
Suppose 0 = 100529*l - 100552*l + 115. Determine r, given that -27/4*r**3 + 0 - 9/4*r**4 - 15/4*r**2 + 3/4*r**l + 0*r = 0.
-1, 0, 5
Let u be 6 - (-4 + -14)*1. Let o be u/3 + (-8)/3. Factor 8/3*m**3 - 16/3*m - o - 4/3*m**4 + 4*m**2.
-4*(m - 2)**2*(m + 1)**2/3
Let c = -11 - -23. Let q be (3*(-4)/c)/((-2)/8). Suppose 5 - 3 + 6*z + q - 2 + 2*z**2 = 0. Calculate z.
-2, -1
Let d = 14802 - 177623/12. Let p(l) be the first derivative of -8 + d*l**3 + 25*l + 5/2*l**2. Factor p(i).
(i + 10)**2/4
Let z(v) = 2*v - 20. Let l be z(11). Suppose 0*g + l*g - 5*n - 19 = 0, n = -2*g + 1. Solve -2*w**g - 6*w**4 - 56 + 8*w**3 + 56 = 0 for w.
0, 1/3, 1
Let a(h) be the second derivative of -h**8/6720 + h**7/2520 + h**6/360 + 5*h**4/4 + 51*h + 1. Let m(j) be the third derivative of a(j). Factor m(y).
-y*(y - 2)*(y + 1)
Let o(k) = -23*k - 939. Let m be o(-41). Let h(d) be the first derivative of 4/3*d + 0*d**2 + 1/12*d**m - 1/3*d**3 - 3. Factor h(u).
(u - 2)**2*(u + 1)/3
Factor -132/5 + 14/5*v**2 + 302/5*v.
2*(v + 22)*(7*v - 3)/5
Let t(f) be the second derivative of 17*f**5/70 - 13*f**4/14 + 9*f**3/7 - 5*f**2/7 - 4026*f. Suppose t(g) = 0. Calculate g.
5/17, 1
Suppose 0 = 4*o - o - d - 12, -d = o. Determine i so that -23*i + 6*i + 81*i**3 + 72 - 213*i**2 + 94*i**o - 13*i - 70*i**3 = 0.
-4/7, 3/5, 2
Solve -598 + 142 + 1686875*f - 1687105*f - f**2 = 0 for f.
-228, -2
Let d = 6266/4081 + -30/371. Factor 2/11*g**2 + d - 12/11*g.
2*(g - 4)*(g - 2)/11
Let m be (-9 - (-1968)/80) + 3 + -18. Factor -m - s + 1/5*s**3 - 1/5*s**2.
(s - 3)*(s + 1)**2/5
Suppose 38 = 7*w + 17*w - 58. Let j(z) be the first derivative of -5/2*z**w + 35/3*z**3 + 0*z - 10*z**2 - 8 - z**5. Factor j(o).
-5*o*(o - 1)**2*(o + 4)
Factor -1340*m**2 + 111*m**3 + 1 + 1454*m**2 - 73 + 12*m**4 - 57*m.
3*(m + 1)**2*(m + 8)*(4*m - 3)
Let d(f) be the third derivative of -25*f**7/14 - 1499*f**6/2 - 2244001*f**5/25 + 35976*f**4 - 5760*f**3 - 3581*f**2. Find h such that d(h) = 0.
-120, 2/25
Factor -683*o**2 + 1776 + 234*o**2 - 904*o + 568*o**2 - o**3.
-(o - 111)*(o - 4)**2
What is y in -15*y + 109*y + 787 + 216*y**3 + 2330*y + 249*y - 301 + 2235*y**2 = 0?
-9, -9/8, -2/9
Let t(y) = -4*y**3 - 2*y**2 - 3*y - 5. Let n be t(-2). Factor -n*d**2 - 21*d**2 + 3 + 6*d + 76*d**2 - 27*d**2.
3*(d + 1)**2
Let g(z) be the second derivative of 17*z - 16/3*z**3 + 1 - 1/6*z**4 - 64*z**2. Factor g(l).
-2*(l + 8)**2
Let a(i) = 6*i**3 - 7*i**2 + 4*i - 7. Let r be a(2). Suppose 0 = 5*b + 5*j + 5, 3*b - 3*j - r = 0. Factor 11/4*p + 7/4*p**2 + 5/4 + 1/4*p**b.
(p + 1)**2*(p + 5)/4
Let c be (((-350)/28)/25)/(1/(-10)). Suppose 4*s + 5*x = 18, -4*s = -c*x - 3 + 5. Factor 2/7*k**3 - 2*k + 4/7*k**s + 8/7.
