35*c**3 + 30*c**3.
2*c**4*(c + 53)
Suppose -72 + 177 = 35*h. Let c(j) be the first derivative of -18 + 0*j**2 + 0*j + 0*j**h - 1/2*j**4. Let c(r) = 0. What is r?
0
Let l(c) be the second derivative of -c**5/5 + 10*c**4/3 - 62*c**3/3 + 60*c**2 + 458*c. Factor l(w).
-4*(w - 5)*(w - 3)*(w - 2)
Factor 26/5*n**3 - 108/5*n**2 - 16/5 + 24*n.
2*(n - 2)**2*(13*n - 2)/5
Let w = 190748 - 381461/2. Factor w*d + 15/2 + 5*d**2.
5*(d + 3)*(2*d + 1)/2
What is h in -307*h**2 + 730*h**5 - 51*h**4 + 7*h**2 - 1456*h**5 + 723*h**5 - 144*h - 204*h**3 = 0?
-12, -2, -1, 0
Let v(h) be the second derivative of h**7/14 - h**6 - 369*h**5/20 - 89*h**4 - 194*h**3 - 216*h**2 + 721*h - 1. Let v(q) = 0. What is q?
-4, -2, -1, 18
Let a(k) = 6*k**3 + 2*k**2 - 2*k. Let q be a(-2). Let r be 169/2 + (-18)/q. Suppose 3*i**2 + r + 2*i + i**3 - 41 - 44 = 0. Calculate i.
-2, -1, 0
Let y(o) be the second derivative of -o**6/105 - 2*o**5/35 - o**4/14 + 4*o**3/21 + 4*o**2/7 + 61*o + 6. Solve y(s) = 0 for s.
-2, -1, 1
Let g(p) be the second derivative of -5/3*p**2 + 23/54*p**3 + 2*p - 1/180*p**5 + 2/27*p**4 - 228. Factor g(a).
-(a - 10)*(a - 1)*(a + 3)/9
Let o = 144499 + -1300489/9. Let -40/3*y**2 - 16000/9 + o*y**3 + 800/3*y = 0. What is y?
20
Let y(u) be the second derivative of 2*u**6/15 - 19*u**5/5 - u**4/3 + 38*u**3/3 + 1416*u. Let y(j) = 0. Calculate j.
-1, 0, 1, 19
Let z(t) be the first derivative of 2*t**3/9 + 74*t**2 + 8214*t - 1214. Solve z(u) = 0 for u.
-111
Let a be (-65)/(-13) + (-23 - 1530/(-40)). Factor 73/4*s**2 + a + s**3 + 171/2*s.
(s + 9)**2*(4*s + 1)/4
Let n(m) be the first derivative of -5*m**6/18 + 13*m**5/15 + m**4/12 - 17*m**3/9 + 2*m**2/3 + 4*m/3 + 335. Solve n(k) = 0.
-1, -2/5, 1, 2
Factor 1533/2*i + 3/2*i**3 - 120*i**2 + 0.
3*i*(i - 73)*(i - 7)/2
Let y(o) = -80*o**2 - 4570*o + 4625. Let l(h) = -13*h**2 - 762*h + 771. Let s(u) = -25*l(u) + 4*y(u). Find m such that s(m) = 0.
-155, 1
Let g(s) be the second derivative of -15/2*s**2 - 12*s + 0 + 0*s**3 + 0*s**4 - 1/180*s**5. Let b(m) be the first derivative of g(m). What is x in b(x) = 0?
0
Let g(v) = -7*v**2 - 15*v + 1. Let x be g(-2). Determine b, given that 464*b**x - 64*b**2 - 100*b**5 + 59 - 213 + 20*b**4 + 90 - 256*b = 0.
-2, -2/5, 1, 2
Let m be (2/(-4))/(10/420). Let p = m + 24. Factor 5*t - 8*t**4 - 10*t**p - 22 + 3*t**4 + 5*t**5 + 10*t**2 + 17.
5*(t - 1)**3*(t + 1)**2
Let z be (-58 + 32)/156*0. Factor 46/19*f + 90/19*f**2 - 2/19*f**4 + 42/19*f**3 + z.
-2*f*(f - 23)*(f + 1)**2/19
Let c(o) be the second derivative of -1/7*o**7 + 42 + 11/5*o**5 - 19/3*o**3 + 11/15*o**6 - 2*o - 5*o**2 - o**4. What is f in c(f) = 0?
-1, -1/3, 1, 5
Factor s**2 + 123/4*s + 45/2.
(s + 30)*(4*s + 3)/4
Let 188/21*i**2 + 0 - 26/3*i**3 - 2/21*i**4 + 368/21*i = 0. Calculate i.
