**2/6
Let q(m) be the second derivative of m**5/15 + 13*m**4/9 - 2704*m**3/9 - 17576*m**2 + m + 3171. Factor q(n).
4*(n - 39)*(n + 26)**2/3
Find x such that 212*x**2 + 167*x + 13*x - 784 + 588*x - 1771*x**4 + 1767*x**4 - 192*x**3 = 0.
-49, -2, 1, 2
Let 39 + 28*j + 73*j**2 + 21 - 74*j**2 = 0. What is j?
-2, 30
Let u(f) be the second derivative of f**4/32 - 37*f**3/16 + 405*f**2/8 + 1492*f. Factor u(n).
3*(n - 27)*(n - 10)/8
Let w(l) be the first derivative of 9*l**4/4 - 74*l**3 - 831*l**2/2 - 252*l + 5356. Suppose w(j) = 0. What is j?
-3, -1/3, 28
Let y(k) be the first derivative of 1/7*k**4 + 2 - 2/35*k**5 + 0*k + 2/21*k**3 - 2/7*k**2. Suppose y(b) = 0. Calculate b.
-1, 0, 1, 2
Determine c so that -26/15*c**2 - 298/15*c + 108/5 = 0.
-162/13, 1
Let y(a) = -37*a - 46*a + a**3 - 2 + 84*a + a**2. Let m(k) = -9*k**3 + 61*k**2 - 54*k - 112. Let i(g) = m(g) + 4*y(g). Determine x, given that i(x) = 0.
-1, 2, 12
Let z(v) be the third derivative of v**8/2520 + 31*v**7/1260 - 8*v**6/135 - 41*v**3/2 - 2*v**2 - 21*v. Let g(d) be the first derivative of z(d). Factor g(a).
2*a**2*(a - 1)*(a + 32)/3
Let z(q) = 2*q**2 + 1078*q - 22357. Let n be z(20). Determine t, given that 8/5 - 2/15*t**2 + 2/15*t**n - 16/15*t = 0.
-3, 2
Let d(i) be the second derivative of 0 - 1/4*i**4 + 1/6*i**3 - 1/2*i**2 - 10*i. Let w(r) = -1. Let q(u) = d(u) - 3*w(u). Factor q(c).
-(c - 1)*(3*c + 2)
Suppose 417*x = 427*x - 30. Let l(h) be the first derivative of 0*h + 0*h**2 - 25/8*h**x + 15/16*h**4 - 3/40*h**5 + 10. Suppose l(q) = 0. What is q?
0, 5
Let g(p) be the third derivative of -p**7/2520 - p**6/360 + p**5/5 + 43*p**4/4 + 122*p**2. Let y(m) be the second derivative of g(m). Find z such that y(z) = 0.
-6, 4
Let p(z) = -z**3 + 29*z**2 - 34*z + 200. Let u be p(28). Suppose j = l - 29 + u, 9 = -j - 3*l. Solve 2/7*a**4 + j + 0*a + 0*a**3 - 2/7*a**2 = 0 for a.
-1, 0, 1
Let t(b) be the second derivative of -b**5/5 + 7*b**4/3 + 418*b**3/3 - 3630*b**2 - 3930*b. What is o in t(o) = 0?
-15, 11
Let n(k) be the third derivative of 1/420*k**7 + 10 - 11/120*k**5 - 1/16*k**4 + 1/80*k**6 + 0*k + 5/6*k**3 + 6*k**2. Find x such that n(x) = 0.
-5, -1, 1, 2
Let f(z) = -245*z**4 - 620*z**3 - 755*z**2 + 55. Let l(w) = w**4 + 8*w**4 + 27*w**3 - 4*w**3 + 28*w**2 - 2 + 0. Let a(y) = -2*f(y) - 55*l(y). Factor a(j).
-5*j**2*(j + 2)*(j + 3)
Let u(y) be the second derivative of y**7/21 + y**6/15 - 9*y**5/10 - 5*y**4/6 + 16*y**3/3 + 12*y**2 - 834*y. Solve u(q) = 0.
-3, -1, 2
Factor -18221/2*g + 17689 - 1/2*g**3 + 134*g**2.
-(g - 133)**2*(g - 2)/2
Let c = 1443/1372 - -68/343. Suppose -1/4*d**2 - 3/4 + 1/4*d**3 - c*d = 0. What is d?
-1, 3
Let q(n) be the first derivative of 98*n**5/25 + 91*n**4/2 - 592*n**3/5 + 396*n**2/5 + 473. Factor q(b).
2*b*(b + 11)*(7*b - 6)**2/5
Factor -1632*u**2 - 533*u**2 - 5*u - 14*u**3 + 19*u**3 + 2165.
