+ 581 = 0. Let x = -74 - s. Find m, given that 10 + 88*m + 12*m**2 - 53*m + x*m**2 + 5*m**4 + 25*m**3 - 17*m**2 = 0.
-2, -1
Let b(v) be the first derivative of -7*v**6/4 - 321*v**5/10 - 132*v**4 + 290*v**3 + 816*v**2 + 384*v + 457. Find f such that b(f) = 0.
-8, -1, -2/7, 2
Suppose 8*w**3 - 2*w**4 + 1268*w + 9*w**2 + 144 + 9*w**2 - 1400*w + 4*w**2 = 0. Calculate w.
-4, 2, 3
Suppose 27 = t + 24. Let p(r) be the second derivative of 0 + 1/30*r**5 + 5/54*r**4 + 6*r + 2/27*r**t + 0*r**2. Find a, given that p(a) = 0.
-1, -2/3, 0
Let z(t) be the third derivative of t**7/1575 - t**6/450 + t**4/90 - t**3/45 + 103*t**2. Factor z(p).
2*(p - 1)**3*(p + 1)/15
Let l(q) = -8*q**3 + 16*q**2 + 4*q. Let o(m) be the second derivative of -1/6*m**3 - 1/12*m**4 + 0*m**2 + 4*m + 0. Let u(p) = l(p) + 6*o(p). Factor u(n).
-2*n*(n - 1)*(4*n - 1)
Let t(j) = -2*j + 10. Let p be t(5). Let k(l) be the first derivative of 1/6*l**4 + p*l**2 - 4 + 2/9*l**3 + 0*l. Suppose k(n) = 0. What is n?
-1, 0
Let f(m) be the second derivative of 5*m**4/12 + 55*m**3/3 - 120*m**2 + 408*m. Solve f(x) = 0 for x.
-24, 2
Suppose 29*z + 4*z + 16*z - 11*z - 45*z**4 + 37*z**2 - 9*z**5 + 8 + 18*z**3 - 47*z**3 = 0. Calculate z.
-4, -1, -2/3, -1/3, 1
Let s = -49 - -51. Determine w so that -5*w**5 + 7*w**3 - s*w**3 - 5*w**2 + 99*w**4 - 94*w**4 = 0.
-1, 0, 1
Let h(n) be the second derivative of n**5/5 - 5*n**4/3 + 16*n**3/3 - 8*n**2 + 25*n + 1. Let h(l) = 0. What is l?
1, 2
Let y(l) be the second derivative of -l**5/120 - 5*l**4/72 - 7*l**3/36 - l**2/4 + 2*l - 78. Factor y(z).
-(z + 1)**2*(z + 3)/6
Let x = -3431/5 - -3447/5. Suppose x*k + 0 - 118/5*k**3 + 4*k**2 + 28/5*k**4 = 0. What is k?
-2/7, 0, 1/2, 4
Determine t so that 8*t**3 + 2*t**2 + 5165*t**4 - 2*t**2 - 2*t**5 - 5171*t**4 = 0.
-4, 0, 1
Let p(i) be the first derivative of 6/17*i**3 + 4/17*i - 7 - 9/17*i**2. Let p(l) = 0. What is l?
1/3, 2/3
Suppose 2*w = 25 - 21. Factor -5*h + 47*h**2 + 54*h**2 - 96*h**w.
5*h*(h - 1)
Let b(s) = -10*s - 55. Let r be b(-6). Let m(u) be the second derivative of 1/4*u**2 - 3*u + 0 + 1/4*u**3 + 1/40*u**r + 1/8*u**4. Solve m(w) = 0 for w.
-1
Let o = 12680 - 38039/3. What is h in 0 + 0*h - 1/3*h**2 + o*h**3 = 0?
0, 1
Factor 148/9 - 76/9*w + 1/9*w**2.
(w - 74)*(w - 2)/9
Factor -4/3*u**2 + 100/3*u + 0.
-4*u*(u - 25)/3
Let c(a) be the first derivative of -a**4/4 - a**3/3 + 2*a**2 + 4*a + 71. Factor c(z).
-(z - 2)*(z + 1)*(z + 2)
Let o = 12509/25022 - -1/12511. Determine i so that -o*i + 3 - 1/2*i**2 = 0.
-3, 2
Let l be 5 - (1 + 1) - -12. Let m = l + -13. Factor 18*z**2 - 18*z**2 - 2 + 10*z**m - 8*z.
2*(z - 1)*(5*z + 1)
Let k(v) be the first derivative of 9/11*v**3 - 196/11*v + 31 - 84/11*v**2 - 1/44*v**4. Let k(h) = 0. Calculate h.
