p) = 1729*p + 29396. Let c be m(-17). Factor -1/5*o**c - v*o**2 - 144/5*o + 0.
-o*(o + 12)**2/5
Suppose 41 + 0 = -a + 5*o, -16 = -4*o. Let h = a - -24. What is d in -24*d**4 - 7*d**3 + 4*d + 0*d**h - 8*d**2 + 29*d**4 = 0?
-1, 0, 2/5, 2
Solve -324/5*g**4 - 27024/5*g + 4032/5*g**3 + 59492/5*g**2 + 3024/5 = 0 for g.
-9, 2/9, 21
Let n(b) be the first derivative of b**4/120 + b**3/6 - 11*b**2/20 - 35*b + 64. Let q(z) be the first derivative of n(z). Solve q(y) = 0 for y.
-11, 1
Suppose 5*g - 8815 = -2*y + 7*y, 2*y - 7022 = -4*g. Factor -140*k - 39*k**2 - 1759*k**3 + g*k**3 + 288 + 104 + 13*k**2.
-(k - 2)*(k + 14)**2
Let b(f) be the first derivative of 5*f**6/18 - 22*f**5/3 + 40*f**4 + 1310*f**3/9 + 715*f**2/6 + 2383. What is u in b(u) = 0?
-1, 0, 11, 13
Let d(z) be the third derivative of 0 + 253/18*z**4 + 1/180*z**6 + 80*z - 91/180*z**5 - z**2 + 529/18*z**3. Find t, given that d(t) = 0.
-1/2, 23
Let j = -108434 + 108438. Let b(h) = -h**2 - 7*h - 4. Let v be b(-6). Factor -2/3*k - 2*k**v - 2*k**3 - 2/3*k**j + 0.
-2*k*(k + 1)**3/3
Suppose 29*j + 1771 - 1829 = 0. Factor -1/2*g + j - 1/4*g**2.
-(g - 2)*(g + 4)/4
Let g(p) be the second derivative of -p + 0*p**2 + 11/6*p**4 + 121/3*p**3 + 1/40*p**5 + 3. Factor g(f).
f*(f + 22)**2/2
Find m, given that 155*m**3 + 1/4*m**5 + 13*m**4 - 755/2*m**2 + 729/2 - 621/4*m = 0.
-27, -1, 1, 2
Let h(o) = o**2 - o - 16. Let k be h(-4). Factor 15*d**3 + 17*d**2 + 7*d + 28*d**2 - 20*d**4 - 8*d + k*d + 7*d.
-5*d*(d - 2)*(d + 1)*(4*d + 1)
Let b = 49 + -45. Suppose -44 = -2*h - 2*h. Let g(r) = 5*r**2 + 11*r - 5. Let w(a) = -2*a**2 - 4*a + 2. Let i(m) = b*g(m) + h*w(m). Factor i(o).
-2*(o - 1)*(o + 1)
Let d(b) = b**2 + 19*b - 20. Let w be d(-20). Factor -3*m**3 + w + 16*m**2 - 44*m + 7*m**3 + 24.
4*(m - 1)**2*(m + 6)
Suppose -16*f + 21 = -9*f. Let n be 27/(-18)*(-8)/f. Factor 6*m**5 + 3*m**5 - 135*m - 61*m**n + 190*m**3 - 5*m**4 - 90*m**2 - 27 - 9*m**4.
(m - 3)**3*(3*m + 1)**2
Let w = 72397696 + -160360890891/2215. Let x = w - -2/443. Solve 1/5*t**4 - 12/5*t + x*t**2 + 4/5 - 6/5*t**3 = 0.
1, 2
Find d, given that 0 + 699/2*d - 2793/4*d**2 - 3/2*d**3 = 0.
-466, 0, 1/2
Let g be 38*13181/145236 + (-1)/39*-2. Find i, given that -9/2*i**2 - 7/2*i + 1/2*i**4 + 4 + g*i**3 = 0.
-8, -1, 1
Let j(t) = -t**2 + 16*t + 63. Let r be j(19). Suppose 3*p + 16 = r*p - 4*k, 5*p - 4*k - 24 = 0. Factor 0 - 3/7*h**2 - 15/7*h**3 + 3/7*h**p + 15/7*h.
3*h*(h - 5)*(h - 1)*(h + 1)/7
Let g(t) be the second derivative of t**5/45 - 19*t**4/54 + 38*t**3/27 - 7*t**2/3 + 37*t + 6. Factor g(d).
2*(d - 7)*(d - 1)*(2*d - 3)/9
Let h be (-416)/(-39)*(-36)/(-3). Let p = -126 + h. Factor 0 - 2/9*u**p - 2/9*u.
-2*u*(u + 1)/9
Suppose 69*m = 76*m - 14. Solve 30*c**m - 29*c**2 - 33 + 2*c + 30*c = 0 for c.