5*(u - 433)*(u - 1)*(u + 1)
Suppose 16 + 9 = t - 5*m, 4*m + 20 = -2*t. Factor t*d**3 - 9*d - 6*d**3 + 19*d**3 + 30*d**2 - 40 - 12*d**4 + 13*d**4 + 5*d.
(d - 1)*(d + 2)**2*(d + 10)
Let y(g) be the first derivative of -12*g**5/5 + 821*g**4/3 - 3968*g**3/9 + 120*g**2 + 3056. What is f in y(f) = 0?
0, 2/9, 1, 90
Let a be (-13)/(-2)*252/819. Let l(p) be the second derivative of 0*p**a - 12*p + 0 + 0*p**3 + 1/24*p**4 + 1/80*p**5. Suppose l(d) = 0. What is d?
-2, 0
Let q(r) = 12*r + 734. Suppose 4*v = 4*s + 292 - 60, -v + 180 = -3*s. Let b be q(s). Factor 15/7*p + p**b + 1/7*p**3 + 9/7.
(p + 1)*(p + 3)**2/7
Let i(s) = 7*s**3 + 12*s**2 - 27*s + 3. Let l(u) = 7*u**3 + 19*u**2 - 28*u + 2. Let b(x) = -6*i(x) + 5*l(x). Factor b(w).
-(w - 4)*(w + 1)*(7*w - 2)
Let 2/5*t**2 - 76/5*t + 138 = 0. What is t?
15, 23
Let r(b) = b**3 - 17*b**2 - 24*b + 115. Let g be r(18). Let n = 49 - 29. Factor 5*o**3 + g*o - 4*o - 3*o - n*o**2.
5*o**2*(o - 4)
Let k(j) be the second derivative of -j**6/135 + j**5/30 + 5*j**4/54 - j**3/9 - 4*j**2/9 + 588*j. What is t in k(t) = 0?
-1, 1, 4
Let v(d) be the third derivative of d**5/180 - 53*d**4/8 + 4040*d**2. Let v(q) = 0. Calculate q.
0, 477
Let x(w) be the third derivative of w**7/70 + 93*w**6/20 - 113*w**2 + 2*w. Factor x(c).
3*c**3*(c + 186)
Let q(p) = 13*p - 61. Let b be q(5). Find t such that 2*t**5 + 8*t**b + 0*t**5 - 10*t**2 - 30*t**3 + 40*t - 4*t**4 + 18*t**2 = 0.
-5, -1, 0, 2
Let p(c) be the second derivative of c**7/6 - 358*c**6/15 + 18411*c**5/20 - 867*c**4/2 + 8621*c. Solve p(s) = 0 for s.
0, 2/7, 51
Let t(r) be the second derivative of r**7/294 - 17*r**6/210 - 19*r**5/70 + r - 453. Let t(c) = 0. Calculate c.
-2, 0, 19
Let g(d) be the first derivative of 1/10*d**4 - 4/5*d - 1/5*d**2 - 36 + 4/15*d**3. Let g(q) = 0. What is q?
-2, -1, 1
Let w(b) = 2*b**3 - b**2 + 2*b + 15. Let a be w(0). Solve -114*u - 112*u + 5*u**3 - 10*u**5 + 231*u + a*u**4 - 15*u**2 = 0.
-1, 0, 1/2, 1
Let m = 2633 - 2629. Let b(g) be the first derivative of g + 15 - 1/8*g**m + 3/4*g**2 + 0*g**3. Factor b(c).
-(c - 2)*(c + 1)**2/2
Suppose k = -4*y + 94, 0 = -3257*k + 3261*k - 4*y - 56. Let -k*c - 22/3 - 8/3*c**2 = 0. What is c?
-11, -1/4
Suppose d - 364 = -0*d. Let k = d + -362. Factor 1/7*v - 1/7*v**k + 0.
-v*(v - 1)/7
Let 100*r**4 + 609*r - 565*r + 9*r**3 - 272*r**4 + 45*r**5 + 294*r**2 - 24 = 0. Calculate r.
-1, -2/5, 2/9, 2, 3
Suppose 22 - 19 = -3*k - o, 0 = -5*o. Let v be k*(-6)/((-175)/(-10) + 2). Find r, given that 2/13 - 24/13*r**3 + 18/13*r**4 + 8/13*r - v*r**2 = 0.
-1/3, 1
Let n be (57 + -54)*((-2)/(-6) + 4/3). Suppose -1/2*f**n - 5/2*f**3 + 0*f + 0*f**2 + 0 + 3*f**4 = 0. What is f?
0, 1, 5
Suppose 2*n - 2*r - 602 = 0, 0*n + 4*r + 286 = n. Let w = -306 + n. Factor 10/7*q**2 + w - 8/7*q**3 - 2/7*q.
