 -2486/3 + 9946/3*y - 8/3*y**2 = 0.
1/4, 1243
Suppose 17*z - 340 = -306. Let y(h) be the first derivative of -2/5*h - 14 + 2/15*h**3 + 1/10*h**4 - 1/5*h**z. Suppose y(s) = 0. Calculate s.
-1, 1
Let r = -19731 - -19733. Factor -3/5 - 4/5*a**5 - 12/5*a**3 - 2/5*a**r + 8/5*a + 13/5*a**4.
-(a - 1)**4*(4*a + 3)/5
Let a = -64359/82 - 846/41. Let u = a + 808. Suppose -15/4*d**4 + 15*d - u*d**3 + 45/4*d**2 + 5 = 0. Calculate d.
-1, -2/3, 2
Let k(f) = 2*f**3 + 413*f**2 + 215*f + 1856. Let d be k(-206). Let 5/3*q**d - 24 + 178/3*q = 0. What is q?
-36, 2/5
Let q(t) be the second derivative of -5*t**4/12 + 490*t**3/3 + 84*t - 15. Factor q(z).
-5*z*(z - 196)
Suppose 99 + 27/2*o - 1/2*o**2 = 0. What is o?
-6, 33
Let h(k) be the second derivative of 2*k**6/135 - 4*k**5/45 + k**4/9 + 8*k**3/27 - 8*k**2/9 - k - 506. Determine s so that h(s) = 0.
-1, 1, 2
Let w = 58 - 53. Suppose -4*z + 4 = 0, 4*z + 13 = w*g - 3. Solve 16 - 6*d + 7 + 60*d**2 - 30*d**3 - 44*d + 5*d**g - 8 = 0 for d.
1, 3
Let t(b) be the third derivative of -9245*b**5/6 - 215*b**4/6 - b**3/3 + 3063*b**2 + 2*b. Factor t(j).
-2*(215*j + 1)**2
Let v = -12/25241 + 25325/176687. What is y in -1 + v*y**2 + 6/7*y = 0?
-7, 1
Suppose -35*y = -v - 34*y + 11, -3*v - 21 = 3*y. Find b, given that 1/3*b**5 + 0 + 0*b - 5/3*b**4 + 0*b**v + 2*b**3 = 0.
0, 2, 3
Suppose -584*k + 96*k + 785*k**3 - 138*k - 1250*k**2 - 781*k**3 = 0. What is k?
-1/2, 0, 313
Let s = 1716710 - 1716707. Let -38/9*c + 8/9*c**4 + 4/3 + 32/9*c**s + 10/9*c**2 = 0. What is c?
-3, -2, 1/2
Solve 8/21*z**3 - 1016/21 + 2018/21*z**2 - 3560/21*z = 0 for z.
-254, -1/4, 2
Suppose 2 = 2*h + 24. Let z be (-55)/h*(-1 - 632/(-10)). Suppose 69*o**2 + 48*o + 165*o**3 - 107*o**2 - 282*o**2 + 196*o**4 + z*o**3 = 0. Calculate o.
-3, 0, 2/7
Suppose -40 = 7*d - 54. Let 6*g**3 + 4*g**2 - 310*g - 4*g**2 - d*g**2 + 306*g = 0. What is g?
-2/3, 0, 1
Let b(f) be the third derivative of -f**7/630 + 283*f**6/180 - 81769*f**5/180 + 19810*f**4/3 - 39200*f**3 - 11869*f**2. Factor b(g).
-(g - 280)**2*(g - 3)**2/3
Let f(w) be the second derivative of -w**5/5 + 46*w**4/3 - 178*w**3/3 + 88*w**2 + 276*w. Factor f(q).
-4*(q - 44)*(q - 1)**2
Let r be 3/(-3)*(0 - 1). Let h(x) = x**4 - x**3 + x**2 + x + 1. Let z(f) = -5*f**4 - 13*f**3 + 37*f**2 - 23*f - 2. Let o(k) = r*z(k) + 2*h(k). Factor o(s).
-3*s*(s - 1)**2*(s + 7)
Let j(o) = -3*o**3 + 82*o**2 - 181*o + 90. Let m(i) = 3*i**3 + i**2 + 2*i. Let u(c) = j(c) + 2*m(c). Determine n so that u(n) = 0.
-30, 1
Let x be 6/(-6) + (-1 - -81). Let f = 81 - x. Factor -4*l**4 - 82*l**f + 12*l**3 + 74*l**2 + 0*l**4.
-4*l**2*(l - 2)*(l - 1)
Factor -90*b**2 + 63*b**3 - 27*b**3 - 255*b**3 + 15*b**4.
