the first derivative of -112*r**4 + 0*r**2 - 1/3*r**6 - 58/5*r**5 + 93 - 392/3*r**3 + 0*r. Let x(o) = 0. Calculate o.
-14, -1, 0
Let g(m) be the first derivative of -2*m**3/33 - 32*m**2/11 - 512*m/11 - 1982. Let g(b) = 0. Calculate b.
-16
Suppose 6*t - 71 = 1093. Suppose 11*p - t = 4. Factor -17*g - p*g + 17*g + 8 + 5*g**2 - 2*g**3 + 7*g**2.
-2*(g - 4)*(g - 1)**2
Factor -604 + 24*u**4 - 64*u**2 - 49*u**3 + 181*u + 4*u**5 + 9*u**3 - 49*u + 548.
4*(u - 1)**3*(u + 2)*(u + 7)
Determine j, given that -215/3*j**4 - 2095/3*j**3 - 1885/3*j**2 - 5/3*j**5 + 0*j + 0 = 0.
-29, -13, -1, 0
Determine u so that 63 + 222*u + 657/4*u**3 + 141/4*u**4 + 3/4*u**5 + 1155/4*u**2 = 0.
-42, -2, -1
Factor 114 - 3/8*y**3 + 27*y**2 + 225/2*y.
-3*(y - 76)*(y + 2)**2/8
Let w be 15/((-4875)/52)*5/(-7). Let j(u) be the first derivative of -388/21*u**3 + 288/7*u**2 + 18/7*u**4 - w*u**5 + 1 - 256/7*u. Find k such that j(k) = 0.
1, 8
Let o(r) be the third derivative of r**6/120 - 43*r**5/45 + 25*r**4/8 - 28*r**3/9 + 664*r**2 - 2*r. Find n such that o(n) = 0.
1/3, 1, 56
Let h(p) be the third derivative of p**8/264 - 4*p**7/385 + p**6/220 + p**5/165 + 1382*p**2. Factor h(k).
2*k**2*(k - 1)**2*(7*k + 2)/11
Determine s so that -112/13 + 12/13*s + 2/13*s**3 + 18/13*s**2 = 0.
-7, -4, 2
Factor 2*l**4 - 19*l**3 + 27*l**3 - 66*l - 2*l**2 + 4*l**3 + 20*l + 34*l**3.
2*l*(l - 1)*(l + 1)*(l + 23)
Let c(z) be the third derivative of 0*z**3 + 1/160*z**6 - 16*z**2 + 0 + 0*z - 1/8*z**4 + 3/80*z**5. Suppose c(d) = 0. Calculate d.
-4, 0, 1
Let z(w) be the third derivative of -w**5/15 - 25*w**4/6 - 104*w**3 - 1132*w**2. Find x, given that z(x) = 0.
-13, -12
Suppose 5*n - 17 = 4*z + 17, -16 = n + 3*z. Let u(j) be the third derivative of 1/280*j**6 + 0 - 1/56*j**4 + 0*j**3 - 17*j**n + 0*j + 0*j**5. Factor u(x).
3*x*(x - 1)*(x + 1)/7
Let u be (9/(-6))/(6/(-8)). Let y(v) = -v**2 + 22*v - 19. Let a be y(21). Determine h, given that 15*h**3 + 38*h**a + 3*h**4 - 14*h**u - 6*h + 18*h = 0.
-2, -1, 0
Let -9*l - 205/4 + 1/4*l**2 = 0. Calculate l.
-5, 41
Find j, given that -178/3*j - 50/21*j**2 + 100/21 = 0.
-25, 2/25
Solve -11560 + 325*p**3 - 1863498*p**4 - 6039*p**2 + 1863493*p**4 + 1269*p**2 - 16660*p = 0.
-2, -1, 34
Suppose 147*d - 145*d = -44. Let c(s) = -s**5 + 4*s**4 - 17*s**3 + 4*s**2 + 10*s. Let x(q) = q**3 - q. Let w(r) = d*x(r) - 2*c(r). Factor w(p).
2*p*(p - 1)**4
Let i be (-1564)/(-34) - (-54600)/(-1190). Factor 0*x**4 - 12/17*x**3 + 16/17*x**2 + i*x**5 - 6/17*x + 0.
2*x*(x - 1)**3*(x + 3)/17
Suppose -p + 197 = 192. Let d be (-6 - (-231)/35)*p. Factor 2/15*k**4 + 8/15*k + 0*k**2 + 0 - 2/5*k**d.
2*k*(k - 2)**2*(k + 1)/15
Let w(i) be the first derivative of 2 + 1/12*i**4 - 1/3*i**3 + 1/3*i**2 + 0*i. Suppose w(m) = 0. What is m?
