
-6, 2
Suppose -6*y - 381 = -63. Let r = -50 - y. Solve 8*d**4 + 2*d + 4*d**2 + 2*d**5 - 12*d**4 + 4*d**5 - 8*d**r = 0.
-1, -1/3, 0, 1
Let j = -256823/5 + 51509. Factor 76/5*n + 2/5*n**2 + j.
2*(n + 19)**2/5
Factor 0 + 3/5*d**4 + 0*d - 36/5*d**2 + 12/5*d**3.
3*d**2*(d - 2)*(d + 6)/5
Let u(w) = -261*w**2 + 5*w - 5. Let k be u(1). Let h = -257 - k. Find l, given that -1/2*l**5 - l**2 + 1/2 - 1/2*l + 1/2*l**h + l**3 = 0.
-1, 1
Suppose 0 = 16*p - 20*p + 20. Suppose 3*q + 1 = 2*y, 42*y - 44*y = -5*q + p. Find t, given that -3/4*t**q + 3/4*t + 0*t**2 + 0 = 0.
-1, 0, 1
Let w be 5*12/(-60)*(-1 + -2). Determine q so that -44*q**2 + 4*q**4 - 29282 + 48*q - 8*q**w + 29282 = 0.
-3, 0, 1, 4
Factor 2351/2*j**3 + 9396*j**2 - 256 + 24992*j + 49*j**4.
(j + 8)**3*(98*j - 1)/2
Let d(f) be the first derivative of f**5/35 + 60*f**4/7 + 237*f**3/7 - 2*f**2/7 - 948*f/7 - 6184. Factor d(z).
(z - 1)*(z + 2)**2*(z + 237)/7
Suppose 6*k + r = 10*k - 8, 0 = -2*k - r + 4. Solve 4*l**k - 18*l - 15*l + 16*l - 25*l = 0 for l.
0, 21/2
Let d(m) be the second derivative of -m**6/75 - 141*m**5/25 - 3168*m**4/5 + 41472*m**3/5 - 2445*m. Suppose d(r) = 0. Calculate r.
-144, 0, 6
Let d(q) be the third derivative of -q**6/240 - 3*q**5/40 - q**4/2 - 4*q**3/3 + 4581*q**2 + 2. What is y in d(y) = 0?
-4, -1
Let c(k) be the first derivative of -15/2*k**4 - 6/5*k**5 - 34/3*k**3 - 6*k**2 + 1/3*k**6 + 0*k + 1. Factor c(r).
2*r*(r - 6)*(r + 1)**3
Let p(y) = -2*y**2 - 11*y - 7. Let f(n) = -19*n**2 - 20*n - n + 16*n**2 - 12. Let z(r) = -5*f(r) + 9*p(r). Find j such that z(j) = 0.
1
Let f(v) = v**2 - 6*v + 14. Let s be f(3). Suppose -s*h + 14*h - 162 = 0. Factor -41*x**2 + h*x**2 - 3*x**3 - 14*x + 11*x**2 + 5*x**3.
2*x*(x - 7)*(x + 1)
Let w(r) = 3*r**2 + 3*r. Suppose -g = -3*g + 22. Let z = g - 5. Let k(u) = 1. Let j(l) = z*k(l) - w(l). Factor j(v).
-3*(v - 1)*(v + 2)
Let b be (-2)/((-6)/84 - 0). Suppose 14*q**4 + 4*q + 30*q**5 + 2 - 66*q**5 - 16*q**2 + 4*q**3 + b*q**5 = 0. Calculate q.
-1, -1/4, 1
Let f be (-42)/84*(72/610)/(-1). Let u = 4654/305 - f. Factor -64/5*t - 128/5*t**2 + 0 + u*t**3 - 2*t**4.
-2*t*(t - 4)**2*(5*t + 2)/5
Suppose -6693 + 6591 = -51*r. Suppose 0 - 10/13*o**3 - 16/13*o + 44/13*o**r = 0. Calculate o.
0, 2/5, 4
Let b(z) be the third derivative of z**8/4032 - z**7/336 + z**6/72 - z**5/20 + z**4/3 - 18*z**2 - 2. Let w(y) be the third derivative of b(y). Factor w(h).
5*(h - 2)*(h - 1)
Let o(l) = -3*l**3 + 89*l**2 - 29*l - 93. Let i(m) = -15*m**3 + 444*m**2 - 153*m - 465. Let g(u) = -4*i(u) + 21*o(u). Determine f so that g(f) = 0.
-1, 1, 31
Let b(s) be the third derivative of -2*s**2 + 7/20*s**5 + 0*s**3 + 35 + 0*s + 0*s**4 - 1/120*s**6. Solve b(p) = 0.
