et -18*h**2 + 25/2*h**5 - 4*h + 0 + 45/2*h**4 - r*h**3 = 0. Calculate h.
-2, -2/5, 0, 1
Suppose 81 - 25 = -2*m - 4*x, 4*m = -2*x - 82. Let t be ((-12)/(-9))/((-12)/m). Find a such that -1/8*a**t - 1/2 + 1/2*a = 0.
2
Suppose 0 = -101*y + 29 + 274. Let f(s) be the first derivative of 0*s**2 + 0*s + 0*s**4 + 0*s**y - 1/10*s**5 + 7 + 1/12*s**6. Factor f(t).
t**4*(t - 1)/2
Let z(t) be the third derivative of t**6/120 - 9*t**5/20 + 17*t**4/8 - 25*t**3/6 + 12*t**2 - 15*t. Find v such that z(v) = 0.
1, 25
Let i be (-12)/44 - ((-2398)/363 - -5). Suppose -20*s**2 + 0 + i*s + 75*s**3 = 0. Calculate s.
0, 2/15
Let l(s) be the first derivative of -2*s**6/45 + s**5/90 - 19*s**2/2 - 2*s + 40. Let d(o) be the second derivative of l(o). Factor d(r).
-2*r**2*(8*r - 1)/3
Let n(w) = w**3 + 10*w**2 - 11*w. Let p be n(-11). Suppose 0 = -2*u + 2*s + 2, 4*s + p = u - 4. Factor 2/15*r**3 + 0 + 2/5*r**5 + 2/3*r**4 - 2/15*r**2 + u*r.
2*r**2*(r + 1)**2*(3*r - 1)/15
Solve 7/4*k**2 - 20*k - 144 + 1/4*k**3 = 0 for k.
-8, 9
Factor 354375*r + 675*r**2 + 62015625 + 3/7*r**3.
3*(r + 525)**3/7
Let f = -45208 + 497292/11. Find c, given that -2/11*c**2 + f + 2/11*c = 0.
-1, 2
Let s(p) be the second derivative of -55/4*p**4 - 95*p - 1/6*p**6 + 0 - 100/3*p**3 - 5/2*p**5 - 40*p**2. Find a such that s(a) = 0.
-4, -1
Let t(x) be the first derivative of -86 + 10/7*x**2 - 4/7*x**3 + 0*x + 1/28*x**4. Factor t(g).
g*(g - 10)*(g - 2)/7
Let i = 10270550 - 11431121396/1113. Let q = -4/371 + i. Factor 2*a - 2*a**3 + q*a**2 - 4/3 + 2/3*a**4.
2*(a - 2)*(a - 1)**2*(a + 1)/3
Let c(z) be the third derivative of 0*z**3 + 1/24*z**4 + 0 - 11*z**2 - 1/120*z**5 - 3*z. Factor c(m).
-m*(m - 2)/2
Let w(t) be the third derivative of t**5/135 - 5*t**4/18 + 8*t**3/3 - 14*t**2 + 76*t. Solve w(i) = 0 for i.
3, 12
Let u be 130/60 + (-1)/6. Suppose -5*g = -3*r - 16, 3*g - 4*r - 16 = -2. Suppose -2*t + 4*t**u + t - g*t - t**2 = 0. Calculate t.
0, 1
Let t be ((570/(-21))/(-19))/(5/14). Let r(x) be the third derivative of 0*x**5 + 1/30*x**6 + 0*x + 4/3*x**3 + 0 - 1/2*x**t + 7*x**2. Factor r(b).
4*(b - 1)**2*(b + 2)
Let v(q) = 20*q + 3*q**2 - 12*q**3 + 3*q**2 + 8*q - 34*q**3 - 8*q**2 + 2*q**4. Let w(o) = -o**3. Let f(x) = 2*v(x) - 36*w(x). Find r such that f(r) = 0.
-1, 0, 1, 14
Let n(k) = 8*k**3 - 46*k**2 - 83*k - 51. Let p(g) = 7*g**3 - 47*g**2 - 85*g - 51. Let w(f) = 10*n(f) - 11*p(f). Let w(c) = 0. What is c?
-17, -1
Suppose -188*a + 2*q = -191*a - 16, 0 = -a + 4*q + 4. Let p be (287/82)/((-7)/a). Suppose 2/7*x + 0 - 1/7*x**p = 0. Calculate x.
0, 2
Suppose 8*v + 14*v + 88 = 0. Let z be ((-6)/v)/((-2)/(-4)). Suppose 4/7 - 8/7*b**z + 2*b - 10/7*b**2 = 0. Calculate b.
-2, -1/4, 1
Let t(z) be the third derivative of 0*z**3 + 7/2*z**4 - 3/20*z**5 - 1/40*z**6 - 155*z**2 + 0 + 0*z. Let t(o) = 0. What is o?
