1
Let t(h) be the second derivative of -7/24*h**3 + 69*h + 3/80*h**5 + 1/16*h**4 + 0 - 1/120*h**6 - 3/4*h**2. Factor t(f).
-(f - 3)*(f - 2)*(f + 1)**2/4
Let c(j) be the second derivative of -3*j**4/20 + 791*j**3/15 + 176*j**2/5 + 6023*j. Find s, given that c(s) = 0.
-2/9, 176
Let a = 12136 + -12133. Let z(g) be the first derivative of -5/2*g**2 - 5/4*g**4 - 1 + 0*g + 10/3*g**a. Let z(h) = 0. Calculate h.
0, 1
Let h(g) be the third derivative of -g**7/210 - 53*g**6/120 - 17*g**5/20 + 53*g**4/24 + 26*g**3/3 + 1575*g**2. Determine b, given that h(b) = 0.
-52, -1, 1
Let h be -52 + 80/60*41. Factor -5*z**2 - h*z**3 + 16/3*z**4 + 0 + 3*z.
z*(z + 1)*(4*z - 3)**2/3
Suppose p - s - 7 = 0, -4*p - 266 = -2*s - 286. Factor -7/2*f - 2 - f**2 + 1/2*f**p.
(f - 4)*(f + 1)**2/2
Let t(l) be the third derivative of l**7/630 + l**6/36 + 29*l**5/180 + 4*l**4/9 + 2*l**3/3 + 917*l**2. Factor t(g).
(g + 1)**2*(g + 2)*(g + 6)/3
Suppose 40 = t + 2*l, 0 = 2971*t - 2966*t + 3*l - 74. Factor -64/9*u**3 + 1088/9*u - 2/9*u**t - 148/3*u**2 - 578/9.
-2*(u - 1)**2*(u + 17)**2/9
Suppose -3*y + 9 = 501*z - 504*z, 0 = z + 2*y - 15. Factor 0*b - 1145/3*b**z + 10/3*b**2 + 0.
-5*b**2*(229*b - 2)/3
Let x(r) be the second derivative of 8*r**2 - 5*r**3 + r**4 - 4*r + 1/10*r**5 - 5. Suppose x(f) = 0. What is f?
-8, 1
Let b(h) be the third derivative of -h**6/2 - 2*h**5/5 - h**4/18 - 3340*h**2. Factor b(f).
-4*f*(3*f + 1)*(15*f + 1)/3
Suppose 10*h - 26 = 64. Suppose 466*j + 3*j**4 - 466*j - h*j**3 = 0. What is j?
0, 3
Let d(x) be the first derivative of -3/2*x**2 + 19/9*x**3 + 0*x + 1/15*x**5 - 11/12*x**4 + 77. Factor d(h).
h*(h - 9)*(h - 1)**2/3
Suppose 3*l = 4*l - 224. Suppose 4*k = -3*k + l. Determine x, given that -4*x**2 - 18 - 28*x**3 + 9 + 9 + 64*x**5 - k*x**4 = 0.
-1/4, 0, 1
Let y(j) be the first derivative of -j**7/42 - j**6/10 - j**5/10 + 38*j + 22. Let t(k) be the first derivative of y(k). Find f such that t(f) = 0.
-2, -1, 0
Suppose 4*m = -5*p + 40, 0 = -3*p - 29 + 14 + 27. Factor -45/4*r**4 + 27/4*r**m + 0 + 0*r - 3/4*r**2 + 21/4*r**3.
3*r**2*(r - 1)*(3*r - 1)**2/4
Let u be 3 - (12/(-10) - 5/(-25)). Factor 6*t**4 - 15*t**u - 8*t**2 + 2*t**4 + 9*t**4.
2*t**2*(t - 2)*(t + 2)
Let y(a) be the second derivative of -77*a - 26/5*a**3 - 507/5*a**2 - 1/10*a**4 + 0. Suppose y(c) = 0. What is c?
-13
Let u(g) be the third derivative of -1/360*g**6 + 0*g + 1/8*g**4 - 1/2*g**3 + 89*g**2 + 1/180*g**5 + 0. Factor u(n).
-(n - 3)*(n - 1)*(n + 3)/3
Let b(d) be the third derivative of -d**5/540 + 49*d**4/216 + 17*d**3/9 + 1382*d**2. Factor b(l).
-(l - 51)*(l + 2)/9
Suppose 276 + 36 = 156*k. Let r(o) be the third derivative of 0 + 0*o**4 - k*o**2 + 0*o**3 + 1/540*o**6 - 1/945*o**7 + 1/135*o**5 + 0*o. Factor r(f).
-2*f**2*(f - 2)*(f + 1)/9
Let f(z) be the third derivative of -z**5/150 - 1343*z**4/60 + 1422*z**2. Factor f(o).
