 66579 - 66576. Find j such that 0*j + 0 + 2/3*j**2 - 2/15*j**v = 0.
0, 5
Factor 75 - 19430*p**2 + 38860*p**2 - 19431*p**2 + 74*p.
-(p - 75)*(p + 1)
Let q(n) = 3*n**3 - 3*n**2 - 18*n + 18. Let u(y) = -5*y**2 + 30*y + 3. Let t be u(6). Let l(i) = -i**2 + i. Let d(a) = t*l(a) + q(a). Solve d(x) = 0 for x.
-2, 1, 3
Let x(d) be the second derivative of 11/3*d**3 + 1 - 1/10*d**5 - 2/3*d**4 - 6*d**2 + 62*d. Factor x(r).
-2*(r - 1)**2*(r + 6)
Factor 3/2*r**3 + 123/2 - 243/2*r + 117/2*r**2.
3*(r - 1)**2*(r + 41)/2
Let o(p) be the second derivative of -p**6/6 + 61*p**5 - 24805*p**4/4 - 610*p**3/3 + 37210*p**2 - 2900*p. Solve o(x) = 0.
-1, 1, 122
Let r = -4191/4 - -1093. Let f = r - 45. Suppose -y**2 + 0 + f*y**4 + 1/2*y**3 - 2*y = 0. What is y?
-2, 0, 2
Let u be 8/6*36/16. Suppose -2*j + j - 7 = -3*i, 4*i = -u*j + 18. Determine q, given that -9/4*q**j - 1 + 5*q = 0.
2/9, 2
Let i(s) = -27*s - 30*s + 41*s + 188 - 15*s. Let x be i(6). Factor 2/11*q**3 - 1/11*q**5 + 0 + 0*q - 1/11*q**4 + 0*q**x.
-q**3*(q - 1)*(q + 2)/11
Factor 1/2*z**4 + 0 + 55/2*z**3 + 729/2*z + 783/2*z**2.
z*(z + 1)*(z + 27)**2/2
Suppose -15 = 5*l + 5*c, -14709*l + 14710*l + 9 = -2*c. Let 4/9*h**2 - 4/9*h**l + 0 + 0*h = 0. What is h?
0, 1
Let p(c) = c**2 - 13*c - 11. Let f be p(11). Let b = f - -39. Suppose -16*n**2 + 14*n**2 - 8*n + b*n**2 = 0. Calculate n.
0, 2
Let h(z) = -12*z**2 - 6944*z + 152. Let r(n) = n**2 + 534*n - 12. Let i(k) = -3*h(k) - 38*r(k). Solve i(s) = 0 for s.
0, 270
Let a be ((-981)/11118 - (-166)/340)/(2/20). Suppose 2/3*k + 0 + 13/6*k**3 - 2*k**2 - k**a + 1/6*k**5 = 0. What is k?
0, 1, 2
Let s(n) be the first derivative of 2/45*n**5 + 0*n**2 + 0*n - 27 + 2/9*n**3 - 2/9*n**4. Let s(d) = 0. Calculate d.
0, 1, 3
Let q(b) be the first derivative of 14*b**6/3 - 3676*b**5/5 + 6415*b**4 - 45364*b**3/3 + 14156*b**2 - 4960*b + 3556. Solve q(d) = 0.
2/7, 1, 5, 124
Let 0 + 170/7*r**3 + 368/7*r**2 + 104/7*r + 6/7*r**4 = 0. What is r?
-26, -2, -1/3, 0
Let m(h) = -28*h - 66 - 7*h**2 - 7 - 68 - 30*h. Let a(z) = -15*z**2 - 115*z - 285. Let v(l) = -2*a(l) + 5*m(l). Determine p, given that v(p) = 0.
-9, -3
Let z(t) be the third derivative of t**7/1260 - t**6/90 - t**5/12 + t**4/6 + 10*t**3/3 + 6*t**2. Let v(u) be the second derivative of z(u). Factor v(h).
2*(h - 5)*(h + 1)
Let r(p) be the first derivative of -p**5 - 325*p**4 - 29020*p**3 - 166400*p**2 - 327680*p - 195. Factor r(w).
-5*(w + 2)**2*(w + 128)**2
Let q(c) be the second derivative of c**4/126 + 254*c**3/63 + 24*c**2 + 2576*c + 1. Factor q(s).
2*(s + 2)*(s + 252)/21
Let x(i) be the second derivative of i**5/120 + 14*i**4/9 - 227*i**3/36 + 19*i**2/2 - 111*i - 12. Factor x(a).
(a - 1)**2*(a + 114)/6
Let x(o) = o - 5. Let f be x(5). Let w be (6 - 69/12)*f. Suppose 0 - 9/7*c**3 + 3/7*c**4 + 12/7*c + w*c**2 = 0. What is c?
