 -2, 0
Let h(l) be the second derivative of -l**5/240 - 3*l**4/32 - 82*l**2 - 105*l. Let m(a) be the first derivative of h(a). Find r, given that m(r) = 0.
-9, 0
Let u = -48677/20 + 2434. Let i(h) be the second derivative of 3/70*h**6 + u*h**5 + 0*h**4 - 2/7*h**3 + 0 + 0*h**2 - 13*h. Solve i(c) = 0 for c.
-2, -1, 0, 2/3
Let c(t) = -43*t - 2. Let y be c(-10). Factor -1072*m + 116*m**2 + 580*m**2 - 284*m**2 - 36*m**3 + y*m**2 + 352.
-4*(m - 22)*(3*m - 2)**2
Suppose -f + 18 = -4*w, 0*w = -2*f + w + 8. Factor 3*r**f + r - r**2 - 2 + 7*r - 7*r - r**3.
-(r - 2)*(r - 1)*(r + 1)
Suppose 53*j + 528 = 61*j. Factor 64*p + 2*p**2 - 5*p**2 - 3*p**2 - 3*p**2 - j*p.
-p*(9*p + 2)
Let d(b) be the first derivative of 0*b**2 - 20*b - 19 - 5/6*b**3 - 5/12*b**4. Let u(a) be the first derivative of d(a). Solve u(q) = 0.
-1, 0
Let p(k) be the first derivative of -1/2*k**2 + 30 + 11/36*k**3 - 1/12*k**4 + 1/120*k**5 - 14*k. Let l(x) be the first derivative of p(x). Factor l(a).
(a - 3)*(a - 2)*(a - 1)/6
Let t = -8152 - -163043/20. Let m(r) be the second derivative of 0 + 0*r**2 + t*r**5 - 8*r + 0*r**4 - 1/30*r**6 + 0*r**3. Factor m(f).
-f**3*(f - 3)
Let y(d) = -d**3 + 33*d**2 - 240*d + 102. Let u be y(10). Let j(l) be the first derivative of -22 + 0*l + 6/7*l**u - 2/21*l**3. Suppose j(z) = 0. Calculate z.
0, 6
Suppose 36*g - x = 41*g - 389, 2*g - 5*x - 134 = 0. Let o = -73 + g. Suppose 2/3*h**2 + o - 10/3*h = 0. What is h?
2, 3
Let j(z) = -2*z**3 - 7*z**2 + 2*z - 4. Suppose 46*t + 20 = 41*t. Let i be j(t). Solve 7*v**3 - 2672*v**5 - 8*v + 5*v**3 + 2668*v**5 - i*v**4 + 4*v**2 = 0 for v.
-2, -1, 0, 1
Let x(h) = 2*h**2 + 51*h + 75. Suppose p = 5*u + 122, -5*u = 4*p + 127 - 15. Let v be x(u). Find w, given that 28/3*w**2 + 4/9*w**v + 400/9 + 160/3*w = 0.
-10, -1
Let w be (599/2995)/((-9)/(-5)). Suppose -w*o**2 + 13/9 - 4/3*o = 0. What is o?
-13, 1
Let x(b) = -13*b**2 - 7*b + 6. Let f(g) = 9*g**2 + 5*g - 4. Let i(h) = -h**2 - 23*h - 5. Let y be i(-23). Let q(j) = y*x(j) - 7*f(j). Factor q(o).
2*(o - 1)*(o + 1)
Let u = -2492351/4 - -623088. Factor 3 + u*g**2 + 2*g.
(g + 2)*(g + 6)/4
Let q be 2 + (7/(-21))/((-2)/42). Suppose -4*n - 2*r - 8 = -q*n, -10 = -3*n - 4*r. Determine x so that x - n*x**4 - 2*x + 6*x**3 - 5*x**3 + 0*x**2 + 2*x**2 = 0.
-1, 0, 1/2, 1
Let d(t) = -10*t**2 - t + 1. Let s(k) = 9*k**2 - k. Let n(r) = -r**3 + 7*r**2 - 13*r + 19. Let h be n(5). Let y(p) = h*d(p) + 5*s(p). Factor y(a).
(a - 1)*(5*a - 4)
Let b(s) be the third derivative of -s**8/1176 + 2*s**7/245 + 53*s**6/210 + 66*s**5/35 + 27*s**4/4 + 90*s**3/7 + 3*s**2 + 31*s. Find n, given that b(n) = 0.
-3, -2, -1, 15
Let g(m) be the first derivative of -m**4/4 + 5*m**3 + 36*m**2 - 85*m - 13. Let v(b) be the first derivative of g(b). Determine a, given that v(a) = 0.