-2*o*(o + 1343)/5
Let x(c) be the first derivative of -1/3*c**3 - 1/24*c**6 - 3/8*c**4 - 1/5*c**5 - 1/8*c**2 + 40 + 0*c. Factor x(o).
-o*(o + 1)**4/4
Let p be 2 + -9 + ((-14858)/76)/(-23). Find b, given that 3*b - 3/4 - 3*b**3 - p*b**2 + 9/4*b**4 = 0.
-1, 1/3, 1
Suppose c - 690 = 24*c. Let f be (c/(-20))/((-14)/(-8)). Factor 0 + 0*d**3 + 2/7*d**4 - f*d**2 + 4/7*d.
2*d*(d - 1)**2*(d + 2)/7
Let i be 14/(-70) + (-150705)/(-25). Factor -i*m + 24 - m**3 + 7*m**3 + 6094*m + 39*m**2.
3*(m + 2)*(m + 4)*(2*m + 1)
Factor -1/2*g + 9/4*g**2 - 1/8*g**4 - 3/8*g**3 - 3.
-(g - 2)**2*(g + 1)*(g + 6)/8
Determine h so that -172/7*h + 534/7 - 2/7*h**2 = 0.
-89, 3
Let o(q) = q**3 + 14*q**2 - 36. Let w be o(-10). Let z = w - 2546/7. Factor -24/7*t + 12/7*t**2 + 16/7 - z*t**3.
-2*(t - 2)**3/7
Let r = -2486/15 - -17627/105. Factor -r*v**2 - 6/7*v + 0 - 9/7*v**3.
-3*v*(v + 1)*(3*v + 2)/7
Let z be 41 + ((-30)/(-25))/((-9)/(-15)). Factor z - 5988*i - 3*i**2 + 6042*i + 14.
-3*(i - 19)*(i + 1)
Let z(s) be the third derivative of -s**8/168 + 9*s**7/35 - 133*s**6/30 + 568*s**5/15 - 160*s**4 + 1024*s**3/3 - 2049*s**2. Solve z(k) = 0.
1, 2, 8
Let a(o) be the first derivative of -o**6/18 - 28*o**5/15 + 29*o**4/12 - 5869. Determine p so that a(p) = 0.
-29, 0, 1
Let b(t) = -11*t**2 - 687*t + 8. Let r(f) = -8*f**2 - 684*f + 6. Let i(s) = 6*b(s) - 8*r(s). Suppose i(x) = 0. Calculate x.
0, 675
Suppose -3*r - 2*z - 15 = z, -5*r + 3*z = -15. Suppose r = 10*m - 79 - 1. What is v in -8*v + 12*v**4 + m*v**3 - 4/3 - 32/3*v**2 = 0?
-1, -1/3, 1
Let c(m) be the first derivative of -m**6/3 + 10*m**5/3 - 28*m**4/3 + 32*m**3/9 + 2385. Determine u so that c(u) = 0.
0, 1/3, 4
Let y(f) be the first derivative of f**5/5 - 3*f**4/8 + 18*f**2 - 63. Let s(i) be the second derivative of y(i). Find u such that s(u) = 0.
0, 3/4
Let a be (272/1020)/((-1)/(-12)) - 2. Let g(q) be the second derivative of -2/5*q**3 + 0 + 17*q + 1/20*q**4 + a*q**2. Factor g(u).
3*(u - 2)**2/5
Suppose 5*d - 4*m = 21, 5*d = 3*d + 5*m + 22. Suppose 5*f + 25 = 5*s, 6*s + 3*f = 5*s + d. Factor -4/9*c**3 + 0 - 14/9*c**s + 0*c + 0*c**2 - 10/9*c**5.
-2*c**3*(c + 1)*(5*c + 2)/9
Factor -4499456/7 + 620/7*a**3 + 63648/7*a**2 + 2/7*a**4 + 302848*a.
2*(a - 2)*(a + 104)**3/7
Solve -25*h**2 + 64*h + 16*h - 47216*h**3 - 20 + 47181*h**3 = 0.
-2, 2/7, 1
Let g be 15/((390/(-100))/(-13)*10). Let j(i) be the second derivative of 1/2*i**4 + 0 - i + 0*i**3 + 1/10*i**6 + 9/20*i**g + 0*i**2. Solve j(a) = 0.
-2, -1, 0
Factor -68/9*s + 2*s**2 + 2/9*s**3 + 16/3.
2*(s - 2)*(s - 1)*(s + 12)/9
Let l(d) = -4*d**3 + 12*d**2 - 8*d. Let q(u) = -u - 313 + u**3 - 2*u**2 + 2*u**2 + 313. Let b(k) = l(k) + 5*q(k). Determine j so that b(j) = 0.