-33, 1
Let i(s) = -14*s**2 + 89*s + 3060. Let v(q) = -25*q**2 + 175*q + 6120. Let h(c) = 5*i(c) - 3*v(c). Factor h(g).
5*(g - 34)*(g + 18)
Let z(k) be the first derivative of -8*k**2 + 32*k - 65 + 2/3*k**3. Find i, given that z(i) = 0.
4
Let h be ((-5)/(-3))/(76 - 66211/876). Factor -1/5*j**2 + 0 - h*j.
-j*(j + 20)/5
Let r(k) = 2*k**5 - 7*k**4 + k**3 + 24*k**2 + 21*k + 7. Let v(q) = 2*q**5 - 7*q**4 + 23*q**2 + 20*q + 6. Let m(d) = 6*r(d) - 7*v(d). Solve m(f) = 0 for f.
-1, 0, 2, 7/2
Find l such that 6*l**2 + 36/7*l - 2/7*l**5 - 10/7*l**4 - 2/7*l**3 + 0 = 0.
-3, -1, 0, 2
Factor -2*g**4 - 12114*g**2 + 12284*g**2 - 3*g**4 + 0*g**4 - 75*g**3.
-5*g**2*(g - 2)*(g + 17)
Let p(b) be the second derivative of -3*b**5/20 - 39*b**4/4 - 507*b**3/2 - 6591*b**2/2 - 1152*b. Factor p(g).
-3*(g + 13)**3
Let m = 685 - 685. Suppose m = 19*y + 560 - 598. What is l in 26/11*l + 1/11*l**y + 169/11 = 0?
-13
Let g(t) = 10*t**2 + 86*t - 179. Let r(i) = -52*i**2 - 432*i + 896. Suppose -48*p - 96 = -42*p. Let v(z) = p*g(z) - 3*r(z). Let v(s) = 0. What is s?
-22, 2
Let a = -70 + 65. Let l(i) = -8*i - 17. Let x be l(a). Factor 21 - 4*t - 2*t**2 - 46 + x.
-2*(t + 1)**2
Let -152/5*n - 4/5*n**4 - 156/5 + 32*n**2 + 152/5*n**3 = 0. Calculate n.
-1, 1, 39
Factor 16182005/3 + 17990/3*x + 5/3*x**2.
5*(x + 1799)**2/3
Let i(b) be the second derivative of -13*b - 490*b**2 - 5/12*b**4 - 70/3*b**3 + 3. Let i(z) = 0. Calculate z.
-14
Let o(v) be the second derivative of -4/105*v**7 - 8/5*v**3 + 2 - 17/30*v**4 - 70*v + 1/25*v**6 + 11/25*v**5 + 4*v**2. Find f, given that o(f) = 0.
-2, -5/4, 1, 2
Let p(z) be the second derivative of -43*z**5/30 - 13*z**4/3 - 3*z**3 + 8*z**2/3 - 8597*z. Factor p(w).
-2*(w + 1)**2*(43*w - 8)/3
Suppose 12 = 4*r - j - 3*j, r + 5*j = -3. Suppose 24 + 10 = r*b. What is w in -6*w**4 + 10*w**5 + 26*w**3 + b*w**3 + 11*w**3 + 4*w - 68*w**3 + 6*w**2 = 0?
-1, -2/5, 0, 1
Factor 1224/5*b - 1/5*b**2 + 0.
-b*(b - 1224)/5
Factor -6/5*r**3 + 0 + 11/5*r + 13*r**2.
-r*(r - 11)*(6*r + 1)/5
Let x = -1 - -1. Suppose 8*p + p - 18 = x. Factor 21*l + 51 + 13 + 11*l + 20*l**2 - 16*l**p.
4*(l + 4)**2
Let z be (105/(-14))/(-1)*(27 - (-802)/(-30)). Factor 1/6*y**3 - 7/6*y**z + 5/3*y + 0.
y*(y - 5)*(y - 2)/6
Let v = 6330 - 6311. Let z(r) be the first derivative of -5*r**2 + 5*r**3 + 0*r + 105/4*r**4 + 15/2*r**6 + 25*r**5 + v. Find m, given that z(m) = 0.
-1, 0, 2/9
Let z(l) = 3*l + 50 - 5*l**2 - 10*l**2 - 3*l**3 + 2*l**3 - l**2. Let p be z(-16). Factor 25*o**4 + 5*o**5 - 3*o + 3*o - 491*o**2 + 15*o**3 + 446*o**p.
5*o**2*(o - 1)*(o + 3)**2
Let l(d) be the first derivative of -d**4/4 + 170*d**3/3 + 715. Factor l(x).
-x**2*(x - 170)
Let y(q) = 7*q**2 + 74*q - 122. Let c(v) = 4*v**2 + 5*v + 1. Let x(m) = 6*c(m) - 3*y(m). Factor x(j).
