**3 + 4*f**2 + 3*f + 6. Let r(j) = 5*t(j) + 4*z(j). Let r(c) = 0. Calculate c.
-1, 1/2, 2/3
Factor -1301 + 1/2*y**2 - 2601/2*y.
(y - 2602)*(y + 1)/2
Let o(r) be the first derivative of -5*r**6/6 - 3*r**5 + 5*r**4/2 + 20*r**3 + 20*r**2 + 917. Let o(a) = 0. What is a?
-2, -1, 0, 2
Let p(k) be the second derivative of -5/18*k**3 + 5 + 0*k**2 + 2*k - 5/72*k**4. What is n in p(n) = 0?
-2, 0
Let s(d) be the second derivative of d**6/60 + 9*d**5/40 + d**4/3 - 121*d + 5. Factor s(g).
g**2*(g + 1)*(g + 8)/2
Let m(p) be the second derivative of 3*p**5/20 - 5*p**4/2 + 6*p**3 + 108*p**2 + 879*p. Factor m(i).
3*(i - 6)**2*(i + 2)
Let i(r) = 0*r**2 + 20*r + 1 + r**2 - 2*r**2 - 15. Let j be i(19). Factor 247 + 5*z**4 - 247 - j*z**2 - 4*z**3 + 5*z**5 - z**3.
5*z**2*(z - 1)*(z + 1)**2
Suppose 1/5*w**4 - 49/5*w**2 + 0 - 9*w - 3/5*w**3 = 0. Calculate w.
-5, -1, 0, 9
Let l(o) be the first derivative of -11*o**6/30 + 64*o**5/25 - 87*o**4/20 - 6*o**3/5 - 1221. Factor l(q).
-q**2*(q - 3)**2*(11*q + 2)/5
Let n(t) be the third derivative of t**6/120 - 301*t**5/20 + 8475*t**4 + 102152*t**3/3 - 5*t**2 - 116*t + 2. Factor n(g).
(g - 452)**2*(g + 1)
Suppose -5*c + 2*l + 414 = 0, -5*c + 0*c = -l - 412. Let g = c + -58. Find u such that 24*u + 23 + g - 11 + 4*u**2 = 0.
-3
Suppose -313 = -6*t + 131. Let f = t - 71. Let 39 + a + 7*a**2 - 46 + 0*a**3 - a**f = 0. What is a?
-1, 1, 7
Determine k so that 3/4*k**4 - 403/4*k**2 - 36 + 569/4*k - 25/4*k**3 = 0.
-9, 1/3, 1, 16
Let p(q) be the second derivative of q**7/5040 - q**6/1440 - q**4/6 + q**3 + 34*q. Let n(g) be the third derivative of p(g). Let n(h) = 0. Calculate h.
0, 1
Let l(s) be the first derivative of 5 - 1/12*s**5 + 1/6*s**4 - 17*s**2 + 1/120*s**6 + 0*s**3 + 0*s. Let m(h) be the second derivative of l(h). Factor m(g).
g*(g - 4)*(g - 1)
Let t = -361966/23 - -15732. Let n = 1462/161 + t. Suppose 1/7*o**5 - n*o**2 + 16/7*o + 0 + 1/7*o**3 + 6/7*o**4 = 0. What is o?
-4, 0, 1
Let f(d) = 4 + 2*d + 15 + 12. Let q be f(-13). Suppose 6*z + z**2 + 3*z**3 + 0*z**3 - q*z + 2*z**2 + z**4 = 0. Calculate z.
-1, 0
Let y(w) be the third derivative of w**6/420 + 186*w**5/35 - 5*w**2 - 23*w - 1. Let y(t) = 0. Calculate t.
-1116, 0
Let i be (285/55 + -5 - 901/1870)/((-77)/110). Factor -4/7*a + i + 1/7*a**2.
(a - 3)*(a - 1)/7
Solve d + 33/2*d**2 + 43/2*d**3 - 15*d**4 + 0 = 0 for d.
-1/2, -1/15, 0, 2
Let d = 2/138839 - -416513/277678. Factor -87*r - 2523/2 - d*r**2.
-3*(r + 29)**2/2
Suppose -2*b - 3*c - 6 = 0, -103*c + 99*c = 8. Let k(g) be the second derivative of -493/96*g**4 + 5*g**3 + 38*g + b - 9/4*g**2 + 289/160*g**5. Factor k(w).
(w - 1)*(17*w - 6)**2/8
Let f = -3063 + 3066. Let q(u) be the second derivative of -u + 1/30*u**4 + 1/100*u**5 + 0 + 0*u**2 + 0*u**f - 1/150*u**6. Suppose q(p) = 0. Calculate p.