-13, 0, 1
Let v(t) = 3*t**2 + 4*t - 2. Let p(u) = 6*u - 62. Let j be p(10). Let c be v(j). Find a such that -7*a + 2*a + 3*a**c - a + 3*a**3 = 0.
-2, 0, 1
Solve 7744 + 34496*q - 6*q**4 + 214157*q**3 - 16*q**4 - 212203*q**3 - 44172*q**2 = 0 for q.
-2/11, 1, 44
Let y(x) = 15 + 49 + 2*x**2 + 37*x + 79*x - 70*x + 30. Let r be y(-2). Determine n so that -5/2*n**3 - 20*n + r + 25/2*n**2 = 0.
1, 2
Factor -52*h - 2/7*h**2 - 2366.
-2*(h + 91)**2/7
Let m(d) be the second derivative of -d**4/12 - 43*d**3/3 - 164*d**2 + 173*d + 3. Factor m(o).
-(o + 4)*(o + 82)
Suppose -4*h + 86*h - 530 = -24*h. Let v(f) be the third derivative of 0*f + 0 + 2/3*f**3 + 1/5*f**h - 1/30*f**6 - 21*f**2 - 1/2*f**4. Solve v(c) = 0.
1
Let n(c) be the second derivative of -c**6/24 + 3*c**5/4 + 35*c**4/8 + 55*c**3/6 + 95*c**2/2 - 21*c. Let y(b) be the first derivative of n(b). Factor y(x).
-5*(x - 11)*(x + 1)**2
Let -2/9*s**5 + 100/9*s**2 + 0 + 22*s**3 + 32/3*s**4 + 0*s = 0. What is s?
-1, 0, 50
Suppose 0 = -3*x + 17 + 10. Let d be 2 + 2 + 99/x. Factor -g - 5*g**2 + 5*g**4 + d*g**3 + g + 15*g**2.
5*g**2*(g + 1)*(g + 2)
Let v(q) be the third derivative of 13/240*q**5 - 1/24*q**4 - 1/120*q**6 - 1/2*q**3 + 20 + 0*q + q**2. Let v(t) = 0. What is t?
-3/4, 2
Let t(m) be the second derivative of -m**6/150 - 3*m**5/100 + m**4/20 + 11*m**3/30 + 3*m**2/5 + 7581*m. Factor t(q).
-(q - 2)*(q + 1)**2*(q + 3)/5
Let y(m) be the second derivative of 139*m**4/48 - m**3/8 + 2688*m. Suppose y(q) = 0. What is q?
0, 3/139
Let m(z) be the second derivative of 29*z**4/12 + 13*z**3/3 - 3*z**2/2 - z + 732. Suppose m(n) = 0. Calculate n.
-1, 3/29
Suppose 7*v = v + 24. What is g in -4*g**3 + 4*g + 17*g**4 + 2*g**2 - 9*g**v - 10*g**4 = 0?
-2, -1, 0, 1
Let r = 50 - 34. Suppose 0*p - 5*p = -2*o - 12, 5*o = p + r. Factor o - 4 + 2*t**2 + 2 + 234*t - 230*t.
2*(t + 1)**2
Suppose -52 + 4 = -12*p. Suppose -p*h + 2*h + 20 = 3*y, -4*y = -4*h. Factor 25*o**5 + 4*o**4 - 4*o**2 - 23*o**5 - 6*o - 2 + y*o**3 + 2*o**4.
2*(o - 1)*(o + 1)**4
Let t(l) be the first derivative of 3*l**3/5 - 249*l**2/10 - 84*l/5 + 6925. Factor t(q).
3*(q - 28)*(3*q + 1)/5
Factor -251649 - 55596 - 71432 - 34*d - 3056*d - 5*d**2 - 98728.
-5*(d + 309)**2
Let u be 17/5 - (-6)/(-15) - 0. Let i(a) = 25 - 41*a - 31 + 19*a**2 - 11*a**u + 21. Let t(q) = -q**3 - q**2 - q. Let d(z) = i(z) - 6*t(z). Factor d(y).
-5*(y - 3)*(y - 1)**2
Suppose 32*u + 149*u - 1054 = -1054. Determine o so that -69/8*o**3 + 21/4*o**2 + 0*o + 9/8*o**4 + u = 0.
0, 2/3, 7
Let s be -25 - (-3178)/1512*12. Factor -s*b**3 - 8192/3*b + 524288/9 + 128/3*b**2.
-2*(b - 64)**3/9
Let o(x) be the third derivative of 7*x**6/200 - x**5/5 - 9*x**4/40 + 9*x**3/5 + x**2 - 2276. Factor o(s).
3*(s - 3)*(s + 1