*g**3/24 + 3647*g**2. Let w(t) = 0. Calculate t.
1, 65/2
Let p(i) be the second derivative of i**7/735 + i**6/70 - i**5/30 - 40*i**2 - 28*i. Let y(d) be the first derivative of p(d). Suppose y(w) = 0. Calculate w.
-7, 0, 1
Let r(x) be the third derivative of x**6/420 + 52*x**5/105 - 5*x**4/4 - x**2 + 23. Factor r(t).
2*t*(t - 1)*(t + 105)/7
Let b(p) = -28*p**4 + 24*p**3 + 36*p**2 + 16*p. Let u(y) = -y**4 + y**3 + y**2 + y. Let t be 0 + -5 - (28 - 32). Let h(s) = t*b(s) + 24*u(s). Factor h(w).
4*w*(w - 1)**2*(w + 2)
Let s(m) be the third derivative of m**7/105 - 27*m**6/5 + 161*m**5/15 + 27*m**4 - 323*m**3/3 + 796*m**2. Factor s(n).
2*(n - 323)*(n - 1)**2*(n + 1)
Factor -362124*x**3 + 181061*x**3 + 516*x**2 + 2025*x + 181066*x**3 + 1512.
3*(x + 1)*(x + 3)*(x + 168)
Determine y so that 328699*y**2 - 328677*y**2 - 10*y**4 - 4*y + 108*y**3 + 4*y = 0.
-1/5, 0, 11
Let h(r) be the second derivative of r**5/70 - 17*r**4/42 + 4*r**3/21 + 192*r**2/7 + 96*r - 3. Factor h(m).
2*(m - 16)*(m - 4)*(m + 3)/7
Factor -1/5*m + 59/5 + 1/5*m**3 - 59/5*m**2.
(m - 59)*(m - 1)*(m + 1)/5
Let m = -107 + 95. Let k be (78/m - -7)*(-15)/(-6). Find f, given that -k*f**2 - 5/4 + 5/2*f = 0.
1
Let v(t) be the second derivative of 0*t**3 + 0*t**2 + 1/18*t**6 - 1/20*t**5 + 0 + 3*t - 1/4*t**4 - 1/126*t**7. Factor v(x).
-x**2*(x - 3)**2*(x + 1)/3
Let y = 1351/9 - 6746/45. Let n(k) be the third derivative of 0 + 1/30*k**6 + 2*k**3 + 0*k - y*k**5 - 3*k**2 - 1/6*k**4. Suppose n(u) = 0. Calculate u.
-1, 1, 3
Let 0 - 8*m - 2/3*m**4 + 26/3*m**2 + 0*m**3 = 0. What is m?
-4, 0, 1, 3
Let q be (-12)/10 - (-644)/(-455) - -2. Let i = -3/26 - q. Determine o, given that 3/4*o - 3/4*o**4 - 3/4*o**2 + i - 7/4*o**3 = 0.
-1, 2/3
Suppose 5*h = 6 + 9. Solve 29*k + 29 + 3*k**h - 5 - 43*k - 35*k**2 = 0 for k.
-1, 2/3, 12
Let k(g) = -5*g**2 + 5844*g + 8555505. Let c(r) = -r**2 - r - 20. Let x(u) = -30*c(u) + 5*k(u). Determine t, given that x(t) = 0.
-2925
Let x(s) be the first derivative of -2*s**3/9 + 798*s**2 - 955206*s + 4341. Factor x(w).
-2*(w - 1197)**2/3
Let q(b) = b**3 + b**2 + 2*b + 1. Suppose 0*a - 20*a + 400 = 0. Let d(s) = -5*s**3 + 25*s**2 + 25*s + 7. Let u(r) = a*q(r) - 5*d(r). Factor u(f).
5*(f - 3)*(3*f + 1)**2
Let d(x) = x**2 + 4*x - 7. Let z be d(2). Let q(n) = 15*n**2 - 820*n + 32805. Let p(m) = -13*m**2 + 818*m - 32805. Let c(g) = z*p(g) + 4*q(g). Factor c(u).
-5*(u - 81)**2
Let d(l) = 12*l**2 + 5600*l + 2027680. Let o(t) = t**2 - 12*t - 12. Let z(m) = d(m) - 8*o(m). Let z(x) = 0. What is x?
-712
Let z(k) be the first derivative of -k**4/6 - 38*k**3/9 - 68*k**2/3 + 440*k/3 + 930. Factor z(q).
-2*(q - 2)*(q + 10)*(q + 11)/3
Let c(s) be the second derivative of s**7/231 + 4*s**6/165 - s**5/11 - 32*s**4/33 - 29*s**3/11 - 36*s**2/11 + 6*s + 52. Let c(v) = 0. What is v?
