5/3*s**4.
s*(s - 2)*(s + 7)*(5*s + 1)/3
Let f(w) be the second derivative of -9*w**2 - 1/30*w**6 + 9/20*w**5 + 31*w + 0 + 13/2*w**3 - 29/12*w**4. Factor f(k).
-(k - 3)**2*(k - 2)*(k - 1)
Find y, given that 6708 - 8408*y - 76*y + 4*y**3 + 1396*y**2 + 6072 = 0.
-355, 3
Let p(l) be the first derivative of -l**7/420 + l**6/90 + l**5/60 - l**4/6 + 5*l**3/3 + 2*l - 64. Let w(y) be the third derivative of p(y). Factor w(b).
-2*(b - 2)*(b - 1)*(b + 1)
Let h(d) be the second derivative of -1 + 2/3*d**3 + 42*d + 1/54*d**4 + 9*d**2. Factor h(x).
2*(x + 9)**2/9
Let 4*y**4 + 0 + 0*y - 1/2*y**5 + 33/2*y**3 + 0*y**2 = 0. What is y?
-3, 0, 11
Let l(j) be the third derivative of j**7/840 - 9*j**6/160 + 83*j**5/120 + 21*j**4/8 - 49*j**3/3 + 459*j**2 - j. Factor l(f).
(f - 14)**2*(f - 1)*(f + 2)/4
Let l = 3517 + -2038. Factor -1497 + 2*t**3 + 3008 - l + 66*t + 36*t**2.
2*(t + 1)**2*(t + 16)
Let o(m) = 2*m**3 - 6*m**2 + 2*m. Suppose -y = -45 + 36. Let k(i) = 8*i - 11*i**2 - i**3 + y*i**3 - 14*i**2 + 0*i**3. Let u(c) = 2*k(c) - 9*o(c). Factor u(f).
-2*f*(f - 1)**2
Let b = 2128/17 + -127663/1020. Let w(d) be the third derivative of 29*d**2 - 4/3*d**3 - 1/3*d**4 + b*d**6 + 0*d + 1/30*d**5 + 0. Solve w(h) = 0 for h.
-2, -1, 2
Suppose -4*s + 40 = 120. Let t be s*3/((-24)/412). Factor 3*j**5 - 12*j**3 + 15*j**4 + 39*j**3 + 1051*j**2 + 6*j - t*j**2.
3*j*(j + 1)**3*(j + 2)
Let y(d) = -147*d**2 - 7347*d - 3261. Let h(w) = -21*w**2 - 1053*w - 466. Let c(g) = -15*h(g) + 2*y(g). Let c(o) = 0. What is o?
-52, -3/7
Suppose 10*g + 6*g - 60 = -4*g. Let b(x) be the first derivative of -5*x + 14 + 5/3*x**g + 0*x**2. Solve b(o) = 0 for o.
-1, 1
Let z(b) be the first derivative of b**4/2 - 4*b**3 + 11*b**2 - 12*b + 358. Let z(y) = 0. What is y?
1, 2, 3
Suppose -127*f + 451 = -647 + 336. Let z(h) be the second derivative of 0 - 1/60*h**f + 0*h**5 + 1/4*h**4 + 2/3*h**3 + 3/4*h**2 + 22*h. What is q in z(q) = 0?
-1, 3
Suppose 42*d = 15 + 211 - 16. Suppose -5*w + 559 = -391. Solve 3*l - 3*l**3 + 191*l**4 - d + 3 - w*l**4 + l**2 = 0 for l.
-1, 1, 2
Let q(v) be the third derivative of -v**5/100 - 137*v**4/20 - 273*v**3/10 - 34*v**2 + 6. Factor q(z).
-3*(z + 1)*(z + 273)/5
Let d(n) be the third derivative of -n**7/560 - 31*n**6/240 + 73*n**5/160 + 7*n**4/8 - 43*n**3/12 + 108*n**2 + 4*n. What is j in d(j) = 0?
-43, -1, 2/3, 2
Let o be (-6106)/(-3870) - (-6)/27. Let p = 267/95 + -42/19. Solve -6/5 + 3/5*n - 3/5*n**3 + o*n**2 - p*n**4 = 0 for n.
-2, -1, 1
Let m(v) be the third derivative of 0 - 17/600*v**6 + 0*v + 68*v**2 + 0*v**4 - 1/560*v**8 + 0*v**3 + 1/75*v**7 + 1/50*v**5. Let m(n) = 0. Calculate n.
0, 2/3, 1, 3
Let u(t) be the first derivative of 2*t**3/15 - 11*t**2/5 + 12*t - 975. Suppose u(l) = 0. What is l?