-1, 0, 2
Let q(s) be the third derivative of -s**6/40 - 16*s**5/5 - 61*s**4/2 - 120*s**3 + 3*s**2 - 573. Factor q(k).
-3*(k + 2)**2*(k + 60)
Let h(d) be the first derivative of 12*d + 81/5*d**2 - 16 + 1/30*d**4 + 6/5*d**3. Let q(p) be the first derivative of h(p). Suppose q(y) = 0. What is y?
-9
Suppose 104 = -5*i - 191. Let f = i + 62. Solve -89*j**3 + 13*j**f - 50*j - 8 + 8*j**2 + 126*j = 0 for j.
-1, 2/19, 1
Let k be ((-19383)/8307 - (-2)/78*88)/((-6)/13). Find d, given that -5 + 5*d**2 + k*d - 1/6*d**3 = 0.
-1, 1, 30
Let z(q) = 6636*q + 26546. Let r be z(-4). Let 12/5*p - 2/5*p**r - 18/5 = 0. Calculate p.
3
Let x(g) be the first derivative of -g**4/2 + 18*g**3 - 135*g**2 - 1350*g + 165. Find t, given that x(t) = 0.
-3, 15
Suppose 5*i = -2*t + 10, -38*t = 4*i - 39*t + 5. Find z such that 2/5*z**2 - 12/5*z + i = 0.
0, 6
Let i(a) be the second derivative of -a**4/6 + 50*a**3/3 - 49*a**2 - 51*a + 9. Find y, given that i(y) = 0.
1, 49
Suppose -58*n + 54*n = -3*l - 1560, 0 = -5*n. Let i = -520 - l. Factor 0 + 3/7*g**2 + i*g - 3/7*g**5 - 3/7*g**4 + 3/7*g**3.
-3*g**2*(g - 1)*(g + 1)**2/7
Let v(m) = 4*m**4 - 165*m**3 + 381*m**2 - 206*m + 7. Let c(p) = -3*p**4 + 109*p**3 - 254*p**2 + 138*p - 5. Let t(o) = -7*c(o) - 5*v(o). Solve t(a) = 0 for a.
-64, 0, 1
Let t = 2726/13 + -8048/39. Let f = 2 - -1. Suppose 2/3*k**f - t*k**2 + 0 - 4*k = 0. What is k?
-1, 0, 6
Let y be (-2 - -2)/((-3711)/(-1237)). Suppose y*b + 1/7*b**5 - 1/7*b**4 + 0 + 0*b**2 - 2/7*b**3 = 0. What is b?
-1, 0, 2
Let i(v) be the third derivative of 1/90*v**5 + 47*v**2 - 19/18*v**4 + 361/9*v**3 + 0 + 0*v. Factor i(y).
2*(y - 19)**2/3
Let b(f) be the first derivative of -7/11*f**2 + 6/11*f + 123 + 10/33*f**3 - 1/22*f**4. What is i in b(i) = 0?
1, 3
Let o = -119 - -121. Suppose 11 + 10*q**3 - 449 + 1385*q - 30*q**3 - 94*q**2 - 481*q**o + 128 = 0. Calculate q.
-31, 1/4, 2
Let q(o) be the second derivative of -o**4/42 + 2*o**3/3 - 40*o**2/7 + 3*o + 55. Factor q(k).
-2*(k - 10)*(k - 4)/7
Suppose 287/2*p + 0 - 1/2*p**2 = 0. Calculate p.
0, 287
Let l(h) = 36*h**3 - 280*h**2 - 308*h + 8. Let y(p) = -5164*p**2 + 103*p + 5257*p**2 - 3 - 5*p**3 - 8*p**3. Let k(m) = -3*l(m) - 8*y(m). Solve k(j) = 0.
-1, 0, 25
Let l = 1261 + -34031/27. Let k(f) be the first derivative of 7/9*f**2 + 27 - l*f**3 - 4/9*f + 1/6*f**4. Determine s so that k(s) = 0.
2/3, 1
Let u(k) = 3*k**2 + 40*k + 108. Let q(i) = 3*i**2 + 39*i + 108. Let g = 269 + -265. Let d(v) = g*q(v) - 3*u(v). Factor d(f).
3*(f + 6)**2
Suppose -31*q = -30*q - 3, -3*q + 13 = 2*l. Factor 5 + 2266*h**2 - 41 + 32*h - 2262*h**l.
4*(h - 1)*(h + 9)
Let d(w) be the second derivative of -w**5/4 - 275*w**4/12 + 195*w**3/2 + 855*w**2/2 - 364*w + 4. Factor d(y).
