= 0.
-1, 1, 2
Let o(b) be the second derivative of b**5/30 + 43*b**4 + 16641*b**3 - 4869*b. Factor o(z).
2*z*(z + 387)**2/3
Let c(g) be the third derivative of g**7/70 + 7*g**6/40 + 17*g**5/20 + 17*g**4/8 + 3*g**3 - g**2 - 1036*g. Factor c(o).
3*(o + 1)**2*(o + 2)*(o + 3)
Let b = -361 + 384. Let y be 9/(-90) + b/30. Factor y*c**2 - 4/3*c - 2.
2*(c - 3)*(c + 1)/3
Let x be ((-8)/12 - 0)/(-2). Let g be (21/10)/7*5*(-10)/(-15). Determine f so that -g + 2/3*f + x*f**2 = 0.
-3, 1
Let i be -5 - (2 - 18)*3/6. Factor 31381*p + 3*p**i - 31393*p + 2*p**2 - 2*p**2.
3*p*(p - 2)*(p + 2)
Suppose -4*w = 5*o - 7, -3*o = -2*w + 2 - 15. Solve -5*x + 8*x + x**2 + o*x - 4*x**2 = 0 for x.
0, 2
Let t(m) be the second derivative of -4*m - 1/42*m**4 - 1/420*m**6 + 0*m**3 + 0 - 1/70*m**5 - 3/2*m**2. Let h(g) be the first derivative of t(g). Factor h(p).
-2*p*(p + 1)*(p + 2)/7
Let v(m) be the third derivative of -m**7/420 + 7*m**6/240 + m**5/8 - 175*m**4/48 + 125*m**3/6 - 1142*m**2 - 2. Find s, given that v(s) = 0.
-5, 2, 5
Let j(x) be the third derivative of -x**6/96 + 37*x**5/24 - 1745*x**4/96 + 115*x**3/2 - 2*x**2 - 30*x - 5. Factor j(u).
-5*(u - 69)*(u - 4)*(u - 1)/4
Let d(t) be the first derivative of 49*t**5/25 + 35*t**4/2 + 457*t**3/15 - 60*t**2 + 144*t/5 + 560. Factor d(m).
(m + 4)**2*(7*m - 3)**2/5
Let h(z) be the second derivative of 1/147*z**7 - 13/105*z**6 + 0*z**3 - 4 + 0*z**2 + 27*z + 7/6*z**4 + 1/2*z**5. Factor h(r).
2*r**2*(r - 7)**2*(r + 1)/7
Let d(a) be the first derivative of -a**5/10 - 11*a**4/4 + 154*a**3/3 - 114*a**2 - 1152*a - 5805. Factor d(f).
-(f - 6)**2*(f + 2)*(f + 32)/2
Factor 0*t - 3/4*t**4 + 15/4*t**2 + 0 + 3*t**3.
-3*t**2*(t - 5)*(t + 1)/4
Find x such that 90*x**2 + 0 + 81/2*x + 1/2*x**5 + 59*x**3 + 10*x**4 = 0.
-9, -1, 0
Let b = -20 + 19. Let t(s) = -3*s. Let f be t(b). Let 239*h**2 - 239*h**2 - 2*h**f + h + h**5 = 0. What is h?
-1, 0, 1
Determine c, given that -27/4*c - 105/4*c**3 + 3/4 - 9*c**4 - 99/4*c**2 = 0.
-1, 1/12
Let g(r) be the second derivative of -r**6/6 + 10*r**5 + 220*r**4/3 + 8190*r. Find l, given that g(l) = 0.
-4, 0, 44
Let a(w) be the second derivative of -w**6/135 + 22*w**5/9 - 2053*w**4/9 + 23980*w**3/27 - 11881*w**2/9 - 5*w - 3. Solve a(c) = 0.
1, 109
Let l(a) be the second derivative of -a**6/75 + 29*a**5/25 - 211*a**4/30 - 18*a**3 - 6*a - 43. What is w in l(w) = 0?
-1, 0, 5, 54
Let l(u) be the second derivative of 39/2*u**2 - 1/2*u**4 + 22*u + 0 - 25/2*u**3. Determine k, given that l(k) = 0.
-13, 1/2
Let b(y) be the first derivative of -5/8*y**4 - 55/18*y**3 - 10/3*y - 5*y**2 + 40. Factor b(d).
-5*(d + 1)*(d + 2)*(3*d + 2)/6
Solve -5421*q - 525 - 6*q**2 + 317*q**4 + 6474*q - 1050*q**3 - 3*q**5 + 214*q**4 = 0.
