t(u) be the third derivative of u**5/15 + 23*u**4/6 - 100*u**3/3 - 711*u**2. Suppose t(p) = 0. What is p?
-25, 2
Factor 2/7*c**3 + 0*c + 0 - 4/7*c**2.
2*c**2*(c - 2)/7
Find d such that 0 + 6/11*d**3 + 2/11*d + 6/11*d**2 + 2/11*d**4 = 0.
-1, 0
Let o be -508*(22/(-33))/(4/3). Let y = -251 + o. Factor -6/5*f**2 + 3/5*f + 3/5*f**y + 0.
3*f*(f - 1)**2/5
Let p(x) = -x**2 + 2. Suppose 0 = -2*f - t + 11, -6*t + 9 = -3*t. Let r(h) = 9*h**2 - 25*h + 12. Let d(l) = f*p(l) + r(l). Factor d(b).
5*(b - 4)*(b - 1)
Let y be (-80)/(-25) + -4 - 745/(-900). Let l(j) be the second derivative of -1/2*j**2 + 0 - 11*j - y*j**3 + 1/72*j**4. Factor l(r).
(r - 3)*(r + 2)/6
Factor 10*y**2 - 10*y**4 - 2*y**5 + 4*y + y - 6*y**5 + 3*y**5.
-5*y*(y - 1)*(y + 1)**3
Suppose 0 = 5*p - 2*z - 24, -2*p + 2 - 4 = 5*z. Factor 8*a + p*a**2 + 0*a**2 - 6*a**2.
-2*a*(a - 4)
Let b = 31 + 3. Factor 6*c**2 - b*c**4 + 40*c**4 + 0*c**2 + 15*c**3.
3*c**2*(c + 2)*(2*c + 1)
Suppose 2*x + 4*w = 12, -w = 5*x - 4 + 1. Factor x + 0*f + 2/13*f**2.
2*f**2/13
Suppose -3*h = -3485 + 929. Determine i, given that -852*i + 4*i**2 - 4*i**4 + h*i = 0.
-1, 0, 1
Let t(h) = -2*h - 1. Let w(y) = -30*y**2 - 387*y - 61. Let b(g) = 4*t(g) + w(g). Let b(f) = 0. Calculate f.
-13, -1/6
Suppose 0*z = -2*z. Let n be z*(-1 + 2)/(-1). Factor -18*d**2 - d - 13*d - 13*d + n*d**3 - 3*d**3.
-3*d*(d + 3)**2
Solve -3/4*s**4 - 13/4*s**3 + 5 + 7/4*s**2 + 1/4*s**5 + 9*s = 0.
-2, -1, 2, 5
Let g(k) be the second derivative of k**4/4 + 19*k**3 - 120*k**2 - 258*k. Factor g(l).
3*(l - 2)*(l + 40)
Let j(v) be the first derivative of -28 + 3*v**3 - 5/8*v**4 - 3*v**2 - 4*v. Factor j(x).
-(x - 2)**2*(5*x + 2)/2
Determine z so that 0*z - 3/2*z**3 + 15/2*z**2 + 0 = 0.
0, 5
Solve 0 + 9/4*b**5 + 0*b**4 - 25/4*b**3 - 5*b**2 - b = 0.
-1, -2/3, -1/3, 0, 2
Let g = -35 - -35. Factor h + 4*h + g*h - 3*h**2 - 11*h.
-3*h*(h + 2)
Let n = -10599/4 + 2650. Let q = -17/2 - -9. Solve -1/4*d**3 - n*d + 0 + q*d**2 = 0 for d.
0, 1
Find q such that -1/4*q**2 - 47/4 - 12*q = 0.
-47, -1
Let a = 42 - -15. Determine l, given that -4*l**2 + 42*l**4 - 6*l**2 - a*l**4 + 70*l**5 - 45*l**3 = 0.
-1/2, -2/7, 0, 1
Let y(o) = -2*o**3 + 14*o**2 + o + 11. Let k(c) = -c**3 + c**2. Let w(n) = -3*k(n) + y(n). Let v be w(-11). Factor 13*s**2 - 9*s**2 + v*s**2 - 4*s - 20*s**2.
-4*s*(4*s + 1)
Let x(q) be the second derivative of q**7/147 - q**6/35 + 3*q**5/70 - q**4/42 - 144*q. Solve x(n) = 0 for n.
0, 1
Let b(n) be the second derivative of -n**6/60 - n**5/20 + n**4/8 + 2*n**3/3 + n**2 + n + 113. Let b(p) = 0. What is p?
-2, -1, 2
Factor -24/5 + 4/5*z**2 - 4/5*z.
4*(z - 3)*(z + 2)/5
Suppose 3*n - 6 = a, 5*n - 311*a + 314*a + 18 = 0. Factor n - 1/2*k + 3*k**2 - 5/2*k**3.