3*(j - 62)*(j - 2)
Let h(o) be the first derivative of o**5/70 + 23*o**4/42 + 37*o**3/7 + 153*o**2/7 - 142*o + 9. Let a(l) be the first derivative of h(l). Factor a(q).
2*(q + 3)**2*(q + 17)/7
Let a(z) = -z**3 - 6*z**2 + 15*z - 2. Let c be a(-8). Suppose c*j - 20 = j. Factor -8 + 3*h**2 + 5*h**2 - 9*h - j - 5*h**2.
3*(h - 4)*(h + 1)
Let i(b) = b**3 - b**2 - 8. Suppose 0*l = -4*c + l - 56, c - 4*l - 1 = 0. Let h(o) = -o**2 - o - 2. Let a(y) = c*h(y) + 3*i(y). Suppose a(u) = 0. Calculate u.
-2, -1
Determine j, given that -12/5*j**2 + 231/5*j**4 + 96/5*j**3 + 18*j**5 + 0*j + 0 = 0.
-2, -2/3, 0, 1/10
Let v(s) be the second derivative of 15/14*s**2 + 3/2*s**3 + 0 + 9/70*s**6 + 17/14*s**4 + 1/98*s**7 - 197*s + 39/70*s**5. Find f such that v(f) = 0.
-5, -1
Let y(o) be the first derivative of o**6/2 - 27*o**5 + 324*o**4 + 1728*o**3 + 638. Find p such that y(p) = 0.
-3, 0, 24
Suppose 0 = -n + p + 30, -2*n + 109 - 21 = 5*p. Let b(z) be the second derivative of n*z + 3/4*z**2 - 1/2*z**3 + 1/8*z**4 + 0. Factor b(d).
3*(d - 1)**2/2
Let j(q) be the first derivative of -1198*q**2 + 303 + 22*q**3 + 1004*q**2 - 264*q + q**4 - 62*q**3. Factor j(c).
4*(c - 33)*(c + 1)*(c + 2)
Let w = -102 + 107. Let x be (6 - -2)/((-2)/(-4)). Solve 1 + 98*k**w - 220*k**3 - x*k**2 + 46*k**5 + 16*k - 176*k**4 - 1 = 0 for k.
-1/2, 0, 2/9, 2
Let c = -2988112 - -15054533/5. Let h = c + -22719. Factor 12*l**3 - 3/5*l**4 + 588/5*l + 1029/5 - h*l**2.
-3*(l - 7)**3*(l + 1)/5
What is p in 2/5*p**2 - 292*p + 53290 = 0?
365
Let o(g) be the second derivative of 2*g**7/21 - 4*g**6/3 - 27*g**5/5 + 304*g**4/3 + 640*g**3/3 + 3774*g. Let o(v) = 0. Calculate v.
-5, -1, 0, 8
Let v = 270447 - 1081761/4. Factor 27 + v*o - 3/4*o**2.
-3*(o - 12)*(o + 3)/4
Let c be 0/((195/13)/15). Let t(b) be the first derivative of c*b**3 + 0*b**2 - 3 + 0*b + 1/20*b**4. Factor t(p).
p**3/5
Let -1/3*p**2 - 25*p - 198 = 0. Calculate p.
-66, -9
Suppose -1872*c = -1868*c - 28. Suppose -6*z**2 - 2*z**4 + 5 + 1 + 21*z**3 - c*z**4 - 9*z - 3*z**2 = 0. What is z?
-2/3, 1
Suppose 4*q = -5*v - 139, -2*v + 105 = -3*q - 5*v. Let m be (5 + q/9)*0. Factor 2/9*u**2 + 2/3*u + m.
2*u*(u + 3)/9
Let j(y) = -4*y + 4 - 16 + 2*y + 5*y - y. Let h be j(7). Factor -2/7*p**h - 200/7 - 40/7*p.
-2*(p + 10)**2/7
Let c be 10/55 - 9*10/11. Let k be c/(-1) + (-585)/90. Determine y, given that -3/2*y**2 - k*y + 3 = 0.
-2, 1
Determine w, given that -1/2*w**5 + 153*w**2 + 14*w**4 + 195/2*w**3 + 0 + 0*w = 0.
-3, 0, 34
Suppose -55 = -r + 4*i, 2*r + 31 = 2*i + 129. Suppose r*x = -8*x. Let 0*v**3 + x + 0*v - 1/9*v**5 + 2/9*v**4 + 0*v**2 = 0. What is v?
0, 2
Suppose 1555*l + 62 = 1586*l. Find g, given that 3/4*g**l - 3*g + 3 = 0.
2
Let l = -95665/14 - -13687/2. Solve -3/7*q**3 - l*q - 60/7 - 27/7