-1, 1, 175
Let i(v) be the third derivative of -v**6/96 - 140*v**5/3 - 196000*v**4/3 - 98*v**2 + 25*v - 1. Suppose i(f) = 0. What is f?
-1120, 0
Let i(c) be the third derivative of -2*c**7/735 - c**6/42 + 4*c**5/105 + 10*c**4/21 + 803*c**2. Factor i(x).
-4*x*(x - 2)*(x + 2)*(x + 5)/7
Let x be 4 + (3 - (0 + -1)). Suppose -3*t + x*t - 20 = 0. Factor 11*o + 9*o - o**t + 4*o**4 + 2*o**4 - 15*o**3.
5*o*(o - 2)**2*(o + 1)
Let z(f) be the second derivative of f**6/225 - 32*f**5/75 - 11*f**4/15 + 64*f**3/45 + 13*f**2/3 - 222*f - 1. Find v, given that z(v) = 0.
-1, 1, 65
Let t(l) be the second derivative of 5/4*l**3 + 3/40*l**5 + 0 + 27*l - 3/2*l**2 - 1/2*l**4. Solve t(c) = 0.
1, 2
Let w be (462/63 + (-24)/4)*9/3. Let r = 107/2 + -519/10. Solve 0*h - r*h**2 + 0 + 4/5*h**5 + 8/5*h**w - 4/5*h**3 = 0 for h.
-2, -1, 0, 1
Let r(o) be the third derivative of 55*o**8/2016 + 221*o**7/126 + 23*o**6/48 - 221*o**5/36 - 25*o**4/9 + 3*o**2 - 22*o + 9. Solve r(q) = 0.
-40, -1, -2/11, 0, 1
Solve 5841362/7 + 2/7*w**2 - 6836/7*w = 0.
1709
Let m = 261145/21 - 12435. Let v(d) be the third derivative of -m*d**3 + 23/84*d**4 - 23*d**2 + 0 + 0*d + 1/42*d**5. Suppose v(i) = 0. Calculate i.
-5, 2/5
Let o(x) = 141*x + 126. Let z(v) = -v**2 - 6*v. Let y(r) = -o(r) - 3*z(r). Factor y(b).
3*(b - 42)*(b + 1)
Let o(j) be the third derivative of -j**8/2520 - 29*j**7/315 - 287*j**6/900 - 143*j**5/450 - 365*j**2 - 3. What is r in o(r) = 0?
-143, -1, 0
Let n = -86080 + 86083. Determine v, given that 0 - 324*v**n - 2/3*v**5 - 4374*v + 1944*v**2 + 24*v**4 = 0.
0, 9
Let p(h) be the third derivative of -h**8/420 + h**7/70 - h**6/30 + h**5/30 - 7*h**3 - 48*h**2. Let w(n) be the first derivative of p(n). Factor w(j).
-4*j*(j - 1)**3
Suppose -73*b + 319 + 49 = 76. Factor 0*d**2 + 0 + 0*d - 3/5*d**b - 3/5*d**3.
-3*d**3*(d + 1)/5
Let u = 146 + -147. Let x = 11/7 + u. Find m, given that -2/7*m**5 + 4/7 - 8/7*m**3 - 8/7*m**4 + x*m**2 + 10/7*m = 0.
-2, -1, 1
Let s(n) = 2*n**2 + 8*n. Let c(o) = -7*o - 254. Let p be c(-35). Let w be s(p). Suppose -85/2*h**2 - 10 - w*h = 0. Calculate h.
-2, -2/17
Let t be (11 - 0) + 157 + -159. Let p be ((-50)/(-6) - t)*-3. Let -4/7 + 4/7*b - 4/7*b**3 + 4/7*b**p = 0. Calculate b.
-1, 1
Suppose 1254/5*m**2 + 0 - 618/5*m**3 - 6/5*m**4 - 126*m = 0. What is m?
-105, 0, 1
Let u(i) be the second derivative of i**4/3 - 382*i**3/3 - 50*i + 10. Let u(s) = 0. Calculate s.
0, 191
Let g(b) = 2*b**3 - 3*b**2 - 7*b + 11. Let i be g(4). Suppose 0 = i*f - 56*f - 14. Factor -10/3*k + 26/9*k**f + 4/9.
2*(k - 1)*(13*k - 2)/9
Solve 587/6*m + 1/6*m**3 + 293/6 + 295/6*m**2 = 0 for m.
-293, -1
Let o(x) be the first derivative of 11*x**4 - 252*x**3 + 1608*x**2 - 560*x + 10690. Determine v so that o(v) = 0.
2/11, 7, 10
Let g(r) be the first derivative of r**6/15 + 74*r**5/5 + 549*r**4/10 + 1094*r**3/15 + 182*r**2/5 - 4836. Factor g(b).
