 - 14*u. Let a be p(7). Let m be 944/2124 - 23/(-9). Let a + r**2 + 2/3*r + 1/3*r**m = 0. Calculate r.
-2, -1, 0
Factor -3*k**3 - 2358*k - 72*k**2 + 2358*k + k**3.
-2*k**2*(k + 36)
Let a = 252 - 253. Let j be (-16 + 14)/(3*a). Factor -4/3 - 10/3*p - j*p**3 - 8/3*p**2.
-2*(p + 1)**2*(p + 2)/3
Let x(g) be the first derivative of 0*g**4 + 10/3*g**3 - 5/2*g**2 + 5/6*g**6 + 0*g - 61 - 2*g**5. Solve x(z) = 0.
-1, 0, 1
Let v = -2904/5 - -81337/140. Let q(p) be the first derivative of -16/21*p**3 + 5/7*p**5 + 2/7*p**2 + 0*p + v*p**4 - 12. Find u such that q(u) = 0.
-1, 0, 2/5
Factor 30/17*n**2 + 0 + 88/17*n + 2/17*n**3.
2*n*(n + 4)*(n + 11)/17
Let b be 12/22*(6 - -5). Find x such that -3*x**3 - 13*x**3 + b*x**3 - 5*x**3 - 5*x**4 = 0.
-3, 0
Let w be 5246/(-5719) + 264/418 + (-78)/(-7). Factor w + 2/7*m**2 - 6*m.
2*(m - 19)*(m - 2)/7
Let m be (-18)/24*(-1)/3. Let c(d) be the first derivative of -m*d**4 - d**3 + 20 + 1/2*d**2 + 3*d. Find u, given that c(u) = 0.
-3, -1, 1
Let m(t) = 59*t**3 - 1228*t**2 - 1251*t - 6. Let g(v) = 50*v**3 - 1230*v**2 - 1250*v - 5. Let z(s) = -6*g(s) + 5*m(s). Suppose z(r) = 0. What is r?
-1, 0, 249
Let w(a) be the first derivative of 5*a**3/3 - 5*a**2/2 + 4*a + 50. Let q(j) = 9*j**2 - 9*j + 7. Let s(i) = -4*q(i) + 7*w(i). Determine k so that s(k) = 0.
0, 1
Solve 23 + 1/4*k**2 + 27/4*k = 0.
-23, -4
Let h = -16239 - -81207/5. Factor -h + 13/5*a - 1/5*a**2.
-(a - 12)*(a - 1)/5
Let r = -1203 + 2264. Let t = 4245/4 - r. Factor -t*d**2 + 0 - d.
-d*(d + 4)/4
Let p be 1418/585 + 198/891 + (-4)/(-26). Factor 49/5 - p*x + 1/5*x**2.
(x - 7)**2/5
Let m(x) = x**3 - 5*x**2 - 2*x + 3. Let d be m(0). Find f such that -2*f**2 + 20*f**3 - 22*f**3 - 1 + d*f - 232*f**4 + 235*f**4 - f**5 = 0.
-1, 1
Let d = 4661/46 + -12511/138. Let 0*s**2 + 2/3*s**5 + 0*s**4 + 0 - d*s**3 + 0*s = 0. What is s?
-4, 0, 4
Suppose -2*w - 1 = -3*g, 2*g + 28 = 4*w + 6*g. Let t be -2 - ((-7)/(-5) - w). Find n, given that t*n**2 + 6/5*n + 0 = 0.
-2, 0
Let r(k) = 3*k**2 + 7*k - 16. Let c be r(6). Let j = c - 129. Suppose 320 + 61*s**j + 65*s**4 + 800*s + 740*s**2 + 61*s**5 - 117*s**5 + 320*s**3 = 0. What is s?
-4, -2, -1
Suppose -4*n - n + 20 = -4*m, -3*m + 3*n = 12. Suppose -d + m + 12 = 0. Factor d + 8*l**2 - 8*l**2 + 2*l**2 - 5*l**2.
-3*(l - 2)*(l + 2)
Let v = -7417 + 7419. Let m(x) be the first derivative of -4/7*x**3 - 1/7*x**4 - 4/7*x**v + 0*x + 21. Find a such that m(a) = 0.
-2, -1, 0
Factor 45/2*a - 3/4*a**3 + 0 + 87/4*a**2.
-3*a*(a - 30)*(a + 1)/4
Suppose -762 = -4*i - j, i - 4*j - 209 = -10. Let 3*z**2 + i*z - 1645 - 5*z**2 - 403 - 63*z = 0. Calculate z.
32
Let y(u) be the second derivative of 7*u**4/12 + 8*u**3 - 49*u**2/2 + 2*u - 62. Let c(d) = 36*d**2 + 240*d - 244. Let i(n) = 3*c(n) - 16*y(n). Factor i(o).
-4*(o - 1)*(o + 13)
Factor -1484*t**2 + 811*t**2 - 155*t**3 + 348