-k*(k - 1)*(5*k - 1)/2
Let h(u) be the first derivative of -21 - 12/35*u**5 - 2/21*u**6 - 4/21*u**3 + 0*u**2 + 0*u - 3/7*u**4. Factor h(y).
-4*y**2*(y + 1)**3/7
Let s be ((-58)/8)/((-2)/8). Let s*j**4 - j**5 - 8*j**3 + 4*j**2 - 55*j**4 + 31*j**4 = 0. What is j?
0, 1, 2
Suppose 0 = -33*w + 188 - 188. Solve -2/3*x + x**2 - 1/3*x**4 + w + 0*x**3 = 0.
-2, 0, 1
Let u be (-3)/(42/4) - (148/(-28) + 3). Factor -2/11*p**u - 6/11 - 8/11*p.
-2*(p + 1)*(p + 3)/11
Let d(m) be the second derivative of m**6/135 + 4*m**5/45 + 91*m - 1. Determine q, given that d(q) = 0.
-8, 0
Let v(i) = -2*i**3 - 1037*i**2 - 181663*i - 10536048. Let g(m) = m**3 + 518*m**2 + 90832*m + 5268024. Let s(x) = -7*g(x) - 4*v(x). Find t such that s(t) = 0.
-174
Let f(g) be the second derivative of g**7/1260 + g**6/180 + g**5/60 + g**4/12 - 17*g. Let z(k) be the third derivative of f(k). Find s such that z(s) = 0.
-1
Let x be (31/4216)/(4/64). Find h, given that -x*h**3 + 0*h**2 + 4/17 + 6/17*h = 0.
-1, 2
Let q = -1/1245 + 1253/9960. Factor 1/4*b**2 + 0 - 1/8*b**4 - q*b**3 + 0*b.
-b**2*(b - 1)*(b + 2)/8
Let a(b) be the third derivative of -b**6/32 + 3*b**5/80 + 96*b**2. Factor a(t).
-3*t**2*(5*t - 3)/4
Suppose 3*k = r + 97, -3*k + 2*r = 2*k - 162. Suppose 15*h**3 - 37 + 1 - 24*h - 2*h**3 + 11*h**3 + 4*h**4 + k*h**2 = 0. What is h?
-3, -1, 1
Let q = -1279 + 1281. Suppose 1/6*b**3 + 0 + 1/2*b**q + 1/3*b = 0. Calculate b.
-2, -1, 0
Let s(n) be the first derivative of -2*n**3/39 + 3*n**2/13 - 4*n/13 + 379. Let s(x) = 0. Calculate x.
1, 2
Let g be -3 + 3/(3/5). Suppose -3*o = 4*r + g - 1, 0 = -5*r - o + 7. Suppose -3*z**2 + 8*z + 2*z + z**r - z**3 - 11*z = 0. What is z?
-1, 0
Let t(x) = -x**2 - x + 1. Let r(f) = -2*f**2 + 6*f + 21. Let z(l) = 2*r(l) - 6*t(l). Factor z(w).
2*(w + 3)*(w + 6)
Let p(k) be the second derivative of -k**4/3 + 20*k**3 - 450*k**2 + 350*k. Factor p(n).
-4*(n - 15)**2
Let b(f) be the first derivative of 1/4*f**3 - 1/16*f**4 - 1/24*f**6 - 18 + 1/4*f**2 + 0*f - 3/20*f**5. Find p such that b(p) = 0.
-2, -1, 0, 1
Find o such that 0*o + 0*o**3 + 0 + 1/6*o**4 - 1/6*o**2 = 0.
-1, 0, 1
Suppose 0 = 2*d + r - 9, 2*d + 3*r - 11 = -0*d. Solve -d*x**3 - 4*x**2 + 2*x - 5*x + 5*x + 4*x**4 + 2*x = 0.
-1, 0, 1
Let f(x) be the second derivative of -x**7/3780 - x**6/540 - x**5/180 + 5*x**4/12 + 10*x. Let w(n) be the third derivative of f(n). Let w(d) = 0. What is d?
-1
Let x(d) be the third derivative of -d**6/120 + d**5/60 + 5*d**4/12 + 4*d**3/3 - 38*d**2. Factor x(y).
-(y - 4)*(y + 1)*(y + 2)
Let u(g) be the first derivative of -16 + 1/4*g**3 + 5/8*g**2 + 1/2*g - 1/16*g**4 - 1/20*g**5. Factor u(x).
-(x - 2)*(x + 1)**3/4
Suppose 10*h - 3*h - 17 - 18 = 0. Factor 0*y + 0*y**2 - 2/9*y**h + 0 - 2/3*y**4 - 4/9*y**3.