2*b*(b + 1)**3*(b + 182)/5
Let a be 1083/(-2 - -59) + -15 + 0. Let -3/2*m**a + 19/2*m**2 + 0 - 11/2*m**3 - 5/2*m = 0. Calculate m.
-5, 0, 1/3, 1
What is j in -499 + 9 + 485*j**2 - 59*j + 47*j**4 - 196*j - 92*j**4 + 255*j**3 + 50*j**4 = 0?
-49, -2, -1, 1
Let n = -402 + 6032/15. Let b(w) = 10*w - 60. Let y be b(6). Factor 8/15 + y*m - 2/5*m**2 - n*m**3.
-2*(m - 1)*(m + 2)**2/15
Let d(o) be the first derivative of -o**4 + 1980*o**3 - 1470150*o**2 + 485149500*o + 9668. Let d(t) = 0. What is t?
495
Let b(d) be the second derivative of d**6/24 - d**5/12 + 23*d**2 - 25*d. Let x(f) be the first derivative of b(f). Find v, given that x(v) = 0.
0, 1
Let k = -609 - -613. Let n(p) be the second derivative of 10*p + 2/75*p**6 + 0 - 1/30*p**3 - 1/10*p**2 - 11/100*p**5 + 3/20*p**k. Factor n(h).
(h - 1)**3*(4*h + 1)/5
Let d = -52 + 87. Suppose -13*k = -6*k - d. Suppose -30*f**2 - 3*f**k - 2*f**4 - 6*f - 27*f - 3 - 30*f**3 - 13*f**4 + 18*f = 0. Calculate f.
-1
Let a be 3*((-20)/6 - (-10 - -7)). Let l(p) = -140*p + 1. Let w be l(a). Factor -15*m**2 - w + 141 - 5*m - 10*m**3.
-5*m*(m + 1)*(2*m + 1)
Let n be 15*21/(-6615)*-3. Factor -10/7*f - 2/7*f**3 + 0 - 13/7*f**2 + n*f**4.
f*(f - 5)*(f + 1)*(f + 2)/7
Let z(j) be the third derivative of -1/1620*j**6 + 1/18*j**4 + 9/2*j**3 - 25*j**2 + 0*j + 0 + 1/540*j**5. Let p(o) be the first derivative of z(o). Factor p(l).
-2*(l - 3)*(l + 2)/9
Let q(b) = -2*b - 56 + b + b - 8*b - 4*b. Let c be q(-5). Factor -56/5*z + 10*z**c + 138/5*z**2 + 8/5 - 28*z**3.
2*(z - 1)**2*(5*z - 2)**2/5
Factor -144/7 - 3/7*u**2 - 21*u.
-3*(u + 1)*(u + 48)/7
Solve -3/8*w + 0 - 3975/8*w**2 + 1989/4*w**3 = 0 for w.
-1/1326, 0, 1
Let w(r) = 12*r**4 + 35841*r**3 + 26748597*r**2 + 108*r + 9. Let n(k) = 3*k**4 + 8960*k**3 + 6687149*k**2 + 24*k + 2. Let i(o) = 9*n(o) - 2*w(o). Factor i(q).
3*q**2*(q + 1493)**2
Let k(o) = -85*o + 1363. Let v be k(16). Let d(z) be the first derivative of -2 + 2/3*z**v + 0*z - 2/5*z**4 + 2/25*z**5 - 2/5*z**2. Factor d(p).
2*p*(p - 2)*(p - 1)**2/5
Let k(g) = 189*g**2 - 78*g - 93. Let s(b) = -93*b**2 + 39*b + 46. Let x(q) = -4*k(q) - 9*s(q). Solve x(d) = 0.
-14/27, 1
Let w(z) be the second derivative of -52/3*z**3 + 8/3*z**4 - 2*z + 9 - 1/10*z**5 + 48*z**2. What is n in w(n) = 0?
2, 12
Let r be (-13 - -13)/(1*-3). Determine j, given that 2*j**2 - 3*j**2 + r + 3*j + 2 + 2 = 0.
-1, 4
Suppose -5*a - 4 = -14. Suppose -a*k - 8 = -6*k. Factor k*u**2 - 6*u + u**2 + u + 2*u**2.
5*u*(u - 1)
Let s(v) = -6*v**4 - v**3 + v**2 + 11*v + 1. Let o(c) = c**4 - 2*c**3 + c**2 - 3*c. Let n(f) = 2*o(f) + s(f). What is z in n(z) = 0?
-1, -1/4, 1
Let i(h) = 3*h**3 + 6*h**2 - 3*h - 3. Let z be i(-3). Let f(j) = -j**3 - 17*j**2