for s.
-476, 2
Let h(x) be the third derivative of -x**8/728 + 4*x**7/1365 + 37*x**6/780 - 7*x**5/195 - 2*x**4/13 - 23*x**2. Determine q so that h(q) = 0.
-3, -2/3, 0, 1, 4
Factor 450/7*g**3 + 162/7*g**4 + 0 - 106/7*g**2 + 6/7*g.
2*g*(g + 3)*(9*g - 1)**2/7
Let y = -209 - -219. Suppose -2*c - 12 = -z, -13*z + y*z = 3*c + 9. Factor -z*j - 5/3 - 1/3*j**2.
-(j + 1)*(j + 5)/3
Suppose -1/4*x**5 - 5/4*x**4 - 7*x + 29/4*x**3 + 37/4*x**2 - 8 = 0. Calculate x.
-8, -1, 1, 4
Suppose -3*k = 36, -2*k + 770 - 784 = 5*g. Suppose -44/3*m + 2/9*m**g + 242 = 0. What is m?
33
Let o(t) = -t**2 - 5*t + 2. Let j be o(-5). Factor -8 - 12*l - 200*l**3 + 199*l**3 - 6*l**2 + 0*l**j.
-(l + 2)**3
Suppose -20 = -5*r, 1 + 11 = a + 5*r. Let w be 3 + 387/(-36) - a. Determine m, given that 0*m + 0 - 1/8*m**2 - 1/8*m**4 + w*m**3 = 0.
0, 1
Let r = 179 + -191. Let v be (-1 + 4/r)*(-171)/76. Factor 3/7*o - 9/7*o**2 - 3/7*o**4 + 9/7*o**v + 0.
-3*o*(o - 1)**3/7
Factor 249/4 - 993/4*q - 3*q**2.
-3*(q + 83)*(4*q - 1)/4
Let l(y) be the first derivative of -2*y**3/3 + 115*y**2 + 232*y + 6670. Factor l(k).
-2*(k - 116)*(k + 1)
Let y(n) be the second derivative of 1/36*n**4 - 7/18*n**3 - 4/3*n**2 + 0 + 245*n. Find o, given that y(o) = 0.
-1, 8
Let r = 495 + -239. Factor 228 + 25*n**4 + 397*n**2 + 23*n**4 - 47*n**4 + r - 42*n**3 + 924*n.
(n - 22)**2*(n + 1)**2
Let u = 81 + 85. Let q(h) be the first derivative of 5 - 14*h - h + 146*h**2 - u*h**2 + h**5 - 10*h**3. Solve q(g) = 0 for g.
-1, 3
Let v(u) = -7*u**2 + 451*u - 12547. Suppose -5*g + 619 = 604. Let y(c) = 22*c**2 - 1354*c + 37642. Let p(n) = g*y(n) + 10*v(n). Factor p(a).
-4*(a - 56)**2
Let g(a) be the first derivative of -1/12*a**6 - 24 - 1/5*a**5 + a + 4/3*a**3 + 1/4*a**4 + 7/4*a**2. Let g(c) = 0. What is c?
-1, 2
Let x(i) be the first derivative of 1/9*i**3 + 0*i - 43/2*i**2 + 1/180*i**5 + 1/24*i**4 + 22. Let k(s) be the second derivative of x(s). Factor k(q).
(q + 1)*(q + 2)/3
Suppose c + 35 = -5*p, -69 = 3*c + 2*p - 55. Let h(l) be the second derivative of c + 20*l - 1/15*l**4 + 0*l**2 - 4/15*l**3. Factor h(q).
-4*q*(q + 2)/5
Let h(w) be the second derivative of w**4/102 + 18*w**3/17 - 1120*w**2/17 - 2*w + 1482. Let h(m) = 0. What is m?
-70, 16
Let l(d) be the second derivative of -d**4/9 - 104*d**3/9 - 258*d**2 + 7188*d. Let l(u) = 0. What is u?
-43, -9
Let q be 38/9 - (-23440)/(-10548). Let d be 3 - (26/6 - 2). Determine i so that -4/9*i + 0 + 4/9*i**3 - 2/3*i**q + d*i**4 = 0.
-1, -2/3, 0, 1
Let g(z) be the first derivative of 3*z**4/4 + 1314*z**3 + 7875*z**2/2 + 3936*z + 4031. Factor g(k).
3*(k + 1)**2*(k + 1312)
Let d be (104/78)/(32/120). Let x(p) be the third derivative of 3/320*p**6 + 0*p + 0*p**d - 1/16*p**4 + 0 - 1/560*p**7 + 0*p**3 + 43*p**2. Factor x(y).
-3*y*(y - 2)**2*(y + 1)/8
Let c(j) be the first derivative of 4*j**3/3 - 220*j**2 + 12100*j + 1776. Factor c(q).
