 = -x**3 - 4*x**2 - 5*x - 2. Let p be o(-3). Determine c, given that 19 + p*c - 5*c**3 - 30*c**2 + 11 + 3*c - 2*c = 0.
-6, -1, 1
Determine r, given that 237/2*r**4 + 27*r**3 - 1458*r**2 - 324*r - 27/2*r**5 + 0 = 0.
-3, -2/9, 0, 6
Let f(j) = -j**2 - 11*j - 15. Let g be f(-9). Determine m so that 2*m**g - m**4 + 0*m**4 - 2*m + 58 - 57 = 0.
-1, 1
Let j(l) be the first derivative of l**6/21 - 4*l**5/35 + l**4/14 + 661. Factor j(x).
2*x**3*(x - 1)**2/7
Factor 67041/2*b + 41067/4 + 147*b**4 + 119271/4*b**2 + 4011*b**3.
3*(b + 13)**2*(14*b + 9)**2/4
Let l(g) be the second derivative of g**4/20 - 2128*g**3/15 + 1418*g**2/5 - 15*g + 16. Let l(q) = 0. Calculate q.
2/3, 1418
Let m(c) be the second derivative of c**7/168 + 7*c**6/120 - 27*c**5/80 + 29*c**4/48 - 5*c**3/12 + 3546*c. Determine l so that m(l) = 0.
-10, 0, 1
Let k(v) be the second derivative of 3*v**5 + 155/12*v**4 - 20*v**2 - 178*v + 5*v**3 + 0 - 5/6*v**6. Let k(o) = 0. What is o?
-1, 2/5, 4
Let u = -14669 - -14673. Let h(x) be the third derivative of 0 + 0*x + 0*x**3 - 1/25*x**5 - 29*x**2 - 1/40*x**u. Determine z, given that h(z) = 0.
-1/4, 0
Let g(m) = -5*m**2 + 96*m - 274. Let q(i) = -76*i**2 + 1454*i - 4108. Let n(l) = -92*g(l) + 6*q(l). Factor n(t).
4*(t - 20)*(t - 7)
Let u be 162/(-92) - (-54)/9. Let x = u - -6/23. Solve 1/2*l**5 + x*l**3 + l + 0 - 5/2*l**4 - 7/2*l**2 = 0.
0, 1, 2
Let a be (15 + 1)*28/(-8). Let t = 71 + a. Factor t - 5*s**2 - 18*s + 1 + 43*s + 54.
-5*(s - 7)*(s + 2)
Factor 115*t**2 + 11*t**3 - 20*t**4 - 27*t**2 - 4*t**5 - 148*t + 60 + 13*t**3.
-4*(t - 1)**3*(t + 3)*(t + 5)
Let b(s) be the third derivative of 1/2*s**4 + 0*s + 0*s**3 - 1/105*s**7 + 2/15*s**6 - 13/30*s**5 + 0 + 203*s**2. Suppose b(z) = 0. What is z?
0, 1, 6
Let w = 190189/166397 - 3/23771. Factor 2/7*s**2 - 2/7*s**3 - 8/7 + w*s.
-2*(s - 2)*(s - 1)*(s + 2)/7
Find d, given that -48/7*d**2 - 13/7*d**3 - 1/7*d**4 - 36/7*d + 0 = 0.
-6, -1, 0
Let a(f) be the first derivative of -f**4/20 - 4*f**3/15 - f**2/2 - 2*f/5 - 220. Suppose a(k) = 0. What is k?
-2, -1
Suppose 50*n + 299*n - 14580 = -489*n + 28*n. Suppose -12*f + 15/2*f**4 + 0 + n*f**2 + 27*f**3 = 0. Calculate f.
-2, 0, 2/5
Let d be 7 + (-8 + 126/4)*(-8)/28. Determine n, given that -d*n**3 + 16/7*n**2 + 18/7*n + 0 = 0.
-1, 0, 9
Let l = 28791 - 28784. Let n(r) be the third derivative of 0*r**4 - 2/15*r**5 + 18*r**2 - 1/15*r**6 + 0*r + 0*r**3 + 0 - 1/105*r**l. Solve n(s) = 0 for s.
-2, 0
Suppose 33 = -b + 35. Let o(x) be the first derivative of 0*x + 25 + 1/6*x**b + 1/9*x**3. Factor o(p).
p*(p + 1)/3
Let z(k) be the first derivative of -k**3/12 + 37*k**2/2 + 149*k/4 - 2996. Factor z(f).
-(f - 149)*(f + 1)/4
Let f(n) be the third derivative of n**5/120 - 29*n**4/6 + 77*n**3/4 - 1639*n**2. Factor f(o).