-5*(y - 3)*(y + 1)*(y + 57)
Let s(d) = d**2 + 7*d - 6. Let l be s(-8). Find y such that 792 + 28*y**5 - 132*y**4 + 11*y**l - 776 + 212*y**3 - 135*y**2 = 0.
-2/7, 1, 2
Factor 35*o**4 - 34*o**4 + 5747*o - 5739*o + 7*o**3 + 14*o**2.
o*(o + 1)*(o + 2)*(o + 4)
Let b(j) = -11*j**2 + 17*j - 18. Let y(t) = -12*t**2 + 18*t - 18. Let a(r) = -4*b(r) + 3*y(r). Let q(w) = 2. Let c(d) = -2*a(d) + 22*q(d). Solve c(m) = 0.
-1/4, 2
Factor -2 - 1/5*o**2 + 11/5*o.
-(o - 10)*(o - 1)/5
Let d(c) be the second derivative of 2/9*c**3 - 32/21*c**2 + 1/126*c**4 + 0 - 69*c. Let d(y) = 0. What is y?
-16, 2
Let p(d) = -23*d - 228. Let a be p(-10). Solve -214 - f**a - 461 + 56*f - 24 - 85 = 0 for f.
28
Suppose 3*p - 6*p = 29*p. Let z(a) be the third derivative of 23*a**2 + 0 + p*a - 3/4*a**4 - 9*a**3 - 1/40*a**5. Factor z(b).
-3*(b + 6)**2/2
Let w(n) = n**2 - 7*n - 16. Let j be w(8). Let h(f) = f + 11. Let z be h(j). Solve -6 + 4*u**2 + 3*u**5 - 6*u**4 + 3*u - 6*u**z + 16*u**2 - 8*u**2 = 0.
-1, 1, 2
Let y(d) be the first derivative of -d**3/15 + 333*d**2/5 - 133*d + 5440. Factor y(b).
-(b - 665)*(b - 1)/5
Let z = 22551 + -22548. Factor 3/2*p**z + 4*p**2 + 0 + 2*p.
p*(p + 2)*(3*p + 2)/2
Let k be (6/(-5))/(-2 + 82/40). Let v be ((k/(-5))/6)/(6/15). What is o in -22*o - 20*o**v + 5*o**3 + 3*o**3 + 10*o**5 + 0 - 4 + 4*o + 24*o**4 = 0?
-1, -2/5, 1
Let f(p) = 63*p + 45*p**3 + 11*p**4 + 121*p**2 - 50 + 12 + 15*p**3 - 4*p - 3*p. Let y(t) = t**4 - t**2 - 2*t - 1. Let x(d) = f(d) - 2*y(d). Factor x(k).
3*(k + 2)**2*(k + 3)*(3*k - 1)
Let n(q) = q**3 - 3*q**2 + q + 1. Let h(m) = -6*m**3 + 239*m**2 + 11874*m - 7. Let b(l) = 2*h(l) + 14*n(l). Find v, given that b(v) = 0.
-109, 0
Solve -495*y + 35562*y**2 + y**3 + 272 - 48*y - 35292*y**2 = 0.
-272, 1
Let o be (41965/11445)/(11/12). Find g such that 1/5*g**3 - 9/5*g + 0 + 2/5*g**o - 18/5*g**2 = 0.
-3, -1/2, 0, 3
Let c(i) = -2*i + 80. Let f be c(-16). Factor -f - 531 + 0*p**2 + 143 - 100*p - 5*p**2.
-5*(p + 10)**2
Let j(o) be the second derivative of -35*o**2 - 5/12*o**4 + 1 - 39*o - 25/2*o**3. Find l such that j(l) = 0.
-14, -1
Suppose 0*r - 5*r = 225. Let b = -43 - r. Solve -5*q**3 - 5*q**b + 10*q - 907 + 907 = 0.
-2, 0, 1
Let 2/5*c**4 - 2200 - 510*c**2 + 1960*c + 196/5*c**3 = 0. What is c?
-110, 2, 5
Let o be (-1)/(-3)*(-151 - -157). Let n(k) be the second derivative of 0 + k + 3/8*k**o + 1/2*k**4 - 21/160*k**5 - 11/16*k**3. Suppose n(f) = 0. Calculate f.
2/7, 1
Suppose -5 = w - 7. What is c in -150*c**2 + 306*c**w - 151*c**2 + 20 + 25*c = 0?
-4, -1
Let b be (-42)/((-9996)/(-170)) + 6 + (-1 - 4). Factor -b*c**2 - 22/7 + 24/7*c.
-2*(c - 11)*(c - 1)/7
Let z(q) be the third derivative of -q**6/30 + 41*q**5/15 + 22*q**4/3 - 56*q**3 - 2853*q**2. Find k, given that