4*(q - 55)**2
Let y = 294 - 265. Factor 11*v - 10*v + y*v - 5*v**2 + 25 + 10*v**2.
5*(v + 1)*(v + 5)
Find i such that 192/7*i + 318/7*i**3 + 0 + 96/7*i**4 + 424/7*i**2 + 10/7*i**5 = 0.
-4, -3, -8/5, -1, 0
Let w = -77 - -118. Let d = -39 + w. Find o such that 1 + d + 2*o + o**3 - 3*o**3 - o**4 - 2 = 0.
-1, 1
Solve -1204*g**2 - 6 + 6 - 3725*g**3 + 5519*g**2 + 3750*g**3 - 1730*g = 0.
-173, 0, 2/5
Suppose -2565*z + 39 = -732*z + 39. Factor -1/3*f**3 + 0*f - 64/3*f**2 + z.
-f**2*(f + 64)/3
Suppose 65 = -5*k + 5*q, -14*k - 3*q = -190 + 151. Factor -2*r**4 + k - 56/3*r - 38/3*r**3 - 80/3*r**2.
-2*r*(r + 2)**2*(3*r + 7)/3
Let b(l) = 4*l + 71. Let m be b(-17). Factor -r**m - 329*r - 32*r + 15693*r**2 - 15731*r**2.
-r*(r + 19)**2
Solve -2/9*p**3 + 4/3 - 4/3*p**2 + 2/9*p = 0.
-6, -1, 1
Let j = -1/11562 - -7709/11562. Let j*l + 4/3*l**2 - 4/3 - 2/3*l**3 = 0. What is l?
-1, 1, 2
Determine i, given that 27*i**3 - 17*i**3 - 33*i**2 - 6*i + 14*i + 180 - 13*i**3 - 20*i = 0.
-10, -3, 2
Let y(w) be the third derivative of -w**6/144 - 53*w**5/120 - 15*w**4/8 - 2*w**2 + 20*w - 3. Factor y(r).
-r*(r + 30)*(5*r + 9)/6
Factor 29*p + 884 - 4*p**2 + 38*p - 105*p + 22*p.
-4*(p - 13)*(p + 17)
Let o(q) be the second derivative of -q**7/21 - 13*q**6/15 + 34*q**5/5 - 8*q**4/3 - 256*q**3/3 + 272*q**2 - 6533*q. Solve o(i) = 0.
-17, -2, 2
Factor 47748*y - 47610 + 1/10*y**3 - 1381/10*y**2.
(y - 690)**2*(y - 1)/10
Let q(p) be the first derivative of p**7/2520 - p**6/1080 - p**5/72 - p**4/24 - 232*p**3/3 - 188. Let s(u) be the third derivative of q(u). Solve s(m) = 0.
-1, 3
Let x(f) be the third derivative of f**6/80 - 2*f**5/5 - 55*f**4/16 - 19*f**3/2 - 747*f**2. Determine u so that x(u) = 0.
-2, -1, 19
Let z(b) = -18*b**4 + 24*b**3 - 5*b**2 - 33*b - 7. Let r(q) = 8*q**4 - 12*q**3 + 3*q**2 + 17*q + 3. Let t(m) = 7*r(m) + 3*z(m). Suppose t(f) = 0. Calculate f.
-1, 0, 2, 5
Let o(s) be the second derivative of -s**6/3780 + s**5/630 + 2*s**4/63 + 22*s**3 - 94*s. Let l(k) be the second derivative of o(k). Factor l(h).
-2*(h - 4)*(h + 2)/21
Let q(t) be the first derivative of -15*t**2 + 217 + 16/3*t**3 + 0*t - 1/8*t**4. Solve q(h) = 0 for h.
0, 2, 30
Let t be 80/60*(-15)/50 - 12/(-5). Suppose 6*v**t + 16 - 2/3*v**3 - 52/3*v = 0. What is v?
2, 3, 4
Let w(g) = -4*g**4 - 524*g**3 - 11653*g**2 - 21637*g - 5. Let v(t) = -6*t**4 - 796*t**3 - 17480*t**2 - 32456*t - 8. Let k(c) = 5*v(c) - 8*w(c). Factor k(b).
2*b*(b + 2)*(b + 52)**2
Let k(u) = -5*u**4 - 1845*u**3 + 625*u**2 + 1785*u - 580. Let d(s) = -s**4 - 2*s**3 + 2*s**2 - s + 1. Let q(y) = -20*d(y) + k(y). Let q(z) = 0. Calculate z.
-1, 1/3, 1, 120
Let v(z) be the third derivative of z - 33*z**2 - 1/120*z**6 + 0*z**3 + 0 - 1/20*z**5 + 0*z**4. Factor v(c).