-2*q*(q - 1)*(4*q - 1)/7
Let v(x) be the third derivative of x**6/240 + 7*x**5/30 + 2*x**4 - 6*x**2 - 11. Factor v(g).
g*(g + 4)*(g + 24)/2
Let j be (56/(-280))/(2/(-8)). Factor j*b**2 - 2*b**3 + 0*b + 0.
-2*b**2*(5*b - 2)/5
Let q be ((-288)/(-20))/6 + (-294)/735. Determine c, given that 510/7*c**q - 48/7*c**4 + 24/7 - 34*c**3 + 32/7*c**5 - 208/7*c = 0.
-3, 1/4, 2
Solve -72*o**3 + 212/3*o**2 + 0 - 70/3*o - 2/3*o**5 + 76/3*o**4 = 0 for o.
0, 1, 35
Factor -37*u**3 - 56*u + 116*u**3 - 36*u**3 - 20*u**2 - 39*u**3.
4*u*(u - 7)*(u + 2)
Let o be 24 + (20 - 252/(-28)) + -51. Factor -9*s - 54/7 - 3/7*s**3 - 24/7*s**o.
-3*(s + 2)*(s + 3)**2/7
Let c = 463857/7 + -66264. Find g such that 3/7*g**3 - 12/7*g - c*g**2 + 36/7 = 0.
-2, 2, 3
Suppose 48*b - 145*b = 121*b - 872. Let k(p) be the second derivative of 0 + 1/18*p**3 - 1/36*p**b + 22*p + 1/3*p**2. Suppose k(o) = 0. What is o?
-1, 2
Let g = 269839/59367 + 1/5397. Let j = 421/231 - 1/231. What is y in -2/11*y**2 - g + j*y = 0?
5
Suppose -408*u + 9130 = 7*u. Factor -u*s - 16/3*s**2 + 2*s**3 - 20/3.
2*(s - 5)*(s + 2)*(3*s + 1)/3
Let x be 14/378 - (-2230)/5400. Let k(a) be the first derivative of -6*a**2 + 4*a + 14/3*a**3 - 1/24*a**6 - 2*a**4 + x*a**5 + 18. Let k(u) = 0. Calculate u.
1, 2
Let t(g) be the second derivative of 47 - 216*g**2 - 3/8*g**6 - 145/4*g**4 - 45/8*g**5 - 120*g**3 - 1/112*g**7 - g. Factor t(w).
-3*(w + 2)**3*(w + 12)**2/8
Find c, given that -2*c**2 - 41274*c + 41138*c - 98 - 36 = 0.
-67, -1
Let g = -151 + 153. Suppose -3*b - 9*l = -7*l - 8, -b - 3*l = 2. Factor 0*p + 3/7*p**g + 0 + 2/7*p**3 - 1/7*p**b.
-p**2*(p - 3)*(p + 1)/7
Let u(m) be the third derivative of -1/540*m**6 - 14*m**2 - 2/945*m**7 + 0 + 0*m**4 + 1/135*m**5 + 0*m**3 + 1/1512*m**8 + 3*m. Solve u(o) = 0.
-1, 0, 1, 2
Suppose -4*p - 12 = -2*f - 4, -20 = -5*f. Let c(y) be the third derivative of -7/150*y**5 + 0*y + 0*y**3 + p + 7*y**2 - 1/300*y**6 + 0*y**4. Factor c(q).
-2*q**2*(q + 7)/5
Let w(o) be the first derivative of -o**4/42 + 11*o**3/21 + 84*o - 60. Let k(y) be the first derivative of w(y). Factor k(g).
-2*g*(g - 11)/7
Find s, given that -144 - 169*s**3 + 9*s**4 + 3*s**5 + 445*s**3 - 336*s**3 + 192*s = 0.
-6, -2, 1, 2
Suppose 0 = 2*m, 20 = x - 3*m + 4*m. Suppose -3*a = -3, -5*a + 2*a + x = n. Factor -15*v - 5*v**2 + 7 - n + 0.
-5*(v + 1)*(v + 2)
Suppose -40/3*x**3 - 16/3*x**4 + 0*x**2 + 0*x + 0 + 2/3*x**5 = 0. Calculate x.
-2, 0, 10
Suppose 12*a - 420 = -9*a. Determine g so that -38*g**3 - a + 24 + 30*g**3 + 28 - 2*g**4 + 32*g = 0.
-2, 2
Let b(a) be the second derivative of 0 - 1/16*a**4 + 26*a - 243/2*a**2 - 9/2*a**3. Factor b(p).
-3*(p + 18)**2/4
Let h(w) be t