(o - 231)*(o - 1)/2
Let g(r) be the third derivative of 0*r**5 + 0*r**3 + 2*r**2 + 148*r + 1/2016*r**8 + 1/144*r**4 - 1/360*r**6 + 0 + 0*r**7. Factor g(l).
l*(l - 1)**2*(l + 1)**2/6
Find z, given that 325876 + 208220 + 5*z**2 - 34816 - 3160*z = 0.
316
Let a(q) be the second derivative of -q**7/189 + 11*q**6/135 - 8*q**5/45 - 20*q**4/9 + 16*q**3/3 + 48*q**2 + 777*q. Determine r so that a(r) = 0.
-2, 3, 6
Let d = 27106/15247 - 2/137223. Suppose 0*z + d*z**2 + 0 - 2/9*z**4 + 4/9*z**3 = 0. Calculate z.
-2, 0, 4
Let h be (-18 + 17)*(23 + -23). Find j such that -6/5*j**4 + 6/5*j**3 - 6/5*j**5 + 0 + 6/5*j**2 + h*j = 0.
-1, 0, 1
Let i(h) be the third derivative of -h**6/240 - h**5/120 + h**4/24 - 114*h**2 - 6. Let i(g) = 0. What is g?
-2, 0, 1
Let z(s) be the third derivative of s**6/2340 - 3*s**5/260 + 5*s**4/39 - 10*s**3/3 + s**2 + 10*s. Let i(v) be the first derivative of z(v). Factor i(y).
2*(y - 5)*(y - 4)/13
Let j(z) = -4*z**3 + 46*z**2 + 172*z - 496. Let y(c) = -c**3 + c**2 + 3*c - 2. Let r(t) = -j(t) + 6*y(t). Solve r(d) = 0.
-11, 2
Let b(h) be the first derivative of -1/24*h**4 + 7/9*h**3 + 20/3*h + 41 - 11/3*h**2. Factor b(y).
-(y - 10)*(y - 2)**2/6
Factor 0*l**2 - 4188*l + 4038*l + 3*l**2 + 2*l**2 + 568 - 3*l**2.
2*(l - 71)*(l - 4)
Suppose -7*l = -2*l, c = 5*l + 475. Let w = -473 + c. Suppose 0 - 3/2*p**w - 3/2*p = 0. Calculate p.
-1, 0
Let b(c) = 2652*c**2 + 6914*c + 4556. Let d(v) = 2651*v**2 + 6912*v + 4548. Let k(s) = 6*b(s) - 7*d(s). Factor k(i).
-5*(23*i + 30)**2
Let x(k) = -k**3 + 6*k**2 + 18*k - 14. Let p be x(8). Let q(o) = 11*o**2. Let t be q(-1). Factor -2 - 1 + 28*m**p - m**3 - t*m**3 + 7 - 20*m.
-4*(m - 1)**2*(3*m - 1)
Let p(s) be the first derivative of 7*s**3/6 - 335*s**2/4 - 24*s - 1279. Factor p(m).
(m - 48)*(7*m + 1)/2
Let g be ((-30)/4)/((-17)/(-34))*-3. Factor 7 + 17 - 29*b - 4*b**2 + g*b + 6*b**2.
2*(b + 2)*(b + 6)
Suppose 0 = 20*b - 41*b + 1554. Factor -89*t - t**2 + 4*t**2 + 0*t**2 - 195*t + b*t.
3*t*(t - 70)
Let m(d) be the first derivative of -155 + 8/3*d**4 - 27*d**2 - 4*d**3 + 16/15*d**5 + 1/9*d**6 - 36*d. Solve m(l) = 0.
-3, -1, 2
Let k = 442219 + -442219. Solve -30/13*z**3 + 2*z**5 + k - 22/13*z**2 + 22/13*z**4 + 4/13*z = 0.
-1, 0, 2/13, 1
Let p be 2/(-4)*((-10)/(-35))/((-15)/140). Let x = -41 - -41. Factor 4/3*b**2 + 0*b + p*b**4 - 8/3*b**3 + x.
4*b**2*(b - 1)**2/3
Factor -68/7*y**2 + 112 + 4/7*y**4 - 108*y + 36/7*y**3.
4*(y - 4)*(y - 1)*(y + 7)**2/7
Factor 6272 - 6496*g + 1/2*g**4 - 58*g**3 + 1794*g**2.
(g - 56)**2*(g - 2)**2/2
Factor -9513*d - 888/7*d**2 - 3/7*d**3 - 18522.
-3*(d + 2)*(d + 147)**2/7
Solve 5*p**2 - 229*p**2 + 2*p**3 + 8*p**2 = 0 for p.
0, 108
Suppose -550*q + 8145*q - 8444234 = -1608734. Solve q + 1/4*n**2 - 30*n = 0 for n.