-2, 12
Let p be 8*(4 + 3)*-1. Let s = p - -58. Let -12*g**3 + 156*g - s*g**2 - 156*g = 0. What is g?
-1/6, 0
Let n(a) = -2*a**3 + 27*a**2 + 44*a + 66. Let v(h) = -h**3 + 13*h**2 + 22*h + 32. Let f(g) = -3*n(g) + 7*v(g). Let i be f(12). Factor 4/11*l + 2/11*l**i + 2/11.
2*(l + 1)**2/11
Let h = 3893/10986 - 77/3662. What is t in -7/3*t**2 + 0 - 2/3*t**3 + h*t**4 - 4/3*t = 0?
-1, 0, 4
Let a(z) be the second derivative of 219*z**5/100 - 437*z**4/60 + 217*z**3/30 + z**2/10 - 4950*z. Factor a(d).
(d - 1)**2*(219*d + 1)/5
Let m(o) = 5*o**4 - 4*o**3 - o**2 + 2*o - 1. Let i(k) = 16*k**3 + 64*k**2 - 138*k - 301. Let f(d) = -i(d) + m(d). Factor f(a).
5*(a - 5)*(a - 3)*(a + 2)**2
Let c be ((-35)/14 + 1)/((-3)/(-4)). Let i be (((-18)/5)/9)/(c/20). Factor 8*a - 5*a**i - 10*a**3 + 5*a**2 + 10*a - 9*a + a.
-5*a*(a - 1)*(a + 1)*(a + 2)
Let b(l) be the first derivative of -l**5/50 + l**4/10 - l**3/5 + l**2/5 - 13*l - 53. Let j(s) be the first derivative of b(s). Determine d so that j(d) = 0.
1
Let b(h) = 21*h**2 + 9. Let g(f) = 29*f**2 - 3*f - 34. Let w(c) = 10*c**2 - c - 12. Let u(y) = 6*g(y) - 17*w(y). Let x(m) = -b(m) + 6*u(m). Factor x(s).
3*(s - 3)*(s + 1)
Factor -72*m**2 - 6*m**3 + 22 - 22 + 58*m**3 + 80*m**2.
4*m**2*(13*m + 2)
Let a(y) be the second derivative of -y**6/120 - 7*y**5/80 - 7*y**4/24 - y**3/3 - 1549*y. Solve a(p) = 0 for p.
-4, -2, -1, 0
Let l = -7225543653 + 59935885002554/8295. Let t = l - -2/2765. Factor 49/3*y**5 - t*y**2 - 175/3*y**4 + 235/3*y**3 + 40/3*y - 4/3.
(y - 1)**3*(7*y - 2)**2/3
Let i = 49506 + -49506. Factor 1/7*h**2 + 1/7*h**3 + i*h + 0.
h**2*(h + 1)/7
Let q = -156 + 162. Solve q + 4 + 29*m**2 + 7 - 30*m**2 + 16*m = 0.
-1, 17
Let v(u) be the second derivative of -169*u**4/20 - 253*u**3/15 + u**2/10 - 2830*u. Solve v(b) = 0 for b.
-1, 1/507
Find x such that 1018/5*x**2 - 26010 + 25806*x + 2/5*x**3 = 0.
-255, 1
Let c be (-12)/14*((-68)/8 + 5). Factor t**c + 6855 - 6855 + 2*t**2 - 3*t.
t*(t - 1)*(t + 3)
Let t(z) be the first derivative of 2/7*z**2 + 0*z**4 + 0*z - 207 + 2/7*z**3 - 2/35*z**5. Factor t(q).
-2*q*(q - 2)*(q + 1)**2/7
Let z(w) be the first derivative of -w**3 - 228*w**2 + 459*w + 532. Factor z(h).
-3*(h - 1)*(h + 153)
Let b be 12/(-2)*(-9)/18. Let l be ((-12)/(-4))/b - -3. Suppose 0 + 2*s + 6*s + l*s**2 + 5 - 1 = 0. What is s?
-1
Let 2 - 1/4*c**3 + 1/4*c**4 + c - 3/2*c**2 = 0. Calculate c.
-2, -1, 2
Let t(n) be the first derivative of -n**7/70 + n**6/30 + n**5/100 - n**4/12 + n**3/15 + 29*n + 25. Let b(a) be the first derivative of t(a). Solve b(w) = 0.
-1, 0, 2/3, 1
What is o in 94/7*o**4 - 22/7*o**2 - 72/7 - 206/7*o**3 - 10/7*o**5 + 216/7*o = 0?
-1, 2/5, 1, 3, 6
Let s be (12/40)/(209/(-55) + 5)*12. Let d = 861/692 - -1/173. Find x, given that 5/4*x**s + 0 - d*x + 0*x**2 = 0.