-1, 0, 2
Let i(b) = 9*b**4 + 318*b**3 + 1272*b**2 + 1242*b - 6. Let o(h) = -17*h**4 - 637*h**3 - 2542*h**2 - 2485*h + 11. Let p(q) = 11*i(q) + 6*o(q). Factor p(s).
-3*s*(s + 2)**2*(s + 104)
Let r be (1/(-2) + 3)/(6768/192 - 34). Factor 5202/11 + 204/11*t + 2/11*t**r.
2*(t + 51)**2/11
Suppose -2*i + 5*i - 47 = -5*f, 3*f - 2*i - 13 = 0. Let p be 143/2*(-46)/(-253). Factor 19 + a**2 - 19 - f*a**4 + 2*a**5 + p*a**3 - 2*a - 7*a**3.
a*(a - 2)*(a - 1)**2*(2*a + 1)
Let u(v) be the second derivative of v**7/336 - 27*v**5/160 + 25*v**4/48 - v**3/2 + 8*v - 105. Let u(n) = 0. What is n?
-6, 0, 1, 4
Let v = -1151 - -1140. Let i be 0/(v + (-8 - -15)). What is s in 16/11*s**3 - 36/11*s**2 + 54/11 + i*s - 2/11*s**4 = 0?
-1, 3
Let u(k) be the third derivative of k**8/84 + 26*k**7/105 + 53*k**6/30 + 71*k**5/15 + 5*k**4 + 11956*k**2. Suppose u(s) = 0. Calculate s.
-6, -5, -1, 0
Let q(l) = -l**2 + 9*l - 16. Let m be q(6). Solve -22*a**m - a**2 + 3*a**2 + 0*a**3 - 16 - 2*a**3 - 34*a = 0.
-8, -1
Let n(k) be the first derivative of -k**4/8 - k**3/4 - 78*k - 2. Let b(j) be the first derivative of n(j). Determine t, given that b(t) = 0.
-1, 0
Let d = 4484 + -4481. Let x(b) be the second derivative of 11*b - 1/50*b**5 + 0 + 0*b**d + 0*b**2 + 1/30*b**4. Factor x(m).
-2*m**2*(m - 1)/5
Suppose 567 = 8*v - 1441. Let a = 251 - v. Factor 2/7*k**5 + 0*k**4 + a*k + 0*k**3 + 0 + 0*k**2.
2*k**5/7
Solve -172/7*j**4 - 144/7 - 736/7*j - 692/7*j**3 - 1124/7*j**2 - 12/7*j**5 = 0 for j.
-9, -2, -1, -1/3
Let k(a) = 209*a**3 - 118*a**2 - 1293*a + 731. Let b(d) = 39*d**3 - 24*d**2 - 258*d + 146. Let j(t) = -33*b(t) + 6*k(t). Let j(x) = 0. What is x?
-4, 6/11, 6
Let t(j) be the second derivative of 0*j**2 + 9/16*j**4 - 9/40*j**5 - 132*j + 1/40*j**6 + 0 - 1/2*j**3. Determine p so that t(p) = 0.
0, 1, 4
Let j = 10909/32709 - 2/10903. Let g(z) = z**2 + 5*z + 2. Let p be g(-5). Determine x so that 2/9 + j*x + 1/9*x**p = 0.
-2, -1
Suppose 89*g - 2181 = 311. Let h(y) be the second derivative of 3/10*y**6 + 0 - 7/6*y**3 - 11/12*y**4 - g*y + 7/20*y**5 + y**2. Factor h(s).
(s - 1)*(s + 1)**2*(9*s - 2)
Factor -2*s**4 - 42*s**3 - 9701*s + 20328*s - 10121*s - 186*s**2 + 1452.
-2*(s - 3)*(s + 2)*(s + 11)**2
Let v be (-3)/15*-15 - 0. Solve 4*r**3 - 9*r**4 + 6*r**v + 6*r**4 - 2*r**4 + 95*r**2 + 60 + 140*r = 0 for r.
-2, -1, 6
Let b(k) be the first derivative of 1/20*k**5 + 1/6*k**3 - 17 - 11*k + 0*k**2 + 1/6*k**4. Let s(y) be the first derivative of b(y). Factor s(a).
a*(a + 1)**2
Let k = 7490/9 + -832. Let x(l) be the second derivative of 0*l**2 + 1/15*l**5 + 0 + 0*l**4 + 3*l - k*l**3. Let x(p) = 0. Calculate p.
-1, 0, 1
Let j(c) = -10*c**2 + 8*c - 126. Let n(r) = -4*r**2 + 4*r - 42. Let x(s) = -3*j(s) + 8*n(s). What is h in x(h) = 0?