-2*y**3*(y + 1)*(y + 2)/9
Let s(b) = -b**2 - 10*b + 14. Let u be s(-11). Suppose 4*r - v = 29, -u*r - 2*v = -0 - 8. Find w, given that w**2 + 12*w**3 + r*w**3 - 19*w**3 = 0.
0, 1
Let s(x) = -36*x**5 + 13*x**4 + 229*x**3 - 388*x**2 + 85*x + 75. Let o(k) = -2*k**5 - k**4 + k**3 - k + 1. Let v(r) = 22*o(r) - 2*s(r). Solve v(z) = 0.
-4, -2/7, 1, 4
Let w(u) be the second derivative of -3/35*u**5 + 55*u - 1/28*u**4 + 0 + 0*u**3 + 0*u**2 - 2/35*u**6. Factor w(i).
-3*i**2*(2*i + 1)**2/7
Let l = -14 - -18. Suppose -3*p = 0, 7*z + 5*p = l*z + 9. Determine u so that -1/6*u**2 + 0*u + 0 + 1/6*u**z = 0.
0, 1
Let z be 15/(-40) + 357/56. Let w(c) be the third derivative of -5*c**2 + 0*c + 1/6*c**4 + 0 + 0*c**3 + 1/60*c**z + 11/90*c**5. Suppose w(q) = 0. Calculate q.
-3, -2/3, 0
Let v(j) be the first derivative of 4*j - 3*j**2 - 11 - 1/16*j**4 + 3/4*j**3. Find g such that v(g) = 0.
1, 4
Let u(p) be the second derivative of p**6/30 + p**5/10 - 54*p - 2. Solve u(h) = 0 for h.
-2, 0
Suppose n - 4*n + 74 = 4*q, -3*n + q + 49 = 0. Let z be (4/(-6))/((-4)/n). Solve -t**5 + t**3 + 29*t - 28*t - z*t**3 + 2*t**5 = 0 for t.
-1, 0, 1
Let f(j) be the third derivative of -j**7/42 + j**5/3 - 49*j**2. Suppose f(p) = 0. What is p?
-2, 0, 2
Let a be (2/(-14))/((-32)/112)*6. Let v(z) be the second derivative of 1/5*z**2 - 4*z + 7/30*z**a + 1/20*z**4 + 0. Factor v(p).
(p + 2)*(3*p + 1)/5
Let i be -9*(2 + -3*1). Let d = -20 + 28. Factor 3*w**5 - 3*w**2 + w**2 + d*w**2 - i*w**3.
3*w**2*(w - 1)**2*(w + 2)
Let q be (-120)/54 + 10/45. Let r be q*(-9)/(-12)*(4 - 6). Suppose -3/4 - 3/2*c**2 + 15/8*c + 3/8*c**r = 0. What is c?
1, 2
Determine m, given that 48/7*m**3 + 2/7*m**5 + 0 + 0*m - 54/7*m**4 + 104/7*m**2 = 0.
-1, 0, 2, 26
Let g be 2*1*6/(-30)*-10. Suppose -16*w + 4 = g. Factor 1/4*a + w + 3/4*a**2 + 3/4*a**3 + 1/4*a**4.
a*(a + 1)**3/4
Let w(z) be the third derivative of -z**5/12 + 65*z**4/3 - 6760*z**3/3 - 162*z**2. Factor w(j).
-5*(j - 52)**2
Let r be ((-324)/(-270))/(4/10). Let f(m) be the first derivative of 8 + 1/2*m**4 - m**2 + 0*m**r + 0*m. Let f(t) = 0. What is t?
-1, 0, 1
Let w(l) be the second derivative of 0 + 25/6*l**3 - 5*l**2 - 15/8*l**4 - 1/24*l**6 + 7/16*l**5 - 9*l. Let w(p) = 0. Calculate p.
1, 2
Let u(d) be the first derivative of -7 - 5*d + 1/18*d**3 + 1/12*d**2 + 1/72*d**4. Let b(t) be the first derivative of u(t). Solve b(r) = 0 for r.
-1
Factor -3/2*r**3 + 3/4*r**2 + 3 - 1/4*r**4 + 5*r.
-(r - 2)*(r + 1)**2*(r + 6)/4
Let o(b) be the second derivative of -b**5/70 - 3*b**4/14 - 23*b**3/21 - 15*b**2/7 + 6*b - 18. Factor o(p).
-2*(p + 1)*(p + 3)*(p + 5)/7
Let m be 7 - 2 - (0 - -2). Let -64*x**2 - 133 - 12*x**3 - 44*x**m - 24*x**4 - 4*x**5 + 125 - 36*x = 0. What is x?
-2, -1
Let s(t) be the second derivative of -t**6/30 + t**5/5 + 5*t**4/12 - t + 100. Find u such tha