-7, 0, 4
Factor -2/11*m**3 - 15416/11*m + 106032/11 - 364/11*m**2.
-2*(m - 6)*(m + 94)**2/11
Let z(b) be the third derivative of -b**6/40 - 171*b**5/20 - 339*b**4/8 - 169*b**3/2 + 57*b**2 + 11*b. Determine v so that z(v) = 0.
-169, -1
Let o(g) = -g**2 + 23*g + 35. Let f be o(28). Let s = -77 - f. Factor a**2 + 69*a - 6*a**2 - 500 + 59*a - s*a.
-5*(a - 10)**2
Let b(w) = -15*w - 42. Let c be b(-3). Determine o so that c*o**2 + 1685 - 222*o - 255 + 2677 = 0.
37
Let o(k) = 7*k**2 - 83*k + 176. Let c(z) = -13*z**2 + 163*z - 354. Let m(s) = -5*c(s) - 9*o(s). Factor m(n).
2*(n - 31)*(n - 3)
Let z(r) be the first derivative of 3*r + 4/3*r**2 + 20 - 1/9*r**3. Factor z(h).
-(h - 9)*(h + 1)/3
Solve 39*v - 21/5*v**2 - 54/5 = 0 for v.
2/7, 9
Let s be 20 + -11 - (9 - 2). Factor 4*g**4 + g**4 + 26*g**2 + g**4 + 13*g**3 - 4*g**s - 5*g**4.
g**2*(g + 2)*(g + 11)
Let w = 42947 - 42945. Let d(u) be the second derivative of -31*u - 1/3*u**4 - 4*u**3 + 14*u**w + 0. Factor d(a).
-4*(a - 1)*(a + 7)
Let s(d) be the third derivative of d**7/105 - 4*d**6/15 - 121*d**5/15 + 204*d**4 + 7803*d**3 + 3*d**2 - 184*d + 2. Suppose s(q) = 0. Calculate q.
-9, 17
Suppose -8*p - 2*p + 20*p = 9*p. Determine y, given that -21/5*y**4 - 133/5*y**2 + 104/5*y**3 + p + 6*y = 0.
0, 2/7, 5/3, 3
Suppose -2/3*t**2 + 1432/3*t - 256328/3 = 0. What is t?
358
Let f(u) = -39*u**2 - 276*u + 1811. Let w(r) = -7*r**2 - 55*r + 362. Let b(o) = 4*f(o) - 22*w(o). Find d, given that b(d) = 0.
8, 45
Let w be (-7)/(-2)*(-6)/(-3). Suppose -b = -w*b + 24. Solve -u**5 - 25*u**b - u**3 + 23*u**4 + 0*u**3 = 0 for u.
-1, 0
Find d, given that -38*d + 31*d + 24*d**2 - 22*d**2 - 520 - 115*d = 0.
-4, 65
Let y(v) = -5*v**2 + 4*v + 61. Let c(j) = j**3 + 8*j**2 + 9*j + 12. Let d be c(-7). Let r(g) = g**2 - g - 12. Let h(b) = d*y(b) - 11*r(b). Factor h(s).
-(s - 5)*(s + 2)
Let f(z) = 17*z + 7. Let n be f(9). Suppose -4*c + 0*p + 128 = -p, -5*c + 5*p = -n. Factor -o - 16*o**2 + c*o**2 - 17*o**2.
-o*(o + 1)
Let -11*n**3 + 87*n + 71*n - 36 - 126*n + 3*n**2 + 12*n**2 = 0. What is n?
-18/11, 1, 2
Let w(q) be the second derivative of -q**7/252 + q**6/180 + 5*q**5/24 + 35*q**4/72 - 2*q**3/3 - 3*q**2 + 5*q + 382. Suppose w(n) = 0. Calculate n.
-3, -2, -1, 1, 6
Suppose -96 = -252*c + 248*c. Suppose 0 = c*t + 14*t - 114. Factor -5/3*h**t + 1/3*h**4 + 2*h**2 - 8/3 + 4/3*h.
(h - 2)**3*(h + 1)/3
Factor -18/7*d**3 + 2/7*d**4 + 58/7*d - 6/7*d**2 - 36/7.
2*(d - 9)*(d - 1)**2*(d + 2)/7
Factor -355*p**2 - 434 - 5*p + 383 + 406 + 5*p**3.
5*(p - 71)*(p - 1)*(p + 1)
Find c, given that 2688/11 + 2/11*c**2 - 680/11*c = 0.
4, 336
Factor -s**4 + 15*s**2 - 6 + 9*s + 11*s**3 - 6 - 9*s - 11*s - 2*s**2.
