
2*i**2*(i + 1)*(i + 4)/7
Let c(q) be the second derivative of -3*q**5/20 + 821*q**4/4 - 84460*q**3 + 252150*q**2 + 13754*q. Find b, given that c(b) = 0.
1, 410
Let c(z) be the third derivative of 0*z + 5/18*z**4 - 2/3*z**3 - 40*z**2 + 0 - 1/90*z**6 - 1/45*z**5. Factor c(x).
-4*(x - 1)**2*(x + 3)/3
Let d(v) be the third derivative of -v**6/220 + 13*v**5/22 - 43*v**4/44 - 38829*v**3/11 - 87*v**2 - 22*v + 1. Suppose d(p) = 0. Calculate p.
-21, 43
Let r be (-18)/477 + 2670/530. Let q(m) be the third derivative of -1/12*m**4 + 0*m + 19*m**2 + 1/60*m**6 + 1/45*m**r - 2/9*m**3 + 0. Let q(u) = 0. What is u?
-1, -2/3, 1
Let n(q) be the third derivative of -q**7/210 + q**6/15 + 2*q**5/5 - 4*q**4/3 - 40*q**3/3 - 2*q**2 - 1153. Determine b so that n(b) = 0.
-2, 2, 10
Let i = 7627/143 - 1/429. Let h = i - 656/15. Suppose 2/5*w**3 - 32/5 + h*w - 18/5*w**2 = 0. What is w?
1, 4
Let p(f) = -205*f**3 - 13735*f**2 - 106030*f - 490. Let t(a) = 5*a**3 + 335*a**2 + 2586*a + 12. Let g(b) = -6*p(b) - 245*t(b). Determine m, given that g(m) = 0.
-58, -9, 0
Let j(v) = v**3 + 4*v**2 + 5*v + 7. Let x be j(-3). Suppose 0 = 8*l - x - 15. Suppose -21*m**l + 2*m - 4 + 20*m**2 - 7*m + m = 0. Calculate m.
-2
Let x be ((-4)/(-10))/(16/200). Suppose 3*z = 9, x*y - 3*z + 4 = 5. Factor 44*v - v**y - 64*v + 25 - 4*v**2.
-5*(v - 1)*(v + 5)
Let -4444 - 3419*o + 65*o**2 - 1027*o - 67*o**2 = 0. What is o?
-2222, -1
Let 6236 - 133*x**3 + 13410*x - 273*x**2 - 7*x**4 - 66*x**2 + 1706 + 12*x**4 + 6331*x = 0. What is x?
-11, -2/5, 19
Let f(n) = -125*n**3 - 32*n**2 + 8*n + 5. Let u = -201 - -196. Let k(w) = 376*w**3 + 96*w**2 - 24*w - 14. Let v(s) = u*k(s) - 14*f(s). Factor v(j).
-2*j*(5*j + 2)*(13*j - 2)
Let r(p) be the first derivative of -18*p**3 + 1/2*p**4 + 0*p - 113 - 28*p**2. Factor r(y).
2*y*(y - 28)*(y + 1)
Let y(w) be the third derivative of 17/6*w**4 + 6*w**3 + 7/15*w**5 - 81*w**2 - 1/30*w**6 + 0*w + 0. Determine a, given that y(a) = 0.
-1, 9
Let v be -1*13/195*0*-1. Solve 4/3*t**5 + 4*t**4 + 8/3*t**3 + 0*t**2 + v*t + 0 = 0.
-2, -1, 0
Factor -19*g - 43 + 3 - 4645*g**3 + 4650*g**3 - g + 30*g**2 + 182*g**4 - 187*g**4.
-5*(g - 2)**2*(g + 1)*(g + 2)
Let j = 1017 + -1014. Suppose -2*u - j*p + 11 = 0, -5*p + 7*p = 5*u - 37. Factor -u*g**3 + 0 + 8/3*g**2 + 4/3*g.
-g*(3*g - 2)*(7*g + 2)/3
Let o(r) be the second derivative of -r**5/4 - 65*r**4/12 - 25*r**3 - 916*r + 2. Factor o(t).
-5*t*(t + 3)*(t + 10)
Suppose i + 72 = 5*m, 7*i - 248 = 10*i + m. Let o = 84 + i. Factor 1/3*x**5 - 2/3*x**o + 0*x**3 + 2/3*x**4 - 1/3*x + 0.
x*(x - 1)*(x + 1)**3/3
Suppose 49*m + 9 = 56 + 100. Determine r so that 1/10*r**m + 1/10*r + 0 - 1/5*r**2 = 0.