3*b**2*(b - 15)*(5*b + 2)
Suppose -u - 105 = -26. Let m = u - -104. Suppose 46*s**2 - s**2 + s - 45*s**4 + m*s**3 + 9*s - 35*s**5 = 0. What is s?
-1, -2/7, 0, 1
Let s(m) = 25*m**3 + 46*m**2 + 14*m. Let a(r) be the first derivative of -127*r**4/4 - 229*r**3/3 - 71*r**2/2 + 33. Let x(h) = 2*a(h) + 11*s(h). Factor x(z).
3*z*(z + 2)*(7*z + 2)
Let m be 3/9 - 4/3 - -1. Factor -2077*v + 3*v**2 + v**2 + 2073*v + m*v**2.
4*v*(v - 1)
Let u(t) be the second derivative of -t**5/5 - 16*t**4/3 - 54*t**3 - 252*t**2 - 2117*t. Factor u(r).
-4*(r + 3)*(r + 6)*(r + 7)
Let q(c) be the first derivative of -3*c**5/5 - 44*c**4/3 + 34*c**3/3 + 60*c**2 - 102*c + 15. Let v(f) be the first derivative of q(f). Factor v(h).
-4*(h - 1)*(h + 15)*(3*h + 2)
Let t(j) be the first derivative of j**4 + 128*j**3 + 4608*j**2 - 1131. Suppose t(s) = 0. What is s?
-48, 0
Suppose 60*k - 33*k - 243 = 0. Let s(u) be the second derivative of -1/6*u**3 - 1/4*u**4 + k*u + 0*u**2 + 1/20*u**5 + 0 + 1/10*u**6. Factor s(v).
v*(v - 1)*(v + 1)*(3*v + 1)
Let w = 4 + -4. Let x(i) = -i**3 - i**2 + 106*i + 456. Let t be x(-6). Factor 0*l**3 + 1/3*l**2 - 1/3*l**4 + w + t*l.
-l**2*(l - 1)*(l + 1)/3
Let i be 0 + 0 - -2 - (2 + -4). Let x(p) = p**3 + 2*p**2 + 1. Let k(u) = 2*u**3 + 34*u**2 - 27*u + 3. Let w(a) = i*k(a) - 12*x(a). Factor w(z).
-4*z*(z - 27)*(z - 1)
Solve -9*g**4 - 57918*g**3 + 116*g + 168 - 2*g**5 + 57*g**4 - 216*g**2 + 57806*g**3 - 2*g**5 = 0.
-1, 1, 6, 7
Let a(w) = -2*w**2 + 1. Let q(s) = 11*s**2 - 49*s - 161. Let h(r) = 15*a(r) + 3*q(r). Find g such that h(g) = 0.
-3, 52
Let k(j) = -j**3 + j**2 + j. Let x be 3 + (2/10 - 13/65). Let d(s) = 5*s**3 - 15*s**2 + 7*s. Let q(h) = x*k(h) - d(h). Factor q(o).
-2*o*(o - 2)*(4*o - 1)
Let w(c) be the second derivative of c**7/70 + 4*c**6/25 + 27*c**5/100 - 9*c**4/10 - 436*c. Suppose w(k) = 0. Calculate k.
-6, -3, 0, 1
Factor 59776471 - 125/3*n**4 + 9650*n**3 + 52896826/3*n - 735080*n**2.
-(n + 3)*(5*n - 391)**3/3
Let y be (-2 + -4 - (0 - (-120)/(-18)))/2. Let b(z) be the first derivative of y*z**2 + 1/9*z**3 + 1/3*z + 18. What is s in b(s) = 0?
-1
Let z(a) be the first derivative of -2*a**4 - 109 + 4*a**2 + 0*a**3 - 4/5*a**5 + 4*a. Solve z(x) = 0.
-1, 1
Factor 19 - 9*q**3 - 110 - 149 + 14*q**3 + 230*q - 65*q**2.
5*(q - 8)*(q - 3)*(q - 2)
Let k(x) be the third derivative of x**8/40320 + x**7/10080 - x**5/20 + x**4/8 - 38*x**2. Let f(m) be the third derivative of k(m). Factor f(n).
n*(n + 1)/2
Let a = 22372 - 22343. Let r(i) be the second derivative of 8/7*i**2 + a*i + 0 + 9*i**5 + 16/3*i**3 + 79/7*i**4. Find m such that r(m) = 0.
-1/3, -2/7, -2/15
Solve 1072 - 50*z**2 + 583*z + 513*z + 22 + 52*z**2 = 0 for z.
-547, -1
Let u(d) be the third derivative of -25/6*d**3 + 23*d - 5/4*d**4 + d**2 + 0 - 1/12*d**5. Find w, given that u(w) = 0.
-5, -1
Let y = -54 - -56. Factor -15*b**4 + 55*b**y - 42*b**3 - 23*b - 5*b**5 + 20 + 47*b**3 + 83*b.
