30*z. Let a(c) be the third derivative of x(c). Factor a(k).
3*k**2*(k - 3)*(k + 1)/4
Let x(a) be the third derivative of a**7/210 - a**6/20 - 4*a**5/15 + 9*a**4/4 + 21*a**3/2 + 26*a**2 - 67*a. Determine s so that x(s) = 0.
-3, -1, 3, 7
Find s, given that -27 + 81/5*s + 51/5*s**2 + 3/5*s**3 = 0.
-15, -3, 1
Let 1/4*p**2 + 1899/2*p + 3606201/4 = 0. Calculate p.
-1899
Let w = 127856/65 + -1967. Let f(o) be the second derivative of 0*o**4 - w*o**5 + 2/39*o**3 - 28*o - 1/13*o**2 + 0 + 1/195*o**6. Factor f(y).
2*(y - 1)**3*(y + 1)/13
Let j(h) be the second derivative of 1/120*h**5 + 7/72*h**4 - 5/4*h**2 + 7/36*h**3 + 3*h + 16. Solve j(s) = 0.
-5, -3, 1
Let d be (-2264)/(-14716) - (-61)/26. Factor -5/2*a - d*a**2 + 5.
-5*(a - 1)*(a + 2)/2
Let u(i) = 39*i + 197. Let p be u(-5). Let s(x) be the second derivative of 36/5*x**p - 15*x + 0 + 1/30*x**4 + 4/5*x**3. Factor s(r).
2*(r + 6)**2/5
Let x(c) be the first derivative of -11/3*c**3 + 0*c - 3/2*c**2 + c**4 - 9. Solve x(f) = 0 for f.
-1/4, 0, 3
Let u(p) be the second derivative of 2*p**6/75 + 8*p**5/25 + 7*p**4/5 + 12*p**3/5 - 2940*p. Find m such that u(m) = 0.
-3, -2, 0
Factor 469/6 - 235/3*m + 1/6*m**2.
(m - 469)*(m - 1)/6
Factor -636*v**3 + 638*v**3 + 4*v**2 + 10*v**4 - 12*v**4.
-2*v**2*(v - 2)*(v + 1)
Let h(u) = -u**2 - 11*u + 14. Let t be h(-12). Suppose -15*x - 15*x - t*x**2 + 28*x = 0. Calculate x.
-1, 0
Let v(z) be the second derivative of -z**7/70 - 13*z**6/25 - 423*z**5/100 + 91*z**4/5 - 98*z**3/5 - 1319*z. Let v(x) = 0. Calculate x.
-14, 0, 1
Let h(y) be the first derivative of 3*y**4/4 - y**3 - 3*y**2/2 + 3*y + 708. Factor h(f).
3*(f - 1)**2*(f + 1)
Let m be (2 - -2) + 34776/4830. Suppose -2*s = 10, 5*v - 5*s + 2*s - 25 = 0. Determine b, given that 2/5*b**v + 392/5 - m*b = 0.
14
Let c be ((-40)/(-6))/(5344/1670). Let m(y) be the third derivative of -125/6*y**3 + 0 + 0*y - c*y**4 + 35*y**2 - 1/12*y**5. Factor m(p).
-5*(p + 5)**2
Let y(m) = m**4 + 10*m**3 - 47*m**2 - 360*m + 1300. Let t = 137 + -131. Let o(x) = 2. Let h(g) = t*o(g) - 3*y(g). Factor h(i).
-3*(i - 4)**2*(i + 9)**2
Let v(c) = -2*c**4 + c**2 - c - 1. Let r(i) = 3*i**5 - 615*i**4 + 32445*i**3 - 31830*i**2 + 3*i + 3. Let m(b) = -r(b) - 3*v(b). Factor m(f).
-3*f**2*(f - 103)**2*(f - 1)
Solve -19 + 6907*h**2 - 225 - 6899*h**2 - 64 + 12*h = 0.
-7, 11/2
Solve -112*m**4 - 398*m - 274*m - 545*m**2 - 20*m**5 - 90*m**3 - 663*m**2 + 16*m**5 - 554*m**3 = 0.
-21, -4, -2, -1, 0
Solve 3/5*s - 3/5*s**3 - 51/5*s**2 + 51/5 = 0 for s.
-17, -1, 1
Determine k so that 160*k**2 - 5*k**3 - 5*k**3 + 3*k**3 - 5*k**3 + 8*k**3 - 1488*k + 4032 = 0.
6, 28
Let h = -104423/5 + 1357509/65. What is g in -12/13*g**2 - 18/13*g - 8/13 - h*g**3 = 0?
-4, -1
Let a = 188/1161 + 11/2322. Let -1/6*j**5 + 7/6*j**3 - j - 1/6*j**4 + a*j**2 + 0 = 0. Calculate j.