0, 1
Let v(m) be the first derivative of 2*m**3/21 - m**2 - 60*m/7 - 1681. Determine t, given that v(t) = 0.
-3, 10
Let h(f) be the first derivative of -f**5/5 + 43*f**4/10 + 56*f**3/5 + 29*f**2/5 - 19*f/5 - 846. Solve h(n) = 0.
-1, 1/5, 19
Let x(b) = -12*b**4 - 15*b**3 - 15*b**2 + 6*b + 42. Let f(i) = -13*i**4 - 16*i**3 - 13*i**2 + 5*i + 35. Let k(q) = 6*f(q) - 5*x(q). Factor k(l).
-3*l**2*(l + 1)*(6*l + 1)
Let x(q) be the first derivative of 2/5*q**2 + 40*q + 25 + 1/30*q**4 - 1/5*q**3. Let k(z) be the first derivative of x(z). Determine m, given that k(m) = 0.
1, 2
Let r(v) be the second derivative of -v**5/20 + 85*v**4/4 - 825*v**3/2 + 6125*v**2/2 + 6481*v. Factor r(y).
-(y - 245)*(y - 5)**2
Let q(n) be the third derivative of n**7/16380 + n**6/390 + 5*n**4/24 + 35*n**3/6 - 78*n**2. Let k(s) be the second derivative of q(s). Solve k(z) = 0.
-12, 0
Let f = 615 - 597. Let w be 0/(((-16)/36)/(f/(-81))). Factor 6/5*s**2 + w - 2/5*s**3 + 0*s.
-2*s**2*(s - 3)/5
Suppose 3*k = 3*m - 18, -12*m + 10*m + 5*k = -12. Let 33*d + 62*d**2 - 20*d**2 - 234 + 198 - 36*d**3 + 3*d**5 - m*d**4 = 0. What is d?
-3, -1, 1, 4
Suppose -4*b + 1/6*b**3 + 1/6*b**4 + 0 - 7/3*b**2 = 0. Calculate b.
-3, -2, 0, 4
Let f(p) be the third derivative of p**5/30 - 211*p**4/12 - 212*p**3/3 + 4*p**2 + 120. Let f(u) = 0. What is u?
-1, 212
Let s(g) be the second derivative of 169*g**5 + 1768*g**4/3 + 526*g**3/5 + 36*g**2/5 + 2763*g. Find x, given that s(x) = 0.
-2, -3/65
Let x(c) be the third derivative of -c**7/315 - 23*c**6/45 - 746*c**5/45 + 2392*c**4/3 - 10816*c**3 - 197*c**2 - 3. Factor x(a).
-2*(a - 6)**2*(a + 52)**2/3
Suppose 1194*r = 1235*r. Let d(s) be the second derivative of -9/13*s**2 + 2/13*s**3 - 1/78*s**4 - 11*s + r. Factor d(l).
-2*(l - 3)**2/13
Let h be (-33)/(-6) + 4 + (-3)/2. Suppose 0 = l - 3*n + 9, 5*l - 35 = 3*n - h*n. Factor 95 + 30*k**2 + 5*k**4 + 246*k - 46*k + 30 + 12*k**3 - 52*k**l.
5*(k - 5)**2*(k + 1)**2
Let q(i) = -i**3 + 9*i**2 + i - 6. Let u be (54/(-45))/((-4)/30). Let g be q(u). Factor 3*d**3 - 19*d**2 + 2*d**g - 6*d**2.
5*d**2*(d - 5)
Let z = 16699/5 + -16687/5. Suppose 0*h - 4*h + 8 = 0. Factor -z*d + 8/5 + 0*d**h + 4/5*d**3.
4*(d - 1)**2*(d + 2)/5
Determine o so that 2*o - 259203*o**2 + 4*o - 260 + 259205*o**2 = 0.
-13, 10
Let z(w) be the second derivative of -w**4/72 - 77*w**3/36 - 713*w**2/6 - 13849*w. Solve z(y) = 0.
-46, -31
Let t(u) be the third derivative of -230*u**2 - 121/20*u**5 + 0*u**3 + 0*u - 11/60*u**6 - 1/630*u**7 + 0 + 0*u**4. Factor t(i).
-i**2*(i + 33)**2/3
Let w = 526 - 486. Suppose -w - 11*l**2 + 8*l**2 + l**2 - 34*l - 44 = 0. What is l?
-14, -3
Suppose 0 = 133*s - 127*s + 714. Let g be (-14)/(-20)*(-68)/s. Determine l, given that 27/5*l**5 - g*l - 3*l**4 + 0 - 5*l**3 + 3*l**2 = 0.