2*(k - 1)**2*(k + 4)/7
Let n(o) = -o**2 + 78*o - 4. Let g(p) = -2*p**2 + 158*p - 10. Let t(k) = -2*g(k) + 5*n(k). Suppose t(z) = 0. Calculate z.
0, 74
Let q(w) be the second derivative of -w**7/3360 + 7*w**6/1440 - 37*w**3/2 - 52*w. Let t(o) be the second derivative of q(o). Solve t(u) = 0.
0, 7
Let q(o) be the first derivative of -83 + 96*o + 50*o**2 + 4/3*o**3. Suppose q(m) = 0. Calculate m.
-24, -1
Suppose 8*t - 54 + 38 = 0. Let s be (-10)/(t + -102) + 2/(-20). Determine b, given that 0*b - 1/2*b**3 - 1/2*b**2 + s = 0.
-1, 0
Let d(w) be the first derivative of -w**6/33 - 36*w**5/55 + w**4/22 + 12*w**3/11 + 686. Let d(n) = 0. Calculate n.
-18, -1, 0, 1
Let y(k) be the third derivative of 4*k**5/105 + 1189*k**4/84 - 149*k**3/7 + 397*k**2 + 10. Find s such that y(s) = 0.
-149, 3/8
Let a(m) be the second derivative of -m**5/90 - m**4/36 + 4*m**3/3 - 32*m**2 + 54*m. Let f(o) be the first derivative of a(o). Factor f(h).
-2*(h - 3)*(h + 4)/3
Let g = -21886 + 21886. Factor -16/7*y**2 + 6/7*y + g.
-2*y*(8*y - 3)/7
Let d = 662480/9 + -73608. Solve -8/9*j - 2/3*j**2 - 2/9*j**4 + 8/9*j**3 + d = 0.
-1, 1, 2
Let r be 76467/19656*-2 - -8. Let u = 1/364 + r. Factor -2/9*f**3 - 4/9*f**2 + 0 - u*f.
-2*f*(f + 1)**2/9
Let n(i) = -i**3 - i**2 + i + 1. Let y be (25/30)/(-5)*-6. Let d(c) = 2*c**3 - 96*c**2 - 3270*c - 35940. Let u(o) = y*d(o) + 3*n(o). Factor u(x).
-(x + 33)**3
Let y(l) be the first derivative of -15 - 1/35*l**5 + 0*l - 3/28*l**4 - 2/21*l**3 + 0*l**2. Find k, given that y(k) = 0.
-2, -1, 0
Let o(z) be the third derivative of -z**9/3780 + z**8/560 - z**6/45 - 3*z**4/2 - z**3/3 - 66*z**2. Let v(q) be the second derivative of o(q). Factor v(w).
-4*w*(w - 2)**2*(w + 1)
Let k(h) be the second derivative of h**6/150 + 27*h**5/100 - h**4/20 - 83*h**3/30 - 27*h**2/5 - 18*h - 13. Solve k(m) = 0.
-27, -1, 2
Let r(p) be the third derivative of 2*p**7/105 - 39*p**6/10 + 671*p**5/15 - 185*p**4/2 + 1201*p**2. Solve r(o) = 0 for o.
0, 1, 5, 111
Let f(l) be the first derivative of -3*l**6/2 + 24*l**5/5 + 2*l**4 - 32*l**3/3 - 8*l**2 - 1664. Determine c, given that f(c) = 0.
-2/3, 0, 2
Let h(a) = 5*a**2 + 2*a + 1. Let y(b) = 5*b**2 + 109*b + 2. Let u(l) = 2*h(l) - y(l). Find q such that u(q) = 0.
0, 21
Let t(k) be the first derivative of 2*k**5/55 + 301*k**4/22 - 404*k**3/11 - 388. Factor t(d).
2*d**2*(d - 2)*(d + 303)/11
Find v, given that -44/17*v**3 + 2/17*v**4 - 320/17 - 76/17*v + 198/17*v**2 = 0.
-1, 2, 5, 16
Let a(m) be the third derivative of -m**5/20 - 65*m**4/2 + 261*m**3/2 - 2*m**2 - 278. Factor a(g).
-3*(g - 1)*(g + 261)
Suppose 138 = 2*d + d. Let b = d - 34. Factor b*i**3 + 3*i**4 - 12*i - 3*i**2 + 45 - 45.
3*i*(i - 1)*(i + 1)*(i + 4)
Suppose 1015*u - 5 = 1113*u - 5. Suppose 48/5*z**3 + u*z + 16/5*z**4 + 0 + 0*z**2 - 4/5*z**5 = 0. Calculate z.