-c**2*(c + 3)
Let d = -31664 - -31676. Factor -8*f**2 + 56/3 - 4/3*f**3 + d*f.
-4*(f - 2)*(f + 1)*(f + 7)/3
Let s = 60 + -58. Factor -18*n - 3867*n**5 + 15*n**3 + n**3 + 12*n**s - 12*n**4 + 3869*n**5.
2*n*(n - 3)**2*(n - 1)*(n + 1)
Let r(g) be the second derivative of g**5/50 + 676*g**4/15 + 456976*g**3/15 + 2760*g. Determine u so that r(u) = 0.
-676, 0
Let 254/13*l**2 + 18/13 - 272/13*l**4 - 32/13*l**5 + 174/13*l**3 - 142/13*l = 0. Calculate l.
-9, -1, 1/4, 1
Let m(a) be the first derivative of 1/12*a**4 + 20/3*a**2 + 180 + 12*a + 13/9*a**3. Factor m(l).
(l + 2)**2*(l + 9)/3
Let x(t) = t**2 + 2*t - 1. Suppose -k + 3*b - 1 = 0, 11*k - 6*k + 5 = 3*b. Let l(m) = 20*m + 12. Let r(q) = k*l(q) + 4*x(q). Solve r(p) = 0.
-1, 4
Let p = 22 + -17. Suppose -5*x + y + 19 = 0, -2*y - 27 = -p*x + y. Factor 2*v**x - v**5 - v - 351 + 351.
-v*(v - 1)**2*(v + 1)**2
Let 158*x + 1/2*x**2 - 317/2 = 0. Calculate x.
-317, 1
Let p = 15290 + -30555/2. Let n(f) be the first derivative of -p*f**2 + 35 - 30*f - 5/3*f**3. Factor n(y).
-5*(y + 2)*(y + 3)
Suppose -22 = -4*v - 18, -4*n = -v + 37. Let i be ((-8)/n)/4 - (1 - 1). Factor -i*t**4 + 2/9*t**2 + 0*t + 0 + 0*t**3.
-2*t**2*(t - 1)*(t + 1)/9
Factor -10/3*w**2 - 4*w + 1/6*w**5 + 5/6*w**4 + 0 + 1/3*w**3.
w*(w - 2)*(w + 2)**2*(w + 3)/6
Factor 2/5*s**4 - 828/5*s + 0 + 114*s**2 - 104/5*s**3.
2*s*(s - 46)*(s - 3)**2/5
Let f be (-11613)/(-790) - (-6)/20. Let -15*x + 145*x**3 + 4*x**2 + f*x**4 + 11*x**2 - 100*x - 20*x**5 - 30 - 10*x = 0. Calculate x.
-2, -1, -1/4, 1, 3
Let m(k) = k**4 - 2*k**3 - 2*k**2 + 2*k - 1. Let f(g) = -8*g**4 + 1276*g**3 - 395615*g**2 - 1597706*g - 1602749. Let u(d) = 4*f(d) + 28*m(d). Factor u(s).
-4*(s - 633)**2*(s + 2)**2
Factor 2361/8*f**2 - 1858107/8*f + 487443403/8 - 1/8*f**3.
-(f - 787)**3/8
Let d(w) be the first derivative of -5*w**4/8 - 795*w**3/2 - 379215*w**2/4 - 20098395*w/2 + 357. Factor d(i).
-5*(i + 159)**3/2
Suppose 61*w - 55*w - 48 = -3*z, z = -4*w + 20. Find p, given that 1/3*p**3 + 2/3*p**w + 0 - p = 0.
-3, 0, 1
Let x(p) be the first derivative of -p**5/240 + 5*p**4/96 + p**2/2 - 17*p - 37. Let s(w) be the second derivative of x(w). Factor s(c).
-c*(c - 5)/4
Factor -10*f**3 + 95*f**5 - 83*f**5 + 30*f**4 + 14*f**4 + 62*f**3 + 20*f**2.
4*f**2*(f + 1)**2*(3*f + 5)
Factor -t**2 - 144*t + 9*t - 990 + 856 + 0*t**2.
-(t + 1)*(t + 134)
Factor 54*r**2 + 37/2*r**3 + 107/2*r + 71/4 + 1/4*r**4.
(r + 1)**3*(r + 71)/4
Let j(p) = 1520*p**2 - 1250*p + 360. Let i(l) = -169*l**2 + 138*l - 40. Let c(v) = 35*i(v) + 4*j(v). Solve c(f) = 0.
4/11, 2/3
Let z be (3220/10626)/(10/6). Let y(b) be the first derivative of z*b**4 + 18 + 0*b - 2/55*b**5 + 2/11*b**2 - 1