-1, 0, 2/9, 1/3, 1
Let d(m) be the second derivative of -m**9/1008 - m**8/140 + m**7/56 + 43*m**3/6 + m**2/2 + 6*m. Let n(o) be the second derivative of d(o). Factor n(a).
-3*a**3*(a - 1)*(a + 5)
Let i = 304478 - 304478. Solve -2*s**3 + 0*s + 0 + 1/3*s**5 - 1/3*s**4 + i*s**2 = 0 for s.
-2, 0, 3
Factor 2406*c**2 - 5215*c**2 - 5*c**3 + 2619*c**2.
-5*c**2*(c + 38)
Let n = 5/101 - -187/303. Let t(y) = 125*y + 250. Let m be t(-2). Determine b, given that 0 - n*b**3 + 0*b**2 + m*b = 0.
0
Let n(d) be the third derivative of d**8/112 + d**7/35 - 3*d**6/40 - 3*d**2 + 201*d + 2. Factor n(h).
3*h**3*(h - 1)*(h + 3)
Let d(b) be the second derivative of -b**6/180 - 13*b**5/120 - b**4/6 + 5*b**3 - 7089*b. Let d(a) = 0. What is a?
-10, -6, 0, 3
Let l(h) be the first derivative of -2*h**5/75 + 5*h**4/6 - 284*h**3/45 + 20*h**2 - 144*h/5 - 3848. Solve l(m) = 0.
2, 3, 18
Let i(f) be the first derivative of -f**5/20 + 5*f**4/6 - 25*f**3/6 + 111*f - 175. Let k(v) be the first derivative of i(v). Find w such that k(w) = 0.
0, 5
Suppose 1017*u + 1097*u = 2196*u - 235 - 11. Factor h**2 + 49/4*h + u.
(h + 12)*(4*h + 1)/4
Let i(d) be the first derivative of -13*d**5 - 5/2*d**6 + 20*d**2 + 20/3*d**3 + 58 + 0*d - 35/2*d**4. Suppose i(n) = 0. Calculate n.
-2, -1, 0, 2/3
Suppose -8*o + 9*o - 735 = 0. Determine i so that 0*i + 273*i**4 + 25*i**3 + 0*i - 12*i**2 - i**3 - o*i**5 = 0.
-1/5, 0, 2/7
Suppose -168*i + 410 = 74. Let y(r) be the first derivative of -35/4*r**i - 25/6*r**3 - 10 - 5*r. Factor y(t).
-5*(t + 1)*(5*t + 2)/2
Solve -4/5*s**2 - 352/5*s - 7744/5 = 0.
-44
Let h = 521688 + -521688. Factor 2/9*s + 1/9*s**2 - 1/9*s**3 + h.
-s*(s - 2)*(s + 1)/9
Let w(i) be the third derivative of -i**6/300 - i**5/150 + i**4/60 + i**3/15 + 49*i**2 + 2. Factor w(y).
-2*(y - 1)*(y + 1)**2/5
Let z = 34658 + -174914/5. Let i = 325 + z. Factor 2/5*d - 1/5*d**4 + 0*d**2 + i - 2/5*d**3.
-(d - 1)*(d + 1)**3/5
Suppose -13*v = -15*v - 3*z - 8, -8 = 4*v + 4*z. Let b(a) be the second derivative of -3/140*a**5 + 0*a**v - 1/14*a**4 + 0 + 17*a + 0*a**3. Factor b(c).
-3*c**2*(c + 2)/7
Let w(r) be the second derivative of -r**4/18 - 110*r**3/9 + 37*r**2 - 3*r + 40. Suppose w(a) = 0. What is a?
-111, 1
Let s be (14/1 - -4)/(-3 - -4). Let t be ((90/120)/(s/20))/5. Suppose o**2 + 2*o + t*o**3 + 4/3 = 0. What is o?
-2
Let w be (494/104)/((-1)/48*-152). Factor -9 + 33/2*v - w*v**3 - 6*v**2.
-3*(v - 1)**2*(v + 6)/2
Let s(l) = l**2 + 4890*l + 92549. Let v be s(-19). Factor -2/11*c**2 - 58/11*c + v.
-2*c*(c + 29)/11
Let x(w) be the first derivative of w**5/270 - w**4/18 - 7*w**3/27 - 35*w**2/2 - w + 17. Let g(s) be the second derivative of x(s). Factor g(d).
2*(d - 7)*(d + 1)/9
Let s = 4966 + -4964. Let h(q) be the second derivative of -q**3 + 7*q + 0 - 3/2*q**s - 1/4*q**4. Factor h(x).
-3*(x + 1)**2
Suppose -2*q - q = -2*p - 14