-3, -1, 4
Let r be (-1)/(14/(-168)*4/(-14)). Let o be (2 - 3/9)*r/(-35). Solve 4/5 - 1/10*j**3 - 6/5*j + 3/5*j**o = 0.
2
Let v be (312/(6 - -7))/(63/1750). Factor 200*a - v - 20*a**2 + 2/3*a**3.
2*(a - 10)**3/3
Suppose 21*n + 32*n = -10*n. Let m(z) be the third derivative of -25/2*z**3 - 5/4*z**4 - 1/20*z**5 + 0 + n*z - 14*z**2. Solve m(v) = 0.
-5
Let d(c) = c**2 - 133*c + 1974. Let n be d(17). Factor 7/3*o + 1/6*o**n + 13/6.
(o + 1)*(o + 13)/6
Let t(m) be the second derivative of -m**9/1890 + m**8/336 - m**7/315 - 20*m**4/3 - 20*m. Let l(o) be the third derivative of t(o). Factor l(n).
-4*n**2*(n - 2)*(2*n - 1)
Let s(z) = -3*z**4 + 1284*z**3 - 3757*z**2 + 3795*z - 1264. Let j(a) = -a**4 + 322*a**3 - 939*a**2 + 949*a - 316. Let k(r) = -22*j(r) + 6*s(r). Factor k(l).
4*(l - 1)**3*(l + 158)
Let q(i) = -3*i**3 - 9*i**2 + 50*i - 54. Let r(b) = -2*b**3 - 10*b**2 + 49*b - 55. Let j(p) = -7*q(p) + 6*r(p). Determine t so that j(t) = 0.
-3, 4/3
Let d(v) = v**2 + v + 1. Let y(h) = 4*h**2 - 90*h + 54. Let k(f) = 2*d(f) + y(f). Find g such that k(g) = 0.
2/3, 14
Suppose -26705 = 35*s + 12425. Let n = s + 8953/8. What is d in -n*d**2 - 1/2*d + 0 - 1/8*d**4 - 3/4*d**3 = 0?
-4, -1, 0
Let a(h) = 3*h**2 - 19*h - 113. Let f be a(19). Factor -730*o - 5*o**5 - 1110*o**3 - 115*o - 469*o**4 + 1820*o**2 + f*o**4.
-5*o*(o - 13)**2*(o - 1)**2
Let t = 312 - 309. Suppose -q - 4*m - 22 = -2*q, 25 = -5*m. Factor -4*z - 4*z**2 - q*z**t + 4*z**4 - 3*z**3 + 9*z**3 + 0*z**2.
4*z*(z - 1)*(z + 1)**2
Let f(j) be the second derivative of 169*j + 15/4*j**2 + 1/3*j**6 + 205/24*j**4 + 137/40*j**5 + 0 + 103/12*j**3. Suppose f(h) = 0. Calculate h.
-5, -1, -3/5, -1/4
Let z be (9 - 368/40) + 37596/(-45). Let p = z - -842. Let -4/3 - 8/3*x**3 - 9*x**2 + 4/3*x**4 - p*x = 0. Calculate x.
-1, -1/2, 4
Suppose -6*g = -27 + 3. Solve 10*y**2 - 21*y**4 + 4*y**3 - 1 - 7*y**5 + 3*y + 9*y**4 + g*y**2 - 1 = 0.
-1, 2/7, 1
Let m(x) be the first derivative of -3/5*x - 1/30*x**3 - 16 - 1/4*x**2. Factor m(b).
-(b + 2)*(b + 3)/10
Let d = 25936 + -25934. Let u(j) be the first derivative of -5 + 21/2*j**d + j**3 + 0*j. Find g, given that u(g) = 0.
-7, 0
Suppose -2*t = -4*o + 22, 129*o - 3*t - 11 = 134*o. Let j = -12 + 27/2. Factor -3 - j*k + 3/2*k**3 + 3*k**o.
3*(k - 1)*(k + 1)*(k + 2)/2
Let l(a) be the third derivative of 1/240*a**6 - 17*a**2 + 0 + 0*a**4 + 0*a**3 - 1/280*a**7 + 0*a + 0*a**5 + 1/1344*a**8. Factor l(o).
o**3*(o - 2)*(o - 1)/4
Factor 2142/13*v - 348/13*v**2 - 2/13*v**3 - 3240/13.
-2*(v - 3)**2*(v + 180)/13
Let y be (-1 + 4)*12*24/2592. Let p = -45 - -48. Factor -4/3 - 2/3*r**2 + 7/3*r - y*r**p.
-(r - 1)**2*(r + 4)/3
Let l(z) be the second derivative of -z**4/36 + 5*z**3/2 - 247*z**2/3 - 651*z. Factor l(v).