5, 6
Let v be (96/(-100)*-5)/((-6)/(-15)). Factor -9*c - 4*c**2 - c**2 - c**2 + 3*c**2 + v.
-3*(c - 1)*(c + 4)
Let d be (-12)/21 - 264/28. Let w = d + 20. Solve 15*f**2 - w - 15*f + 2*f**3 + 8*f**3 + 0*f**3 = 0 for f.
-2, -1/2, 1
Let v(q) be the second derivative of -7/54*q**4 - 2 + 11*q - 5/9*q**2 + 11/27*q**3 + 1/90*q**5. Find z, given that v(z) = 0.
1, 5
Let o(q) be the first derivative of 23/6*q + 96 - 1/18*q**3 + 11/6*q**2. Determine z, given that o(z) = 0.
-1, 23
Let s(n) be the second derivative of -4*n**7/147 - 24*n**6/35 - 25*n**5/14 + 53*n**4/42 + 26*n**3/7 - 32*n**2/7 + 2*n + 12. Let s(p) = 0. Calculate p.
-16, -2, -1, 1/2
Let q(a) be the third derivative of -a**6/60 - 37*a**5/6 + a**4/12 + 185*a**3/3 + 31*a**2 + 11. Factor q(x).
-2*(x - 1)*(x + 1)*(x + 185)
Let d(v) = 1512*v + 12100. Let q be d(-8). Let g(l) be the first derivative of 0*l + 0*l**2 + 1/10*l**q + 25 + 2/15*l**3. Determine c, given that g(c) = 0.
-1, 0
Let u be 5*4/30*(-1320)/(-176). Let a(n) be the third derivative of 0 + 2*n**2 - 1/6*n**3 - 1/36*n**4 + 1/45*n**u + 0*n - 1/630*n**7 + 1/180*n**6. Factor a(y).
-(y - 3)*(y - 1)*(y + 1)**2/3
Let i(m) be the second derivative of m**7/21 - 883*m**6/15 + 96797*m**5/5 + 293045*m**4/3 + 587861*m**3/3 + 196249*m**2 + 14*m + 205. Factor i(g).
2*(g - 443)**2*(g + 1)**3
Let d be 2*18/(-15)*325/(-52). Let j be (-12)/d*85/(-102). Find w, given that -8/3*w**2 + j*w**4 + 2/3*w**5 - 8/3*w**3 + 0*w + 0 = 0.
-2, -1, 0, 2
Suppose -654*a = -319*a - 320*a - 135. Let j(s) be the first derivative of -a - 3/7*s**2 + 0*s + 9/7*s**3. What is q in j(q) = 0?
0, 2/9
Let a(b) be the second derivative of 6*b**2 + 1/3*b**3 + 0*b**5 - 5/3*b**4 + 4/15*b**6 - 1 - 32*b - 1/21*b**7. Find v such that a(v) = 0.
-1, 1, 2, 3
Let k(m) be the third derivative of m**7/42 - 5*m**6/24 - 7*m**5/6 + 15*m**4/2 + 60*m**3 + 605*m**2. Factor k(d).
5*(d - 6)*(d - 3)*(d + 2)**2
Let s(m) be the third derivative of -m**5/90 + 35*m**4/18 + 152*m**3/3 - 3497*m**2. Factor s(r).
-2*(r - 76)*(r + 6)/3
Let o(w) be the third derivative of w**8/8400 - w**7/2100 - w**6/600 + 83*w**3/6 + 55*w**2. Let i(s) be the first derivative of o(s). Let i(y) = 0. What is y?
-1, 0, 3
Let a(b) be the second derivative of -b**7/168 - b**6/12 + 101*b**5/80 - 143*b**4/24 + 83*b**3/6 - 17*b**2 - 1022*b. Factor a(u).
-(u - 2)**3*(u - 1)*(u + 17)/4
Let u = -9 - -11. Let z(w) = -2*w**2 + 4*w**2 - 10*w + 10 + 4*w**u. Let v(f) = f**2 - f + 1. Let r(i) = -10*v(i) + z(i). Suppose r(y) = 0. Calculate y.
0
Let c(v) be the first derivative of -v**6/2 + 9*v**5/5 + 51*v**4/4 - 27*v**3 - 78*v**2 + 180*v + 351. Suppose c(r) = 0. Calculate r.
-3, -2, 1, 2, 5
Let z(n) be the third derivative of -n**2 - 1/525*n**7 + 1/300*n**5 + 3/400*n**6 + 1/30*n**3 - 3/80*n**4 + 0 + 23*n. Determine y so that z(y) = 0.