-2, 0, 6
Factor 1/8*o**4 + 0 - 41/8*o**2 + 1/4*o**3 - 21/4*o.
o*(o - 6)*(o + 1)*(o + 7)/8
Let b(y) be the second derivative of -y**7/56 + 9*y**6/80 - 3*y**5/20 - y**4/4 + 13*y**2 + 3*y - 3. Let q(t) be the first derivative of b(t). Solve q(i) = 0.
-2/5, 0, 2
Suppose 338/5*i - 2/5*i**3 - 104/5*i**2 + 88 = 0. Calculate i.
-55, -1, 4
Suppose 3 = -4*f + 3*i, -3*i + 4*i = -5*f + 1. Let x = 458/1309 - 12/187. Find u, given that f*u + x*u**2 - 2/7 = 0.
-1, 1
Let p(k) = k**4 - k**3 - 3*k**2 + k. Let l(r) = -5*r**4 - 145*r**3 + 595*r**2 - 695*r + 270. Let y(j) = -l(j) - 10*p(j). Factor y(u).
-5*(u - 27)*(u - 2)*(u - 1)**2
Let o(r) be the first derivative of 9/2*r**4 + 166 - 2/5*r**5 + 10/3*r**3 - 1/3*r**6 - 24*r - 16*r**2. What is l in o(l) = 0?
-3, -1, 2
Let p = 901425 + -901423. Factor 36/7 - 7*j + 5/7*j**p.
(j - 9)*(5*j - 4)/7
Let m be 42/(-77) + 28/11. Factor -2*u**2 + 3*u + 0*u**m + u**2.
-u*(u - 3)
Let z be (16 - 22338/1387)*38/(-6). Factor -z*d**3 + 4/3 + 8/3*d - 1/3*d**4 + d**2.
-(d - 2)*(d + 1)**2*(d + 2)/3
Let p(b) = 3*b**2 + 2*b + 4. Let c(f) = 4*f**2 + 3*f + 5. Let m = -245 + 250. Let h(y) = m*p(y) - 4*c(y). Suppose h(r) = 0. What is r?
-2, 0
Let l(f) be the third derivative of -f**5/450 + 19*f**4/180 + 10*f**3/3 - 819*f**2. Factor l(v).
-2*(v - 25)*(v + 6)/15
Let p(g) be the second derivative of -3/80*g**5 - 29*g - 6*g**2 + 0 - 3/4*g**4 + 7/2*g**3 + 1/40*g**6. Factor p(n).
3*(n - 2)**2*(n - 1)*(n + 4)/4
Suppose -10*q - 44*q = -6*q - 144. Factor -1/2*c - 1/4*c**4 + 1/4 + 1/2*c**q + 0*c**2.
-(c - 1)**3*(c + 1)/4
Suppose 2 = -47*v + 49*v, 3*d + 4*v = 10. Let -103 - 17 + 9*j**2 - 10*j + 4*j**2 - 4*j**2 - 4*j**d = 0. Calculate j.
-4, 6
Suppose 3*g + 35 = 4*s, -301*g + 297*g = -3*s + 42. Factor 1/2*a**2 + 5/2*a + s.
(a + 1)*(a + 4)/2
Factor 1414*h + 201*h - 215*h**2 + 5*h**3 - 7404 + 1425*h - 6676.
5*(h - 16)**2*(h - 11)
Factor 0 - 1/4*a**2 - 387/4*a + 1/4*a**4 + 387/4*a**3.
a*(a - 1)*(a + 1)*(a + 387)/4
Let c(s) be the second derivative of -1000*s**3 + 3125/2*s**2 + 0 + 1315/6*s**4 + 1/6*s**6 - 34*s + 12*s**5. Factor c(w).
5*(w - 1)**2*(w + 25)**2
Let i(q) be the third derivative of -363/7*q**3 - q - 11/14*q**4 - 20*q**2 + 0 - 1/210*q**5. Solve i(z) = 0 for z.
-33
Let i(o) be the second derivative of -o**6/15 - o**5 - 17*o**4/6 + 40*o**3/3 + 84*o**2 + 5992*o - 1. Let i(w) = 0. What is w?
-7, -3, -2, 2
Let k(u) = -47*u**3 + 5*u**2 - 329*u + 1863. Let w(a) = -35*a**3 + 5*a**2 - 330*a + 1863. Let s(q) = -3*k(q) + 4*w(q). Suppose s(c) = 0. Calculate c.
-23, 9
Factor -614 - 220*o + o**2 - 247*o + 57*o + 105*o.
(o - 307)*(o + 2)
Let g(t) be the third derivative of -t**5/540 - 449*t**4/216 - 224*t**3/27 + t**2 - t + 324. Factor g(d).
-(d + 1)*(d + 448)/9
Let k(m) be the second derivative of m**7/210 + m**6/18 - m**5/5 +