-1, 14
Let q(p) be the third derivative of -2/3*p**3 - 4/21*p**7 + 9*p**2 + 0 - 2/21*p**8 + 0*p + 11/15*p**5 + 1/6*p**4 + 7/30*p**6. Let q(w) = 0. What is w?
-1, -1/2, 1/4, 1
Let x(a) be the second derivative of -7*a + 0 + 0*a**2 + 1/6*a**4 - 1/3*a**3 + 3/40*a**5 - 1/30*a**6 - 1/84*a**7. Let x(i) = 0. What is i?
-2, 0, 1
Let c be (-26)/(-8) - (-3 - 13/(-4)). Find j such that -4*j + 8 + 2*j**2 - c*j**2 - 3*j**2 + 0*j = 0.
-2, 1
Let d = 2674485127/17840 + -2398597/16. Let c = d - -6/223. Factor -6/5 + 2/5*m**3 + c*m - 2*m**2.
2*(m - 3)*(m - 1)**2/5
Let j(h) be the second derivative of -h**6/180 - h**5/15 + 5*h**4/12 + 7*h**3/3 - 6*h. Let c(g) be the second derivative of j(g). Suppose c(m) = 0. Calculate m.
-5, 1
Let k(i) be the third derivative of -i**5/80 + i**4/4 + 9*i**3/8 - i**2. Determine c, given that k(c) = 0.
-1, 9
Let d be (-1)/(-7)*((-9)/6 - -5). Factor d*i**2 - 2 - 3/2*i.
(i - 4)*(i + 1)/2
Let y(u) be the third derivative of u**9/12096 + u**8/1680 + u**7/672 + u**6/720 + 29*u**3/6 + 41*u**2. Let z(k) be the first derivative of y(k). Factor z(p).
p**2*(p + 1)**2*(p + 2)/4
Let c(q) be the first derivative of 2*q**3/27 - 34*q**2/3 + 578*q + 502. Suppose c(a) = 0. Calculate a.
51
Suppose -774*v + 4*w = -770*v - 48, -2*v + w + 17 = 0. Factor -35/3*z + 25/3*z**4 + 5/3*z**v - 10/3*z**2 + 10*z**3 - 5.
5*(z - 1)*(z + 1)**3*(z + 3)/3
Let m = 1966978 + -2203015193/1120. Let f = m - 1/160. Factor 2/7*v + f*v**3 + 3/7*v**2 + 0.
v*(v + 1)*(v + 2)/7
Let z(s) be the first derivative of -s**4/4 + 58*s**3 - 5046*s**2 + 195112*s - 177. Solve z(t) = 0.
58
Let p(d) = d**5 + 7*d**4 - 2*d**3 + 9*d**2 - 5*d. Let j(a) = -a**4 - a**3 - a**2 + a. Let i(k) = 20*j(k) + 4*p(k). Determine n, given that i(n) = 0.
-4, 0, 1
Let o = 1880 - 3759/2. Let k(f) be the second derivative of -9*f - 3/2*f**2 + 0 + o*f**4 + 0*f**3 + 0*f**5 - 1/10*f**6. Factor k(g).
-3*(g - 1)**2*(g + 1)**2
Let p(k) be the second derivative of k**4/12 - 64*k**3/3 + 2048*k**2 + 8*k + 7. Suppose p(h) = 0. What is h?
64
Factor 106/7*z**2 - 24/7*z**3 + 144/7 + 2/7*z**4 - 204/7*z.
2*(z - 4)*(z - 3)**2*(z - 2)/7
Let z(b) be the first derivative of -3*b**4/8 + 55*b**3/4 + 129*b**2/4 + 87*b/4 + 13. What is y in z(y) = 0?
-1, -1/2, 29
Let j(g) be the first derivative of -g**5/20 + g**4/20 + g**3/15 - 10*g - 15. Let r(k) be the first derivative of j(k). Determine v, given that r(v) = 0.
-2/5, 0, 1
Factor 201*n**2 + 36 - 52*n**3 + 80*n**3 + 276*n - 29*n**2.
4*(n + 3)**2*(7*n + 1)
Let i = 1384/8827 - 2/679. Let 12/13*y**3 - i*y**4 - 24/13*y**2 + 16/13*y + 0 = 0. What is y?
0, 2
Let f = 392 + -387. Let a(j) be the second derivative of 0 + 0*j**2 - 1/78*j**4 + 5*j + 2/39*j**3 - 1/130*j**f. Let a(c) = 0. What is c?
-2, 0, 1
Let f(y) = y**2 + 15*y - 12. Let g be f(-17). Let h = g - 20. Factor -20*r**h + 8*r + 50*r**2 - 28*r**2 + 6.