-1, 1/4, 1, 2
Let h(p) be the first derivative of -17*p + 4/3*p**3 + 24/5*p**6 + 0*p**2 + 5 - 11/3*p**4 + 3/5*p**5. Let z(n) be the first derivative of h(n). Solve z(j) = 0.
-2/3, 0, 1/4, 1/3
What is w in 31/6*w - 1/6*w**2 + 0 = 0?
0, 31
Let a be (21/(42/(-4)))/((-6)/15). Let x(j) be the third derivative of 0*j + 0 - 15*j**2 + 2/135*j**a + 0*j**4 - 1/540*j**6 + 0*j**3. Factor x(v).
-2*v**2*(v - 4)/9
Let t be 12/(-3) + 3 + (199 - -2). Factor 8*z**3 + 20*z**4 + 65*z + 30 - 14*z**3 + 50*z**3 + 41*z**3 - t*z**2.
5*(z - 1)**2*(z + 6)*(4*z + 1)
Let g(r) = -7*r**2 + 17*r. Let k be g(2). Suppose 2*c = z - 3, k = -z + 9. Factor -2/3*w**2 + 1/3*w**3 - w + c.
w*(w - 3)*(w + 1)/3
Let g = -8 - -14. Let m(h) = h**3 + 14*h**2 + 315*h + 3928. Let d be m(-13). Suppose -1/3*t**4 - 8/3 - 20/3*t - g*t**d - 7/3*t**3 = 0. Calculate t.
-2, -1
Let o(p) = 3*p**5 - 30*p**4 + 118*p**3 - 162*p**2 + 81*p. Let m(a) = 3*a**5 - 30*a**4 + 116*a**3 - 162*a**2 + 81*a. Let z(k) = -5*m(k) + 4*o(k). Factor z(i).
-3*i*(i - 3)**3*(i - 1)
Let s be (-21)/(5 + -1 - (-4247)/(-1054)). Suppose s*f - 722*f + 32 = 0. Let 8/7*u**2 - 4/7*u**5 + 4/7 + 12/7*u - 12/7*u**f - 8/7*u**3 = 0. Calculate u.
-1, 1
Let g(w) = -639*w + 82433. Let z be g(129). Factor -12/7 + 2/7*r**z + 2/7*r.
2*(r - 2)*(r + 3)/7
Let l(b) = -55*b**3 - 1425*b**2 + 55*b + 1345. Let c(s) = -8*s**3 - 204*s**2 + 8*s + 192. Let g(z) = 20*c(z) - 3*l(z). Find i, given that g(i) = 0.
-39, -1, 1
Let t = -209667 + 209669. Solve -30/7*u**t - 8*u + 8/7 = 0.
-2, 2/15
Let h(c) = 12*c**3 - 184*c**2 - 912*c - 1080. Let o(p) = -8*p**3 + 123*p**2 + 608*p + 715. Let r(v) = -5*h(v) - 8*o(v). Solve r(k) = 0 for k.
-2, 20
Let d(t) be the first derivative of -1/4*t**4 + 175 - 2*t**3 - 8*t + 15/2*t**2. Factor d(l).
-(l - 1)**2*(l + 8)
Let t be 8/(-36) + (-5363550)/(-243). Let f = -330952/15 + t. Factor -32/15*m + 2/15*m**2 + f.
2*(m - 8)**2/15
Let m = -708 + 710. Let -5*t**2 + 6*t**2 + 26*t - 2*t**2 + 169 - 4*t**m + 6*t**2 = 0. What is t?
-13
Let g = 35 - 30. Let s(a) be the third derivative of -1/60*a**6 + 0*a**3 + 36*a**2 + 0*a - 1/150*a**g + 0*a**4 + 0. Factor s(x).
-2*x**2*(5*x + 1)/5
Let g(c) be the first derivative of -c**7/126 - c**6/45 - c**5/60 - 58*c + 61. Let w(k) be the first derivative of g(k). Factor w(p).
-p**3*(p + 1)**2/3
Suppose -25*n - 25*n = 2*n - 6*n. Let b = 222 + -650/3. Let -10/3*m**4 + 8/3*m**2 + b*m**3 + n*m + 0 = 0. What is m?
-2/5, 0, 2
Let t = -3582/185 - -2164/111. Factor 0*i + 26/15*i**2 + 0 + t*i**3.
2*i**2*(i + 13)/15
Let f(u) be the second derivative of -u**6/1440 + u**5/80 + u**3/2 - u**2 - 2*u + 19. Let d(o) be the second derivative of f(o). Solve d(a) = 0.
0, 6
Suppose -15088/13*t**2 - 2764/13*t**3 - 2/13*t**5 - 132/13*t