-5*(b - 2)*(b + 1)**3*(b + 2)
Let s(n) = 6*n**3 + 181*n**2 - 860*n + 768. Let l(q) = 2*q**3 + 60*q**2 - 288*q + 256. Let r(u) = -19*l(u) + 6*s(u). Factor r(p).
-2*(p - 4)*(p - 1)*(p + 32)
Let w(t) = -5*t**2 - 28*t - 112. Let s(b) = 6*b**2 + 30*b + 115. Let j(u) = 4*s(u) + 5*w(u). Factor j(p).
-(p + 10)**2
Suppose 5*w = -20*w + 125. Suppose w*c + b = 27, 3*c - 5*b + 30 = 7*c. Suppose 0 - 3/2*m**4 + m**2 + m**c + 0*m - 3/2*m**3 = 0. Calculate m.
-1, 0, 1/2, 2
Let c(s) be the first derivative of 1/36*s**4 - 10/9*s + 10/27*s**3 - 1/18*s**2 + 255. Factor c(p).
(p - 1)*(p + 1)*(p + 10)/9
Let k(c) be the third derivative of 0*c - 1/84*c**4 + 0*c**3 - 16*c**2 - 1/42*c**5 + 0 + 1/70*c**6. Suppose k(u) = 0. Calculate u.
-1/6, 0, 1
Let p(v) be the third derivative of 121*v**3 + 59*v**2 + 0 + 0*v - 11/4*v**4 + 1/40*v**5. Factor p(w).
3*(w - 22)**2/2
Let d(s) be the third derivative of s**5/72 - 775*s**4/144 + 755*s**3/9 - 281*s**2 + 3*s. Factor d(j).
5*(j - 151)*(j - 4)/6
Suppose 0 = 5*o - u - 3694, -35*o = -34*o + 3*u - 742. Suppose o = 21*h + 676. Factor -4/7 - 10/7*j - 6/7*j**2 + 2/7*j**h + 2/7*j**4.
2*(j - 2)*(j + 1)**3/7
Let b(x) = 3*x**2 + 3. Let j be b(0). Factor 4*w**5 - 16*w + 184*w**4 + 148*w - 116*w**4 - 30*w + 52 + 110*w + 232*w**j + 328*w**2.
4*(w + 1)**4*(w + 13)
Suppose -6391*r - 5481 = -518*r - 17510 - 58447. Determine l so that -64/3*l + 16/3 - r*l**2 = 0.
-2, 2/9
Let w(z) = z - 28. Let d be w(32). Suppose p**d - 4*p + 1 - 9*p**2 - 6*p**3 - 1 - 2*p**4 = 0. What is p?
-4, -1, 0
Let a = 2843 - 2840. Let u(h) be the first derivative of 2/3*h**3 + 0*h + h**2 + a - 9/2*h**4 - 4/3*h**6 + 22/5*h**5. Factor u(b).
-2*b*(b - 1)**3*(4*b + 1)
Let v(c) be the third derivative of 2 + 1/60*c**4 + 0*c**5 - 2*c**2 - 1/900*c**6 + 0*c - 2/45*c**3. Factor v(u).
-2*(u - 1)**2*(u + 2)/15
Let o be (-8)/26*(21/(-84)*-110 + -34). Factor -1/8*z**4 + 3/4*z + 0 - 11/8*z**o + 3/4*z**3.
-z*(z - 3)*(z - 2)*(z - 1)/8
Let y(r) be the first derivative of 2*r**3 - 3343*r**2 + 2228*r + 1627. Factor y(f).
2*(f - 1114)*(3*f - 1)
Let r be 158/4 + -1 - 72/13536*47. Let -39/4*h**3 + 3/4*h**5 + 0 - 27*h - 9/4*h**4 + r*h**2 = 0. Calculate h.
-4, 0, 1, 3
Let v(d) = -d**3 + 5*d**2. Let x(t) = 4*t**2. Suppose -7*q - 11 = 10. Let n be (-6*1)/(6/(-4)). Let i(b) = n*v(b) + q*x(b). Factor i(g).
-4*g**2*(g - 2)
Let v = 68171 - 68171. Determine q so that -76/3*q**2 + 12*q + v - 4/3*q**4 + 44/3*q**3 = 0.
0, 1, 9
Let q(m) be the first derivative of -3*m**4/20 - 603*m**3/5 - 1465. Suppose q(l) = 0. What is l?
-603, 0
Let j(c) be the second derivative of -c**7/70 - 14*c**6/25 + 9*c**5/10 + 7*c**4/5 - 29*c**3/10 + 2341*c. What is q in j(q) = 0?
-29, -1, 0, 1
Suppose 0 - 426