-3, 7
Let d(a) be the first derivative of -2*a**3 - 503*a**2 - 668*a - 1226. Suppose d(h) = 0. What is h?
-167, -2/3
Let l(d) be the first derivative of -45/2*d**2 - 3*d**5 - 85/3*d**3 + 0*d - 26 + 145/4*d**4. Determine v, given that l(v) = 0.
-1/3, 0, 1, 9
Let n(u) = -44*u**2 + 4291*u + 2061. Let a be n(98). Determine m so that -16*m**a - 26/3*m**2 - 70/9*m**4 + 0 - 4/9*m = 0.
-1, -2/35, 0
Let r(v) be the third derivative of -v**6/1020 - 5*v**5/102 - 14*v**4/17 - 48*v**3/17 - 2416*v**2. What is t in r(t) = 0?
-12, -1
Let j(h) be the second derivative of -h**7/126 - h**6/30 + 2*h**5/5 - 7*h**4/9 - 2*h - 979. Solve j(r) = 0 for r.
-7, 0, 2
Let j(m) = -7*m**2 + 2*m + 17. Let p(g) = -g**3 + 5*g**2 + 5*g. Let z be p(6). Let r(q) = -8*q**2 + 2*q + 18. Let y(n) = z*j(n) + 5*r(n). Solve y(o) = 0.
-2, 3
Let m(r) be the second derivative of -r**6/10 + 12*r**5/5 + 41*r**4/4 - 42*r**3 - 162*r**2 + 598*r. Suppose m(n) = 0. What is n?
-3, -1, 2, 18
Factor -21 + 64/3*y - 1/3*y**2.
-(y - 63)*(y - 1)/3
Let s(o) be the third derivative of -2/525*o**7 + 0*o**3 + 0*o**4 + 4/75*o**6 - 59*o**2 + 0*o - 7/75*o**5 + 0. Factor s(k).
-4*k**2*(k - 7)*(k - 1)/5
Let v be (-9546)/(-259) + (-12)/14. Factor -v*j - 263*j - 13*j**2 - 133*j - 80 + 57*j**2.
4*(j - 10)*(11*j + 2)
Suppose 24*p - 3*c - 6 = 0, -p + 2118*c - 6 = 2121*c. Let s = -2222/7 + 318. Factor -s*j**3 + 0*j**2 + p + 0*j - 2/7*j**4.
-2*j**3*(j + 2)/7
Let b(z) be the third derivative of z**7/525 - 13*z**6/25 + 1089*z**5/25 - 585*z**4 + 3375*z**3 - 4*z**2 + 19. Solve b(f) = 0 for f.
3, 75
Let s = 10346/19 + -72384/133. Solve 6*j**3 + 12/7 + s*j - 128/7*j**2 = 0 for j.
-2/7, 1/3, 3
Suppose -34*x + 117 = -87. Suppose -x = 2*t + t + 3*q, -8 = -2*t + 4*q. Let 0*p + 36/7*p**3 + t + 0*p**2 + 4/7*p**5 + 24/7*p**4 = 0. What is p?
-3, 0
Let y(j) be the first derivative of -4*j**2 - 115 + 5/2*j**4 + 0*j**3 + 0*j**5 + 0*j - 1/3*j**6. Find k such that y(k) = 0.
-2, -1, 0, 1, 2
What is m in 18933*m + 5*m**2 - 37877*m + 18934*m = 0?
0, 2
Let q = -1137 - -1139. Suppose 3*r + 5 = h + 4, -3*r = q*h - 11. Let 0 + 1/2*z**2 - 1/2*z + 1/2*z**3 - 1/2*z**h = 0. What is z?
-1, 0, 1
Let p(u) be the first derivative of -u**4/4 - 12*u**3 + 37*u**2/2 - 2360. Factor p(h).
-h*(h - 1)*(h + 37)
Let m(y) be the third derivative of y**7/1260 - y**6/45 + 7*y**5/60 - 43*y**4/24 + 131*y**2. Let c(v) be the second derivative of m(v). Solve c(z) = 0 for z.
1, 7
Let z(k) be the third derivative of -3*k**2 + 10 + 0*k - 11/24*k**3 - 5/48*k**4 + 1/240*k**5. Factor z(d).
(d - 11)*(d + 1)/4
Let z(r) be the first derivative of -r**6/12 + 2*r**5/5 + 47*r**4/8 - 23*r**3 - 99*r**2 - 108*r + 1457. Let z(q) = 0. Calculate q.
-6, -1, 6
Let t be (984/(-205) - -17) + (-18)/2. Let t