0, 1, 2
Let h(p) = 3*p**4 + 146*p**3 + 5*p**2 - 148*p + 4. Let g(k) = 5*k**4 + 147*k**3 + 7*k**2 - 150*k + 6. Let m(l) = -2*g(l) + 3*h(l). Factor m(q).
-q*(q - 144)*(q - 1)*(q + 1)
Let t(y) be the first derivative of 9/2*y**2 - y**3 - 130 + 12*y. Suppose t(b) = 0. What is b?
-1, 4
Let m(a) be the second derivative of -a**6/6 - 3*a**5/4 + 845*a**4/6 - 1550*a**3 - 5500*a**2 + 2414*a. What is n in m(n) = 0?
-22, -1, 10
Let h be (-4 - (-7579)/1196) + (-1 - (-42)/46). Let d(k) be the first derivative of h*k + 5/4*k**2 + 1/12*k**3 - 12. Determine s, given that d(s) = 0.
-9, -1
Let p be 740/3465 + -2*6/66. Let d(o) be the first derivative of -1/42*o**4 + 4/21*o**2 - 8/21*o - 5 + p*o**3. Solve d(i) = 0 for i.
-2, 1, 2
Let q = -221866 - -221868. What is l in 0 - 22/5*l**q + 12/5*l + 12/5*l**3 - 2/5*l**4 = 0?
0, 1, 2, 3
Let k(v) be the third derivative of -v**4/12 + v**3/6 - 4*v**2 - 1. Let r be k(-1). Factor 9*f**r + 18*f**2 - 13*f**2 - 7*f**3 + 8*f**3 + 5*f**4.
5*f**2*(f + 1)**2
What is c in -3/5*c**2 + 6/5*c + 9/5 = 0?
-1, 3
Find k such that 1742/3*k - 2/3*k**3 - 868/3*k**2 - 872/3 = 0.
-436, 1
Let z be -41 - (4 + 5050/(-100)). Factor -z*u**2 + 12*u - 2.
-(u - 2)*(11*u - 2)/2
Let r(v) be the third derivative of -v**5/30 - 3*v**4 - 35*v**3/3 + 497*v**2 - v. Factor r(k).
-2*(k + 1)*(k + 35)
Suppose 18 = 3*u - 5*a, u + u + 3*a = 50. Let j(f) be the first derivative of 5/6*f**6 - f**5 + 20*f**2 + u - 25/4*f**4 + 20*f + 5/3*f**3. Factor j(r).
5*(r - 2)**2*(r + 1)**3
Determine j so that -73*j**5 + 71*j**5 - 498*j - 14*j**3 + 990*j + 32 - 46*j**2 - 476*j + 14*j**4 = 0.
-1, 1, 4
Let l(j) be the second derivative of -7*j**6/18 + 13*j**5/12 + 5*j**4/18 - 1588*j. Factor l(a).
-5*a**2*(a - 2)*(7*a + 1)/3
Suppose -86*a + 306*a - 783 = -41*a. Factor -a*f**3 - 21*f + 18*f**2 + 15/2 - 3/2*f**4.
-3*(f - 1)**3*(f + 5)/2
Factor 280 - 2/3*b**3 + 50*b**2 - 712/3*b.
-2*(b - 70)*(b - 3)*(b - 2)/3
Let g = 7692 + -7692. Let l(k) be the second derivative of 1/90*k**5 - 1/27*k**3 + 1/9*k**2 + 19*k + g - 1/54*k**4. Factor l(c).
2*(c - 1)**2*(c + 1)/9
Let v = 212 - 210. Suppose s + v*s = s. Factor 2/11*d**2 + 2/11*d - 4/11*d**3 + s.
-2*d*(d - 1)*(2*d + 1)/11
Let j(u) = 9*u**2 + 516*u - 2205. Let a(b) = -b**2 - 74*b + 315. Let c(w) = -15*a(w) - 2*j(w). Solve c(l) = 0.
5, 21
Let x(s) = s**2 - 3*s - 14. Let o be x(6). Suppose -105 + 65 = -4*p. Suppose p*q**2 - 5*q**o + 29*q + 29*q - 5 - 58*q = 0. What is q?
-1, 1
Let b(q) be the first derivative of 5*q**4/78 - 97*q**3/39 + 38*q**2/13 + 79*q - 67. Let x(l) be the first derivative of b(l). Factor x(t).
2*(t - 19)*(5*t - 2)/13
Solve 424/7*c**2 + 0*c - 4/7*c**4 - 204/7*c**3 + 0 = 0.