0, 21
Let o(b) be the second derivative of -5/8*b**4 + 3*b**2 - 1/20*b**5 - 29*b - 2*b**3 + 0. Let c(q) be the first derivative of o(q). Solve c(d) = 0.
-4, -1
Let p = 1586/5 + -17416/55. Find c, given that 0 + 18/11*c**2 - 2/11*c**5 - 10/11*c**4 + 0*c - p*c**3 = 0.
-3, 0, 1
Let u = 1609174/9 - 178797. Factor 1/3 + 4/9*l + u*l**2.
(l + 1)*(l + 3)/9
Let b(k) be the first derivative of 15/4*k**4 + 0*k + 19 - 12/5*k**5 + 0*k**2 - 2*k**3 + 1/2*k**6. Suppose b(h) = 0. Calculate h.
0, 1, 2
Let 1949*u - 1/2*u**2 - 3798601/2 = 0. What is u?
1949
Suppose -5*h + 43*g - 48*g = -35, 3*h - 9 = g. Factor h + u**2 - 59 - u**2 - 60*u - 11*u**2 + 6*u**2.
-5*(u + 1)*(u + 11)
Let j(z) be the third derivative of -z**5/150 + 3*z**4/10 - 24*z**3/5 - 15*z**2 - 16*z. Factor j(p).
-2*(p - 12)*(p - 6)/5
Let q be (-1)/5 + 1073/1015. Let g be (-132)/(-182) + (308/182)/(-11). Solve -g - q*n + 2/7*n**3 + 0*n**2 = 0.
-1, 2
Suppose 735/4 - 3/4*y**3 - 357/4*y + 57/4*y**2 = 0. What is y?
5, 7
Factor 966*w - 9*w**2 + 55*w**2 + 964 - 18*w**2 - 15*w**2 - 11*w**2.
2*(w + 1)*(w + 482)
Suppose -14*m**3 - 1445 - 1390*m - 1096*m**2 + 2454 - 1317 = 0. Calculate m.
-77, -1, -2/7
Determine m, given that -40/7*m - 250/7 + 2/7*m**2 = 0.
-5, 25
Let c(p) be the first derivative of 96 - 1/42*p**6 + 3250/21*p**3 + 41/35*p**5 - 293/14*p**4 - 4901/14*p**2 + 2197/7*p. Factor c(u).
-(u - 13)**3*(u - 1)**2/7
Let y(o) = -o**3 - 9*o**2 - 5*o - 30. Let s be y(-9). Let n be (-10)/2 + -8 + 197/s. Suppose n*f**2 + 8/15*f + 0 = 0. Calculate f.
-4, 0
Let k(m) = -m**2 + 3*m - 2. Let b be k(2). Let j be (-3)/9*b + 3. Factor j*q**3 + 0*q**3 + q**3 + 9*q**2 - q**3 + 3 + 9*q.
3*(q + 1)**3
Let w = 157 - 155. Factor 0*t**w - 2*t**2 + 5 + 15*t - t**2 + 13.
-3*(t - 6)*(t + 1)
Let w(a) be the first derivative of -a**6/3 + 26*a**5/5 - 39*a**4/2 + 46*a**3/3 + 40*a**2 - 72*a + 3044. Find f such that w(f) = 0.
-1, 1, 2, 9
Let q(x) be the first derivative of -x**6/45 + 16*x**5/75 + 31*x**4/30 + 44*x**3/45 + 1071. Let q(h) = 0. Calculate h.
-2, -1, 0, 11
Let -2/9*p**2 - 1489538 - 3452/3*p = 0. Calculate p.
-2589
Let k(i) be the second derivative of 9*i**7/14 + 38*i**6/5 + 443*i**5/20 + 143*i**4/6 + 10*i**3/3 - 12*i**2 - 2*i - 4311. Solve k(b) = 0 for b.
-6, -1, -2/3, 2/9
Factor -2*l**4 - 1124*l + 60*l**3 - 9*l**2 - 478*l**2 - 10*l**2 - 97*l**2 + 3068*l.
-2*l*(l - 12)*(l - 9)**2
Let n(w) = -28*w**3 + 371*w**2 - 2779*w + 5457. Let l(h) = -135*h**3 + 1854*h**2 - 13896*h + 27288. Let q(z) = 5*l(z) - 24*n(z). Solve q(s) = 0 for s.
4, 114
Let n(r) be the third derivative of r**5/270 - 269*r**4/18 - 3232*r**3/27 + 3940*r**2 - 2*r. Solve n(c) = 0.
-2, 1616
Let j = -24157 + 24163. Let b(f) be the first derivative of -j + 8/3*f**2 - 16/3*f - 4/9*f**3. Let b(d) = 0. Calculate d.
2
Find h such that -55*h**4 - 109*h**2 + 21*h**2 - 670*h**3 - 46*h**2 + 14*h**2 = 0.