-(s - 12)*(s - 1)*(s + 1)**2
Let y(c) = 2*c**3 + 648*c**2 + 30790*c + 328572. Let x(q) = q**3 + 646*q**2 + 30793*q + 328578. Let p(t) = -2*x(t) + 3*y(t). Let p(r) = 0. Calculate r.
-74, -15
Let 11*u + 22*u**2 + 8*u**2 - 41*u**3 - 40*u**2 + 40*u**3 = 0. Calculate u.
-11, 0, 1
Suppose 0 = 3*y - 9 + 15, 4*j = -2*y + 1676. Let f = -420 + j. What is t in 0*t + 3/7*t**3 + 6/7*t**2 + f - 3/7*t**4 = 0?
-1, 0, 2
Let g(c) be the second derivative of 0 - 17/11*c**3 - 1/22*c**4 + 54/11*c**2 - 162*c. Factor g(j).
-6*(j - 1)*(j + 18)/11
Let t be (-32864)/448 - (30/14 + -2). Let f = t + 449/6. Factor 0 + 2/3*m**3 + 2/3*m - f*m**2.
2*m*(m - 1)**2/3
Let x(d) be the third derivative of d**3 + 1/120*d**5 + 5*d + 7/48*d**4 - 5*d**2 + 0. Factor x(n).
(n + 3)*(n + 4)/2
Factor -2/3*a**4 - 20/3*a**3 + 0 + 0*a + 16*a**2.
-2*a**2*(a - 2)*(a + 12)/3
Let m be 5300/36 - (3 - 75/27). Determine f, given that -m*f**3 + 10*f**4 - 75*f**2 + 57*f**3 - 30 + 15*f**5 - 105*f**2 - 125*f = 0.
-1, -2/3, 3
Factor 1/4*p**3 + 2009/4*p + 47/2*p**2 - 2401.
(p - 4)*(p + 49)**2/4
Let x = 1390 + -1387. Let h(t) be the third derivative of -14*t**2 + 0*t**x + 0*t - 1/15*t**7 + 0*t**4 + 1/15*t**5 + 0 + 1/12*t**6. Factor h(y).
-2*y**2*(y - 1)*(7*y + 2)
Let y(q) = 13*q**4 + 882*q**3 + 4800*q**2 + 11*q - 11. Let g(n) = 35*n**4 + 2425*n**3 + 13200*n**2 + 30*n - 30. Let p(d) = 11*g(d) - 30*y(d). Factor p(w).
-5*w**2*(w - 48)*(w + 5)
Factor 228/5*d + 4/5*d**2 + 2288/5.
4*(d + 13)*(d + 44)/5
Let c(z) be the first derivative of -324*z - z**4 + 39 - 76/3*z**3 - 198*z**2. Factor c(g).
-4*(g + 1)*(g + 9)**2
Let j(h) be the third derivative of -1/420*h**7 + 1/80*h**6 - 3*h**2 + 0*h**3 + 0 + 0*h**4 - 6*h - 1/60*h**5. Solve j(s) = 0.
0, 1, 2
Suppose -55*i = 63*i - 22*i - 192. Factor 1/11*v**i + 36/11 - 12/11*v.
(v - 6)**2/11
Let 40*y**3 - 336*y**3 + 175*y**3 - 234*y**3 - 5*y**4 - 385*y**3 = 0. Calculate y.
-148, 0
Let j(m) = -m**2 + 5*m + 3. Let i = 153 - 153. Let o be j(i). Factor -1/9*h**4 + 8/9*h**o + 0*h + 0 - 7/9*h**2.
-h**2*(h - 7)*(h - 1)/9
Let u(n) be the first derivative of -n**4/10 + 28*n**3/5 - 117*n**2 + 5408*n/5 - 1832. Factor u(m).
-2*(m - 16)*(m - 13)**2/5
Let b(j) = -41*j**2 - 2328*j + 451624. Let f(m) = -30*m**2 - 2328*m + 451626. Let x(l) = 3*b(l) - 4*f(l). Factor x(v).
-3*(v - 388)**2
Let s be (-13)/(39/9)*4/(-3). Factor -6*t**2 - t**3 + 4*t**2 + 4*t + 5*t**4 - 4*t**s - 2*t**2.
t*(t - 2)*(t - 1)*(t + 2)
Suppose 3*f - 42*f - 234 = 0. Let y be 3 + (3 - -1*(-12 - f)). Factor y + 0*o**2 + 0*o + 3/2*o**3 + 1/2*o**4.
o**3*(o + 3)/2
Let y(c) be the first derivative of -1/7*c**3 - 45/7*c**2 + 31 + 0*c. Factor y(f).
-3*f*(f + 30)/7
Let r(c) be the third derivative of c**6/180 + c**5/15 + c**4/4 + 15*c**3/2 - 112*c**2. Let j(q) be the first derivative of r(q). Solve j(d) = 0 