-92, -1, 0, 2
Let y(r) be the first derivative of 0*r**3 - 7/20*r**5 + 0*r - 13 - 1/10*r**6 - 5*r**2 + 1/4*r**4. Let c(a) be the second derivative of y(a). Factor c(t).
-3*t*(t + 2)*(4*t - 1)
Let x = 2341567/5612 - -10/1403. Let a = x + -417. Suppose -a*n**2 + 3/2*n - 5/4 = 0. What is n?
1, 5
Let q be ((-6)/(-63) - 8/(-42))/(68/28). Let y = -1/14 + 45/238. Factor -q*p**2 + 4/17 + y*p.
-2*(p - 2)*(p + 1)/17
Let m(l) be the first derivative of -3*l**4/8 - 160*l**3 - 957*l**2/4 + 1418. What is f in m(f) = 0?
-319, -1, 0
Let f(o) be the first derivative of -5*o**3/3 + 505*o**2/2 - 1940*o + 2021. Suppose f(r) = 0. Calculate r.
4, 97
Suppose 5481 = 31*i + 1331*i + 1223*i + 311. Suppose 32/7*v - 48/7*v**i + 2/7*v**5 - 16/7*v**3 + 96/7 + 6/7*v**4 = 0. What is v?
-3, -2, 2
Let i(u) = u**2 - 1523*u - 3048. Let w be i(-2). Let x = 8419/19 - 443. Factor 6/19*y**3 + 0*y**w - x*y**4 + 0 - 8/19*y.
-2*y*(y - 2)**2*(y + 1)/19
Let n(w) be the first derivative of -w**5/20 - 13*w**4/16 - 14*w**3/3 - 23*w**2/2 - 12*w + 871. Let n(h) = 0. What is h?
-6, -4, -2, -1
Let w(h) be the third derivative of -5/12*h**4 + 0*h - 1/30*h**5 - 156*h**2 + 0 + 0*h**3. Find x such that w(x) = 0.
-5, 0
Suppose 0 = 4*b - 310 - 426. Suppose -1 - x**4 + b*x - 184*x + 2*x**2 = 0. What is x?
-1, 1
Suppose -3*t = -p - 15, 4*p + 8 = 4*t - 12. Factor g**5 - 4*g**t - 65*g**2 + 71*g**2 - 4*g - 6*g**4 + 7*g.
-3*g*(g - 1)*(g + 1)**3
Suppose 4 = -k, -7*k = 4*g - 11*k - 24. Let j(z) be the first derivative of 5 - 12*z - 4/3*z**3 - 8*z**g. Let j(t) = 0. What is t?
-3, -1
Let r(v) = v**3 + 4*v**2 - v - 1. Let z(o) = 2*o**3 + 48*o**2 - 202*o + 2. Let h(c) = -2*r(c) - z(c). Factor h(t).
-4*t*(t - 3)*(t + 17)
Let l(a) = -a**2 + 13*a - 2. Let b be l(-14). Let y be 16/6*(-57)/b*5. Factor 2/3*v**5 + 0*v**y - 4/3*v**4 + 2/3*v**3 + 0*v + 0.
2*v**3*(v - 1)**2/3
Let r(n) = n - 2. Let c be r(2). Suppose -6*d + d + 0*d = c. Factor -5*v + d*v + 2*v - 3*v**2.
-3*v*(v + 1)
Let -9/2*f**4 - 3/4*f**5 + 0*f - 27/4*f**3 - 3*f**2 + 0 = 0. What is f?
-4, -1, 0
Let l(o) be the second derivative of 31/36*o**3 + 13/60*o**5 + 0 - 1/252*o**7 + 2/3*o**2 + 11/18*o**4 + 1/45*o**6 + 3*o. Factor l(v).
-(v - 8)*(v + 1)**4/6
Let i(c) be the third derivative of -c**5/300 - 92*c**4/15 - 49*c**3/2 - 626*c**2 + 2. Solve i(v) = 0 for v.
-735, -1
Let i(u) = 18*u**3 + 155*u**2 - 11*u. Let p(y) = -10*y**3 - 78*y**2 + 6*y. Let a(w) = 6*i(w) + 11*p(w). Determine l so that a(l) = 0.
0, 36
Let m(j) be the first derivative of -4*j**3/3 + 1236*j**2 - 381924*j - 82. Find f, given that m(f) = 0.
309
Let c(j) be the first derivative of j**7/1155 + j**6/220 + j**5/110 + j**4/132 + 9*j**2/2 - 2*j + 61. Let o(z) be the second derivative of c(z). Factor o(y).