-(v - 26)*(v - 19)/3
Let f(c) = 40*c**3 - 4520*c**2 + c - 109. Let v be f(113). What is m in -2/15*m**v + 0*m**2 + 0 - 6/5*m**3 + 0*m = 0?
-9, 0
Let o(y) be the third derivative of 0 + 1/9*y**3 - 1/15*y**5 + 5/36*y**4 + 20*y**2 + 0*y. Factor o(d).
-2*(d - 1)*(6*d + 1)/3
Suppose 0 = 5*j + 3*o - 0*o - 39, -2*j = -5*o + 3. Let w be -2*10/(-4)*4. Factor w*v**2 + j*v**4 - 31*v**4 - 40*v + 5*v**5 + 26*v**3 + 4*v**3.
5*v*(v - 2)**3*(v + 1)
Let q = -97120/3 + 194243/6. Factor -q*v**2 + 45/2*v + 0.
-v*(v - 45)/2
Let l = 2313 + -2323. Let d be (-154)/(-35) + l + 6. Suppose -1/5*p**4 + 0 - d*p**3 + 2/5*p + 1/5*p**2 = 0. What is p?
-2, -1, 0, 1
Let x(d) be the third derivative of 0*d - 102*d**2 - 1/36*d**6 + 0*d**3 + 1/9*d**4 + 0 - 1/105*d**7 + 2/45*d**5. Determine m so that x(m) = 0.
-2, -2/3, 0, 1
Let r be 4/12 + 13/(1560/50). Let h(d) be the second derivative of 0 + 1/72*d**4 - 1/6*d**3 + r*d**2 + 6*d. Let h(o) = 0. What is o?
3
Let n = 69842/11 + -6349. Factor -1/11*b**5 + 4/11 + 1/11*b**3 + b**2 + 12/11*b - n*b**4.
-(b - 2)*(b + 1)**3*(b + 2)/11
Determine i, given that 105*i - 2487 - 2325 - 2367 + 5*i**2 + 7449 = 0.
-18, -3
Solve 7215*o**2 + 66*o**4 - 1208*o - 44*o**4 + 385*o**3 - 6397*o - 17*o**4 = 0.
-39, 0, 1
Let f(c) = -785*c - 11772. Let l be f(-15). What is d in -1/4*d**4 - 64 - 193/4*d**2 - 120*d + 15/2*d**l = 0?
-1, 16
Factor 1/6*l**2 + 8*l + 215/6.
(l + 5)*(l + 43)/6
Let a(i) be the third derivative of 19/24*i**4 - 1/240*i**5 + 0 - 361/6*i**3 + 0*i - 216*i**2. Factor a(o).
-(o - 38)**2/4
Let q be 180/27*(4 - 502/(-5)). Suppose -4*z**3 - 17596*z + 8341*z - 13361*z - 16692*z - q*z**2 - 1060*z - 780448 = 0. Calculate z.
-58
Let n(y) be the first derivative of y**6/90 + y**5/10 - 4*y**4/9 + 9*y + 100. Let k(r) be the first derivative of n(r). Find o such that k(o) = 0.
-8, 0, 2
Let z = -30 - -31. Suppose 4*h = -2*v + 1 - 15, h = -2*v + z. Find j such that 3 + 2 - 2 - v*j**2 + 0 = 0.
-1, 1
Let 0 + 505/2*b**2 + 0*b + 1/2*b**3 = 0. Calculate b.
-505, 0
Let l(g) = -92*g**2 - 2*g + 118. Let u(q) = 15*q**2 - 1. Let z(n) = l(n) + 6*u(n). Factor z(t).
-2*(t - 7)*(t + 8)
Factor 1056/17*p**2 + 185856/17*p + 10903552/17 + 2/17*p**3.
2*(p + 176)**3/17
Let m(q) = -10*q**2 - 7*q - 7. Suppose 7*f - 4*f - 12 = 0. Let r be 44/4 - f/1. Let p(a) = -5*a**2 - 4*a - 4. Let b(k) = r*p(k) - 4*m(k). Solve b(s) = 0 for s.
0
Let j = 57616 - 57614. Solve 0*o + 2/3*o**j - 2/3 = 0 for o.
-1, 1
Let u(a) be the first derivative of -a**4/72 - a**3/18 + a**2/4 - 34*a - 62. Let n(x) be the first derivative of u(x). Factor n(q).
-(q - 1)*(q + 3)/6
Let v(o) be the first derivative of o**4/42 + 2*o**3/3 - 32*o**2/7 - 54*o + 94. Let c(f) be the first derivative of v(f). Factor c(t).
2*(t - 2)*(t + 16)/7