-3, -1, 0, 1, 2
Let x(z) = 2*z**2 + 1. Let s(b) = 70*b**2 - 34*b + 94. Let a(u) = 2*s(u) - 68*x(u). Let a(p) = 0. Calculate p.
2, 15
Let o(f) = 8*f**3 - 34*f**2 + 8*f + 6. Let n be o(4). Let i be (-5)/6 - (-5)/n. Suppose 1/5*h**3 + i - 4/5*h**2 + 4/5*h = 0. What is h?
0, 2
Let z = 30178/17 - 1774. Let k = z - 23/34. Factor 5/6*r + 1/6*r**2 + k - 1/6*r**3.
-(r - 3)*(r + 1)**2/6
Suppose -10*t = 107*t + 8*t - 250. Let x(u) be the first derivative of 8/11*u**t - 2/33*u**3 + 16 - 32/11*u. Suppose x(y) = 0. Calculate y.
4
Let l be 1494/(-1162) - (-44)/28. Factor l*b**2 + 0 - 12/7*b.
2*b*(b - 6)/7
Let j(h) be the second derivative of 7*h**7/54 + 2219*h**6/135 + 21799*h**5/45 - 17462*h**4/3 - 7040*h**3 - 3072*h**2 - 27*h + 8. Find m, given that j(m) = 0.
-48, -2/7, 6
Suppose -3*z + 6*z - 5*f + 1088 = 0, 0 = -3*f - 15. Let i = 374 + z. Determine q, given that 0*q + 3/4*q**5 + 0*q**2 + 1/2*q**i - 5/4*q**4 + 0 = 0.
0, 2/3, 1
Let u(m) = 15*m**3 - 265*m**2 + 55*m + 115. Let j(q) = -q**3 + 19*q**2 - 4*q - 8. Let i(s) = -55*j(s) - 4*u(s). Factor i(w).
-5*(w - 2)**2*(w + 1)
Let l(w) be the third derivative of w**8/336 - w**7/70 - 13*w**6/40 + 83*w**5/60 - 7*w**4/4 + 3*w**2 + 3*w. Factor l(q).
q*(q - 7)*(q - 1)**2*(q + 6)
Let y(c) = -2*c**3 - 62*c**2 - 116*c + 186. Let u(k) = 2*k + 1. Let w(j) = 124*u(j) + 2*y(j). What is g in w(g) = 0?
-31, -2, 2
Let h(m) be the second derivative of m**6/150 + 3*m**5/25 - 3*m**4/10 - 34*m**3/15 - 39*m**2/10 - 727*m. What is q in h(q) = 0?
-13, -1, 3
Let v = -90 - -96. Let t(n) = 14*n**3 - 8*n**2 - 10*n. Let p(y) = -13*y**3 + 9*y**2 + 9*y. Let o(c) = v*p(c) + 5*t(c). What is m in o(m) = 0?
-1/4, 0, 2
What is p in -27*p**2 + 62*p**2 + 2*p**3 + 214*p**2 + 25*p**2 = 0?
-137, 0
Suppose 247*k - 3*b = 246*k - 30, 3*k + 46 = 5*b. Factor x**k + 6*x + 5/2*x**4 + 0 - 19/2*x**2.
x*(x - 1)**2*(5*x + 12)/2
Let j be 2/(-140)*-7*(-1172)/(-522). Let b = -1/435 + j. Let -2/3 + 2/3*r**2 - b*r + 2/9*r**3 = 0. What is r?
-3, -1, 1
Let b(u) be the third derivative of -u**5/3 + 13*u**4/2 + 36*u**3 + 4350*u**2. Factor b(c).
-4*(c - 9)*(5*c + 6)
Let f be (1728/(-9) - -120)*(-82)/30. Solve -f*o - 396/5 + 3*o**2 = 0 for o.
-2/5, 66
Let d(n) be the third derivative of -n**5/100 - 783*n**4/20 - 613089*n**3/10 - 243*n**2 + 12*n. Solve d(x) = 0.
-783
Let v(l) = 12*l**2 + 20*l - 4. Let i(j) = -j**3 - 10*j**2 - 19*j + 5. Suppose 40 = -5*p - 5*d, 0 = 3*p - p - 5*d - 5. Let o(f) = p*v(f) - 4*i(f). Factor o(b).
4*b*(b - 6)*(b + 1)
Solve -272/15*t**2 - 1064/15*t - 352/5 - 2/15*t**3 = 0.
-132, -2
Let c(d) be the first derivative of -2*d**3/3 + 70*d**2 + 750*d + 6097. Factor c(u).