2*(r + 1)*(r + 3)
Let w(r) be the second derivative of -11*r**4/54 + 89*r**3/27 - 8*r**2/9 - 5*r. Suppose w(a) = 0. What is a?
1/11, 8
Let k be 116/10 + -1*10/(-25). Factor k*j**3 + 9*j**3 - 11*j**3 - 15*j**2 - 8*j - 2*j.
5*j*(j - 2)*(2*j + 1)
Let 75 + 3*q - 9 + 45*q - 22 + 4*q**2 = 0. Calculate q.
-11, -1
What is w in -6*w**3 + 1825 + 2*w**3 + 28*w**2 - 16*w - 1873 = 0?
-1, 2, 6
Let c be ((5/6)/5)/1. Let h be (((-3)/3 - 0)/7)/(120/(-140)). Factor 1/6*q**2 + c*q - h - 1/6*q**3.
-(q - 1)**2*(q + 1)/6
Let b(g) be the third derivative of g**8/4032 - 5*g**7/1008 + 2*g**5/3 + 24*g**2. Let p(i) be the third derivative of b(i). Factor p(o).
5*o*(o - 5)
Let q(b) be the first derivative of -3*b**5/5 + 21*b**4/2 - 25*b**3 + 18*b**2 + 259. Factor q(i).
-3*i*(i - 12)*(i - 1)**2
Let f(g) be the first derivative of g**6/35 - g**5/14 + g**4/21 - 2*g + 2. Let a(q) be the first derivative of f(q). Suppose a(b) = 0. Calculate b.
0, 2/3, 1
Suppose 1 + 1 = 2*x - 2*i, 0 = 2*x - 5*i + 4. Let f(k) be the second derivative of 11/2*k**3 + 21/20*k**5 + 0 + 3*k**2 + x*k + 4*k**4. Factor f(y).
3*(y + 1)**2*(7*y + 2)
Let o(d) = 2*d - 3. Let s be o(3). Suppose 0 = -0*k + k - s*i + 10, -3*i = k - 14. Factor -12*c**2 - k - 12*c**2 - 48*c - 12*c**2 - 14.
-4*(3*c + 2)**2
Suppose 4*f = -0*f + 168. Suppose -p + 18 = 4*c, 0*c - 6 = -5*p + c. Find o such that -f - p - 79*o**3 - 321*o**3 - 20 - 960*o**2 + 500*o**4 - 448*o = 0.
-2/5, 2
Factor 0 + 0*j + 1/8*j**3 - 49/8*j**2.
j**2*(j - 49)/8
Let l(m) be the first derivative of m**4/48 + m**3/4 + 5*m**2/8 - m - 13. Let i(v) be the first derivative of l(v). Let i(g) = 0. Calculate g.
-5, -1
Suppose -q + 7 = 5. Determine f, given that -4*f**2 - 10*f**2 + 4 + 8*f**4 - 10*f + 5*f**2 - 15*f**q - 2*f**3 = 0.
-1, 1/4, 2
Let t be (0 + 4 - 5)*-65. Let w = t + -63. Find h such that -2/5*h**w + 6/5 - 4/5*h = 0.
-3, 1
Let h(z) be the first derivative of -2*z**6/3 - 2*z**5 + 2*z**4 + 22*z**3/3 - 4*z**2 - 8*z - 15. Solve h(k) = 0 for k.
-2, -1/2, 1
Let s = -189 + 194. Let i be 33/15 - 21/105. Solve -3*z**4 + 0 + 0*z + 0*z**i - 3/2*z**s - 3/2*z**3 = 0 for z.
-1, 0
Let s(b) = 6*b - 47. Let f be s(18). Factor 27*k**3 + 15*k**4 + 13*k**3 + 36*k - 59*k**2 - 25*k**2 - f*k**3.
3*k*(k - 3)*(k + 2)*(5*k - 2)
Suppose 0 = 9*y - 5*y + 25*y. Factor -1/2*t**3 + y*t + 1/2*t**4 + 0 + 0*t**2.
t**3*(t - 1)/2
Let q(b) be the third derivative of -b**8/84 - b**7/15 - 3*b**6/20 - b**5/6 - b**4/12 + 37*b**2 - 1. Factor q(v).
-2*v*(v + 1)**3*(2*v + 1)
Let x(d) = -d**2 + d - 1. Let m be x(-1). Let w = -8 + 9. Let o(y) = -1. Let c(k) = -3*k**2 + 6*k - 6. Let l(n) = m*o(n) + w*c(n). Solve l(b) = 0 for b.
1
Let u(r) be the first derivative of 21 - 9/2*r**2 - r