-53, 0, 2
Let f(q) = 374*q**3 + 3533*q**2 + 5364*q + 2294. Let a(l) = -188*l**3 - 1766*l**2 - 2682*l - 1146. Let i(u) = -13*a(u) - 6*f(u). Factor i(y).
2*(y + 7)*(10*y + 9)**2
Let o = 327475/2 - 163737. Suppose o*x**2 + 0 + 27/4*x = 0. What is x?
-27/2, 0
Let r be (2/13)/((6365/(-67))/(-1235)). Factor 3/2*n**r + 99/2*n - 51.
3*(n - 1)*(n + 34)/2
Suppose -5*n = -0*n - 150. Let y = 1368 - 1373. Let q(b) = -5*b**2 + 3*b. Let z(s) = -s**2. Let g(w) = n*z(w) + y*q(w). Factor g(p).
-5*p*(p + 3)
Let a(k) = 2*k**5 + k**4 + k**3 + k + 1. Let p(m) = -2 + 32*m**2 - 18*m**5 - 26*m**4 + 342*m - 16 - 2*m**3 - 346*m. Let z(n) = 12*a(n) + 2*p(n). Solve z(o) = 0.
-3, -1, 2/3, 1
Let k(i) be the third derivative of i**10/5400 + i**9/7560 - i**8/45 - 8*i**7/315 + i**5/4 + 53*i**2. Let f(x) be the third derivative of k(x). Factor f(y).
4*y*(y - 4)*(y + 4)*(7*y + 2)
Let c(g) = -15*g**2 + 615*g + 1292. Let k be c(43). Suppose 15/4*m**4 - 9/2*m**3 - 3/2*m**k + 21/4*m - 3/4*m**5 - 9/4 = 0. Calculate m.
-1, 1, 3
Let g(r) be the second derivative of r**6/720 - 7*r**5/240 + 5*r**4/24 - 13*r**3 + 3*r + 17. Let f(w) be the second derivative of g(w). Factor f(i).
(i - 5)*(i - 2)/2
Factor 2/15*r**3 + 326/15*r**2 - 1346/15*r - 334/3.
2*(r - 5)*(r + 1)*(r + 167)/15
Let t(j) be the third derivative of -59/32*j**4 - 15/4*j**3 + 0 + 0*j - 7/20*j**5 - 118*j**2 + 1/160*j**6. Factor t(h).
3*(h - 30)*(h + 1)**2/4
Let r(f) be the first derivative of -f**3/2 + 3*f**2 - 9*f/2 - 5458. Factor r(o).
-3*(o - 3)*(o - 1)/2
Suppose -55*w - 34 + 53 + 696 = 0. Let c(x) be the second derivative of -2*x**4 + w*x + 26/3*x**3 - 1 - 4*x**2. Factor c(m).
-4*(m - 2)*(6*m - 1)
Let n be 0*((-750)/1080 + ((-23)/9 - -3)). Find b, given that -2/11*b**3 - 6/11*b**2 + n - 4/11*b = 0.
-2, -1, 0
Let x = -194 + 224. Factor r**3 + x*r - 106 + 2*r**3 - r**3 + 18*r**2 + 120.
2*(r + 1)**2*(r + 7)
Let j(s) be the second derivative of -2*s**6/75 - 191*s**5/25 - 938*s**4/15 - 2984*s**3/15 - 1488*s**2/5 - 3997*s. Determine p, given that j(p) = 0.
-186, -2, -1
Let v(w) be the second derivative of -w**4/28 - 426*w**3/7 + 2559*w**2/14 + 1022*w. Factor v(z).
-3*(z - 1)*(z + 853)/7
Let z(w) be the second derivative of w**4/30 + 578*w**3/15 + 2586*w. Factor z(s).
2*s*(s + 578)/5
Let p(c) be the first derivative of -65 - 8/15*c**3 + 0*c - 1/10*c**4 - 3/5*c**2. Factor p(o).
-2*o*(o + 1)*(o + 3)/5
Suppose 18 + 237*t + 233*t + 4*t**4 + 4*t**3 - 473*t - 22*t**2 + 5*t**5 - 6*t**5 = 0. Calculate t.
-2, -1, 1, 3
Let n(r) be the third derivative of -r**7/210 - 71*r**6/60 - 47*r**5/20 - 660*r**2. Find q, given that n(q) = 0.
-141, -1, 0
Let o(h) = 2*h**2 - 31*h - 3. Let y be o(16). Suppose 4*a = -f + 10, -5*a - f - 1 = -y. Solve 9*v**4 + 2 + 5*v - 11*v**a + 7*v**3 - 19*v + 7*v = 0.
-1, 2/9, 1
Let j(c) be the first derivative of -c**6/180 - 11*c**5/30 - 121*c**4/12 - 37*c**3/3