-2*(u - 75)*(u + 5)
Let y(r) be the third derivative of r**6/900 + 3*r**5/100 + 2*r**4/15 - 29*r**3/2 + 55*r**2. Let c(f) be the first derivative of y(f). Factor c(b).
2*(b + 1)*(b + 8)/5
Let u be (1 - -11)*6/9. Solve u*o - 130 + 57 + 2*o**2 + 63 = 0.
-5, 1
Let k be 1 + ((-15)/10)/(42/(-112)). Find u, given that -1/2*u**4 + 5/2*u**2 + 2*u - 5/2*u**3 - 2 + 1/2*u**k = 0.
-2, -1, 1, 2
Suppose -3*c + 89*i - 84*i = 28, -28 = -c - 3*i. Let d(t) be the second derivative of 0 + 1/22*t**c - 3/110*t**5 + 12*t + 0*t**2 + 0*t**3. Solve d(h) = 0.
0, 1
Let l be -3 + 108 + (11 - 14). Suppose l*t = 12*t + 180. Factor 0*o + 0 + 1/7*o**4 - 1/7*o**3 + 1/7*o**5 - 1/7*o**t.
o**2*(o - 1)*(o + 1)**2/7
Factor -2*o**3 - 2246 + 185 + 6*o**3 - 2004*o**2 - 4020*o + 49.
4*(o - 503)*(o + 1)**2
Let o(b) be the first derivative of 5635/2*b**4 - 11664*b - 10836*b**3 + 18468*b**2 - 1372/5*b**5 - 220. Determine a so that o(a) = 0.
1/2, 18/7
Let j(l) be the first derivative of 13/7*l**2 + 23/14*l**4 + 16 - 2/5*l**5 - 18/7*l**3 - 4/7*l. What is g in j(g) = 0?
2/7, 1
Let u(v) be the third derivative of v**6/10 + 1717*v**5/15 - 766*v**4 + 4600*v**3/3 - 208*v**2. Factor u(p).
4*(p - 2)*(p + 575)*(3*p - 2)
Let a = -139 - -141. Factor -18 + 61*t**2 + 8*t - 64*t**a + 7*t.
-3*(t - 3)*(t - 2)
Let m(q) be the second derivative of q**5/5 - 164*q**4/3 + 14378*q**3/3 - 74892*q**2 - 163*q. Solve m(k) = 0.
6, 79
Suppose 67 - 61 = 15*u - 39. Let h(o) be the second derivative of -64*o**2 + 16/3*o**u + 1/15*o**6 + 18*o + 11/10*o**5 + 0 + 6*o**4. Factor h(s).
2*(s - 1)*(s + 4)**3
Solve 3120*h**2 - 84 + 91 + 189 - 1566*h - 519*h**3 + 551*h**3 = 0 for h.
-98, 1/4
Let w(z) be the second derivative of z**9/1890 + 3*z**8/1120 - z**7/126 - z**6/120 - 29*z**4/3 + 9*z. Let v(t) be the third derivative of w(t). Solve v(l) = 0.
-3, -1/4, 0, 1
Factor 1/4*x**3 - 21/4*x**2 + 5*x + 0.
x*(x - 20)*(x - 1)/4
Suppose -718*k + 67*k - 462400 - 62*k**2 + 61*k**2 - 375*k - 334*k = 0. Calculate k.
-680
Let a(o) be the first derivative of -174 - o**2 + 0*o - 1/3*o**6 - 3*o**4 - 8/3*o**3 - 8/5*o**5. Find l such that a(l) = 0.
-1, 0
Let u(a) be the third derivative of -a**8/1512 - 2*a**7/63 + 49*a**6/270 - 2*a**5/15 - 97*a**4/108 + 22*a**3/9 - 3547*a**2 + 2*a. Determine l so that u(l) = 0.
-33, -1, 1, 2
Suppose -5*o = 18*o - 46. Determine g, given that -537*g**2 - 80*g + 541*g**o - 52*g + 128 = 0.
1, 32
Let q(b) = 3*b**2 - 3*b - 87. Let w be q(-7). Suppose -w*m + 63*m = -36. Find y, given that 6/5*y**4 + 0*y**3 + 0*y + 2/5*y**5 - 8/5*y**m + 0 = 0.
-2, 0, 1
Let i(v) = 6*v**2 + 25*v + 11. Let d be i(-6). Suppose -55*k - 65*k**2 - d + 42 + 45 = 0. Calculate k.
-1, 2/13
Let u(v) = -v**3 - 24*v**2 - v - 20. Let f = -558 + 534. Let j be u(f). Factor 3/2*k**j + 0 + 0*k**2 - 3/2*k**3 + 0*k.
3*k**3*(k - 1)/2
Let s(m) be the second derivative of 3