2*y*(y + 1)**3/11
Let u(a) be the second derivative of 42*a + 0 - 1/4*a**3 - 33/160*a**5 + 0*a**2 + 15/32*a**4. Factor u(d).
-3*d*(d - 1)*(11*d - 4)/8
Let k(d) be the third derivative of -279/10*d**5 + 0 + 0*d + 48*d**2 + 1932*d**4 + 1/8*d**6 + 3136*d**3. Let k(o) = 0. What is o?
-2/5, 56
Let i(a) be the first derivative of 158 + 3/2*a**3 + 6/5*a**5 - 1/8*a**6 - 39/16*a**4 + 0*a**2 + 0*a. Solve i(p) = 0.
0, 1, 6
Let g(y) be the third derivative of 0*y**4 + 0*y**3 + 2/9*y**5 + 0 - 1/45*y**6 + 0*y + 97*y**2 + 1/1575*y**7. What is x in g(x) = 0?
0, 10
Let m(x) be the first derivative of -3*x**5/5 - 303*x**4/4 - 99*x**3 + 303*x**2/2 + 300*x + 1437. What is b in m(b) = 0?
-100, -1, 1
Let v = 31309/23 + -153716/115. Factor 126/5*t - 3/5*t**3 + 0 - v*t**2.
-3*t*(t - 1)*(t + 42)/5
Let f(y) be the third derivative of -y**5/135 - 7*y**4/18 + 12*y**3 + 585*y**2 + 2. Factor f(q).
-4*(q - 6)*(q + 27)/9
Suppose 0 = 55*v - 63*v - 3*j + 33, 11 = j. Let -15/2*m + v + 3/2*m**2 = 0. Calculate m.
0, 5
Let q(u) = u**3 - 18*u**2 + 21*u - 53. Let r be q(17). Factor 3*p**2 - 26 - 23 - r*p + 61.
3*(p - 4)*(p - 1)
Let u(p) be the second derivative of -p**5/5 + 19*p**4/6 + 13*p**3/6 + p - 57. Let h(l) = 2*l**3 - 20*l**2 - 6*l. Let x(d) = 13*h(d) + 6*u(d). Factor x(j).
2*j**2*(j - 16)
Let b be (-10706)/(-636) + -2 + -14. Let v(x) be the second derivative of -b*x**4 - 9/4*x**5 + 5*x**2 + 0 + 15/2*x**3 - 9*x. Find m such that v(m) = 0.
-1, -2/9, 1
Let d(p) = -27*p**3 - 6*p**2 + 162*p + 222. Let a(z) = 29*z**3 - 19*z**2 - 161*z - 221. Let s(c) = 3*a(c) + 4*d(c). Factor s(r).
-3*(r + 1)*(r + 5)*(7*r - 15)
Solve j - 55/6 + 1/6*j**2 = 0.
-11, 5
Let j = -35 - 7. Let l = -36 - j. What is p in -3*p**2 + 4*p - 8*p**3 + l*p**4 + 0*p**4 - p**2 + 2*p**2 = 0?
-2/3, 0, 1
Let f = -286 + 411. Let m = 125 - f. Factor -8/5*d**2 - 2/5*d**5 + m - 18/5*d**3 + 0*d - 12/5*d**4.
-2*d**2*(d + 1)**2*(d + 4)/5
Let m(k) be the third derivative of k**7/168 + 17*k**6/72 - 8*k**3 - 65*k**2. Let s(w) be the first derivative of m(w). Solve s(v) = 0.
-17, 0
Suppose -3*a - 3*k + 21 = 0, -2*a + 5*k = -0*k - 35. Suppose 4*u = -4*c + 4, -4*c + 3*u + a + 15 = 0. Factor 149*o**2 - 2 - 161*o**2 + 18 - c*o**3.
-4*(o - 1)*(o + 2)**2
Let o(q) be the second derivative of q**5/10 - 20*q**4/3 + 413*q**3/3 - 1274*q**2 + 1226*q + 1. Find n such that o(n) = 0.
7, 26
Factor -2*v**4 + 21336*v**3 - 10591*v**3 - 10661*v**3 + 1890*v**2 - 1972*v.
-2*v*(v - 58)*(v - 1)*(v + 17)
Suppose 90*w - 3060 = 54*w. Let o = w - 81. Find g such that -9/7 + 3/7*g**o - 12/7*g**3 + 12/7*g + 6/7*g**2 = 0.
-1, 1, 3
Let s(v) be the first derivative of -14/15*v**5 - 8/3*v**4 - 211 - 14/3*v**2 + 10*v**3 - 16/3*v. Determine d so that s(d) = 0.
-4, -2/7, 1
Let r = 196 - 183. Factor -33*b + 29*b**3 - b**3 - 28*b + r*b + 