-12, -2/11, 0
Let z = 27/371 + -45887/640717. Let o = z + 1721/5181. Suppose 0 - o*s - 1/3*s**2 = 0. What is s?
-1, 0
Let w(z) = -2*z**3 + 234*z**2 - 343*z + 99. Let j(n) = -8*n**3 + 234*n**2 - 342*n + 100. Let h(f) = 3*j(f) - 4*w(f). Factor h(g).
-2*(g - 1)*(g + 16)*(8*g - 3)
Factor -96*y**3 - 62*y**4 + 96 - 72*y**2 + 16*y + 60*y**3 - 53*y**4 + 111*y**4.
-4*(y - 1)*(y + 2)**2*(y + 6)
Determine o, given that -58/9*o - 61/9*o**2 - 2*o**3 - 16/9 = 0.
-2, -8/9, -1/2
Solve -1/6*u**2 - 3 + 11/6*u = 0.
2, 9
Let l = -246 + 249. Factor 15*f**4 - 2*f - 8*f - 15*f**2 - 501*f**3 + 511*f**l.
5*f*(f - 1)*(f + 1)*(3*f + 2)
Let g(p) = 18*p + 26. Let b be g(-2). Let r be 5*b/25*-1. Factor -3/4*l**3 + 3/4*l**r - 3 + 3*l.
-3*(l - 2)*(l - 1)*(l + 2)/4
Let b(j) be the second derivative of -37*j - 1/40*j**5 + 1/24*j**4 + 3/4*j**2 + 5/12*j**3 + 0. Find l such that b(l) = 0.
-1, 3
Let h = 18 - 13. Let o(l) be the third derivative of 1/180*l**4 + 0*l**3 + 15*l**2 + 0*l + 0 + 0*l**h - 1/900*l**6. Solve o(q) = 0 for q.
-1, 0, 1
Let l(p) be the second derivative of -2*p**7/63 - 2*p**6/45 + 6*p**5/5 + 52*p**4/9 + 80*p**3/9 - 2*p - 197. Factor l(h).
-4*h*(h - 5)*(h + 2)**3/3
Suppose -6*n - 25 = 5. Let j(s) = s**3 - s**2 + 2*s. Let p(m) = -10*m**2 + 70*m. Let d(r) = n*j(r) + p(r). Factor d(h).
-5*h*(h - 3)*(h + 4)
Suppose 156 = 3*q + 4*s - 7*s, -3*q + 152 = -s. Find k such that 19*k**2 + 29*k**2 - q*k**2 + 48*k - 46 = 0.
1, 23
Let i be 19/(-456)*-226 + (-7 - (-396)/48). Factor -i*a + 128/9 + 94/9*a**3 - 8/3*a**4 - 104/9*a**2 + 2/9*a**5.
2*(a - 4)**3*(a - 1)*(a + 1)/9
Let k(s) be the first derivative of 3*s**4/4 - 82*s**3/3 + 611*s**2/2 - 676*s - 892. What is p in k(p) = 0?
4/3, 13
Let w(n) = -n**3 + 13*n**2 - 13*n + 23. Let u be w(12). Suppose -u*v + 12*v = 2. Factor 5*p**v + 1595 - 1487 - 2*p**2 - 36*p.
3*(p - 6)**2
Suppose 2*q = q + 3, -3*q + 7 = 4*u - 22. Solve -45*j**2 + 81/2*j + 23*j**3 - 27/2 + 1/2*j**u - 11/2*j**4 = 0 for j.
1, 3
Let j(k) be the first derivative of 44 + 0*k - 35/2*k**2 + 5/3*k**3. Determine p so that j(p) = 0.
0, 7
Suppose -2*f = 0, 0 = -3*w - 2*f - 4*f + 2*f + 9. Let q(x) be the first derivative of -1/6*x**w + 3*x**2 + 2 - 18*x. Factor q(g).
-(g - 6)**2/2
Let r be (9/13*(-17)/255)/((-177)/590). What is x in -r*x**3 + 0*x + 0 + 54/13*x**2 = 0?
0, 27
Suppose -10*h + 7*h + 15 = 0, l = 3*h - 10. Suppose 0 = 5*k - l*q - 5, 4*q = -5*k + 39 - 25. Solve -3/2*j + 1 - 1/2*j**5 + k*j**3 - j**2 + 0*j**4 = 0.
-2, -1, 1
Let n(d) be the first derivative of -5*d**4/4 + 20*d**3/3 + 95*d**2/2 + 70*d + 3651. Factor n(f).
-5*(f - 7)*(f + 1)*(f + 2)
Let s = -153 - -157. Suppose -28*a + 41*a**s - a**4 + 23*a + 30*a**3 + 15*a**5 = 0. Calculate a.
-1, 0, 1/3
Suppose 51*u - 47*u = -35*u