-1, 0, 1
Let u be 396/(-11)*(-2 + 4). Let n be 32/12*u/(-42). Find o such that 12/7*o**4 + 4/7 - 2/7*o**5 - 18/7*o - 4*o**3 + n*o**2 = 0.
1, 2
Let k(v) be the third derivative of v**6/720 + 13*v**5/180 + 217*v**4/144 + 49*v**3/3 + 275*v**2. What is p in k(p) = 0?
-12, -7
Suppose -4*o + i = 542, 4*o + 2*i + 712 = 176. Let g be 29/(-22) - o/90. Factor 0*r**2 + 0 - 2/11*r**3 + 0*r + g*r**4.
2*r**3*(r - 1)/11
Let k(x) be the second derivative of -x**7/14 + x**6/30 + 15*x**5/2 - 25*x**4/6 - 49*x**3/2 + 49*x**2/2 - 6349*x. Solve k(b) = 0 for b.
-7, -1, 1/3, 1, 7
Determine d, given that 27*d**3 - 3*d**4 + 6*d**4 - 60633*d**2 + 60678*d**2 - 75*d = 0.
-5, 0, 1
Let b(y) be the first derivative of y**4/20 + 7*y**3/3 - 37*y**2/5 - 739. Factor b(w).
w*(w - 2)*(w + 37)/5
Let z(s) = s**3 - 9*s**2 + 19*s + 7. Let x = 74 + -69. Let v be z(x). Factor 2/17*u**3 - 2/17*u + 2/17*u**v - 2/17*u**4 + 0.
-2*u*(u - 1)**2*(u + 1)/17
Factor -3/2*k**4 - 423/2*k**2 + 0 - 42*k**3 - 297*k.
-3*k*(k + 3)**2*(k + 22)/2
Let y(j) be the second derivative of -j**5/20 + 5*j**4/8 - 2*j**3 + 24*j**2 - 2*j - 15. Let z(v) be the first derivative of y(v). Factor z(c).
-3*(c - 4)*(c - 1)
Let g = 188949 - 188947. Find n such that 2*n - 20/9 + 2/9*n**g = 0.
-10, 1
Let t(g) = -g**2 + 381*g - 754. Let s(r) = 4*r**2 - 1144*r + 2261. Let o(n) = -4*s(n) - 11*t(n). Find b, given that o(b) = 0.
2, 75
Let p be 2250/16500 + 4635/858. What is r in -38/13*r**3 + 72/13*r**4 - 8/13 - p*r - 174/13*r**2 = 0?
-1, -1/4, -2/9, 2
Let b(d) be the second derivative of d**7/147 - 3*d**6/7 - 59*d**5/70 + 191*d**4/14 + 1138*d**3/21 + 552*d**2/7 - 10*d - 204. Solve b(h) = 0 for h.
-3, -1, 4, 46
Let v(i) be the second derivative of -i**5/50 + 59*i**4/60 - 37*i**3/6 + 39*i**2/5 + 2229*i. What is y in v(y) = 0?
1/2, 3, 26
Let f(j) = -9*j**2 + 356*j + 242. Let p(y) = 30*y**2 - 1067*y - 727. Let q(o) = 14*f(o) + 4*p(o). Determine l so that q(l) = 0.
-2/3, 120
Let l = -2/11729 - -35195/46916. Let y(i) be the first derivative of -3/8*i**4 + 0*i + 0*i**3 + 6/5*i**5 + 0*i**2 - l*i**6 + 31. Factor y(c).
-3*c**3*(c - 1)*(3*c - 1)/2
Find x, given that 397*x - 3*x**3 + 284*x - 1431*x - 381*x**2 = 0.
-125, -2, 0
Factor 5*w**5 + 5 + 4114*w**3 + 4109*w**3 + 10*w**2 - 15*w**4 - 15*w - 8213*w**3.
5*(w - 1)**4*(w + 1)
Let f(i) be the first derivative of -2*i**7/21 + i**6/30 + i**5/5 + 5*i**4/48 + 138*i + 88. Let q(s) be the first derivative of f(s). Factor q(h).
-h**2*(2*h + 1)**2*(4*h - 5)/4
Let k be 65*((-8)/4 - (-2 - 1)). Let 1187 - k*n - 1187 + 5*n**3 - 60*n**2 = 0. What is n?
-1, 0, 13
Factor 0 - 32/3*s**2 + 4/9*s**3 + 0*s + 1/9*s**4.
s**2*(s - 8)*(s + 12)/9
Let a = 407 - 405. Factor 6*z**3 + 4*z**a + 24*z + z**4 + z**4 - 24