60
Let l be (20/(-15))/(((-4)/(-213))/(-2)). What is k in 22*k**5 + 472*k + 2230*k**3 + l*k**4 + 6*k**5 - 96 - 468*k**2 - 2298*k**3 - 10*k**4 = 0?
-4, -3, 2/7, 1
Solve 2720503424/7*g - 7365984/7*g**2 - 376789724224/7 - 4/7*g**4 + 8864/7*g**3 = 0 for g.
554
Factor -236/3 + 2/3*b**2 + 38*b.
2*(b - 2)*(b + 59)/3
Let n be (320/(-2880))/(4/(-6)). Let k(g) be the second derivative of -6*g**2 - 28*g - n*g**4 + 0 - 5/3*g**3. Factor k(d).
-2*(d + 2)*(d + 3)
Let v(r) be the third derivative of 2*r + 66*r**2 + 0 + 0*r**3 + 3/2*r**5 + 85/24*r**4 + 1/24*r**6. Find x, given that v(x) = 0.
-17, -1, 0
Let s = -281 + 306. Factor -220*f**2 - 66 + 23 + 60*f + 21 + 185*f**3 - s*f**4 + 22.
-5*f*(f - 6)*(f - 1)*(5*f - 2)
Let p(o) be the first derivative of -o**5/15 - o**4/6 + 29*o**3/9 - 7*o**2 - 964. Factor p(q).
-q*(q - 3)*(q - 2)*(q + 7)/3
Let d be (54 + 27 + -91)*(-1)/85. What is a in 0 + 2/17*a**2 - d*a**3 + 0*a = 0?
0, 1
Factor 338676/7*x + 3/7*x**3 - 685464/7 + 2022/7*x**2.
3*(x - 2)*(x + 338)**2/7
Let h(z) = 10*z**2 + 695*z + 25195. Let u = 275 - 270. Let d(s) = -9*s**2 - 698*s - 25197. Let l(o) = u*d(o) + 4*h(o). Let l(n) = 0. What is n?
-71
Let r(y) be the second derivative of -9*y**5/40 - 23*y**4/6 - 5*y**3/3 + 620*y + 2. Factor r(l).
-l*(l + 10)*(9*l + 2)/2
Let k(p) = -2*p**3 - 13*p**2 - 77*p + 37. Let a(s) = -9*s**3 - 66*s**2 - 375*s + 186. Let c(w) = -5*a(w) + 24*k(w). Factor c(d).
-3*(d - 7)*(d - 1)*(d + 2)
Let m = -154 + 257. Factor 285 - 115*n - 97 - 110 - 60*n**2 - m.
-5*(3*n + 5)*(4*n + 1)
Let y be (3/6)/(18/4). Let f = 28627/7173 + -2738/797. Factor -f*r**2 + 1/9*r**3 + 5/9 - y*r.
(r - 5)*(r - 1)*(r + 1)/9
Let x = 186951 + -1121705/6. Factor -x*c**2 - 32/3 + 8/3*c.
-(c - 8)**2/6
Suppose 3575138/3 - 5348/3*z + 2/3*z**2 = 0. Calculate z.
1337
Let v(f) = 2*f**3 + 5*f**2 - 322*f + 2. Let a be v(-14). Factor 0*t**a + 0*t - 245/4*t**3 - 5/4*t**5 + 0 - 35/2*t**4.
-5*t**3*(t + 7)**2/4
Let b(w) be the second derivative of -w**7/14 - 7*w**6/10 + 351*w**5/10 - 605*w**4/2 + 1175*w**3/2 + 7875*w**2/2 - 149*w + 3. Factor b(q).
-3*(q - 5)**3*(q + 1)*(q + 21)
Find s, given that 0 + 2/5*s**3 + 56/15*s + 16/5*s**2 - 2/15*s**4 = 0.
-2, 0, 7
Let c(j) = j**3 - 11*j**2 + 16*j + 20. Let a be c(9). Factor 6*q**a + 15*q**3 - q**2 + 133 - 133 - 20*q**4.
-5*q**2*(q - 1)*(4*q + 1)
Let m(c) be the third derivative of -c**5/210 - 5*c**4/42 + 8*c**3/3 + 3*c**2 - c + 273. Factor m(l).
-2*(l - 4)*(l + 14)/7
Let g be (7/(-15))/((4/3)/(48/(-42))). Factor 4/15*k**2 - 2/3 + g*k.
2*(k - 1)*(2*k + 5)/15
Factor 2/9*m**2 + 280/3 + 218/9*m.
2*(m + 4)*(m + 105)/9
Let y be 3*12/9 - 6. Let x be (-5)/y + (-12)/24. Find m such that -2/3*m + 0 - 1/3*m**3 + m**x = 0.
0, 1, 2
Let z(c) be the second derivative of 88*c - 95/6*c**4 - 330*c**3