. Factor -9/5*c**3 + 12/5*c**2 + 0 - o*c.
-3*c*(c - 1)*(3*c - 1)/5
Let r(i) = i**2 - 8*i + 9. Let x(l) = 5*l**2 - 41*l + 45. Let a(c) = -c + 2. Let g be a(0). Suppose 51*m - 50*m = -11. Let h(k) = g*x(k) + m*r(k). Factor h(z).
-(z - 3)**2
Suppose 52*g = 11*g + 73 + 50. Factor 9/2*k - 3*k**g - 9/2*k**4 - 3/2*k**5 + 3*k**2 + 3/2.
-3*(k - 1)*(k + 1)**4/2
Let t = -352/31 - -1211/93. Suppose 0 - 10/3*u + t*u**3 + 5/3*u**2 = 0. What is u?
-2, 0, 1
Let u = -152 + 168. Let a = 97 + u. Determine y so that a*y - 4*y**2 - 4*y**3 + 4*y**4 - 211*y + 102*y = 0.
-1, 0, 1
Let y(f) be the second derivative of -11*f**5/5 - 97*f**4/3 - 120*f**3 + 72*f**2 + 26*f + 2. Let y(w) = 0. Calculate w.
-6, -3, 2/11
Factor 330*b**3 - 164*b**3 - 68 - 154 + 110*b**2 - 11*b + 124*b - 167*b**3.
-(b - 111)*(b - 1)*(b + 2)
Let m(u) = -u**4 - 2*u**3 + 5*u**2 + u - 2. Let c(d) = -6*d**4 - 4784*d**3 + 2841768*d**2 + 8*d - 16. Let w(n) = c(n) - 8*m(n). Factor w(f).
2*f**2*(f - 1192)**2
Let b(k) be the second derivative of -k**7/294 - 2*k**6/105 + 4*k**4/21 + 8*k**3/21 - 1101*k - 1. Factor b(h).
-h*(h - 2)*(h + 2)**3/7
Suppose -4*m + 46 = -3*x, 35*m - 34*m - 6 = -2*x. Suppose -m*y + 3 + 27 = 0. Factor 2*w**y - 5/2*w**4 + 0 + w**5 + 0*w - 1/2*w**2.
w**2*(w - 1)**2*(2*w - 1)/2
Let l(v) be the second derivative of 5*v**7/252 + v**6/72 + v**5/240 + 5*v**4/6 - 42*v. Let g(i) be the third derivative of l(i). Factor g(u).
(10*u + 1)**2/2
Let t(q) be the third derivative of 0 - 7/60*q**4 + 22*q**2 + 4/5*q**3 + 1/150*q**5 + 0*q. Factor t(j).
2*(j - 4)*(j - 3)/5
Factor 0 + 19/6*a**4 + 1/6*a**5 + 41/2*a**3 + 305/6*a**2 + 100/3*a.
a*(a + 1)*(a + 5)**2*(a + 8)/6
Let w(d) be the first derivative of -32*d**3/21 + 11*d**2 + 30*d/7 + 3115. Factor w(c).
-2*(c - 5)*(16*c + 3)/7
Let r(i) be the second derivative of -1/90*i**6 + 0*i**3 + 5/36*i**4 + 0*i**2 + 1/15*i**5 + 2 + 26*i. Suppose r(s) = 0. Calculate s.
-1, 0, 5
Let x(a) be the second derivative of a - 1/40*a**5 - 25/2*a**2 + 1/3*a**4 + 8 - 5/12*a**3. Determine t, given that x(t) = 0.
-2, 5
Let n be (-69)/276*(-2 + 2). Factor 2/7*p**2 + n - 32/7*p.
2*p*(p - 16)/7
Let m(k) = 10*k + 99. Let n be m(-49). Let v = -389 - n. Factor 0 - 2/7*t - 1/7*t**v.
-t*(t + 2)/7
Suppose 0 = 6*o - 4*o - 60. Factor 18*c + 69*c**4 + 6*c + 2*c**3 - 65*c**4 + o*c**3 + 52*c**2.
4*c*(c + 1)**2*(c + 6)
Suppose 4*a = -3*s + 2*s - 17, s = a + 8. Suppose 25*j - 5*j**3 + 2*j**2 + 16*j**s - 10*j**3 - 28*j**2 = 0. Calculate j.
0, 1, 25
Let c(j) = 306*j**2 - 301*j**2 + 35*j**3 - 45*j - 10 - 10. Let s(g) = -53*g**3 - 8*g**2 + 67*g + 29. Let w(b) = -7*c(b) - 5*s(b). Find u, given that w(u) = 0.
-1, -1/4, 1
Suppose 3*u - 4*l - 42 = -4, 0 = -3*u + 2*l + 34. Suppose -2*r - 32 = -u*r. Find x, given that 15*x**r - 20*x**2 - 6*x + 24*x**3 - 2*x + 21*x**4 = 0.
-1, -1/3, 0, 2/3
Let s = 240713/3 - 80226. Let -100/3*o + 30*o**2 + s - 5/3*o**4 - 20/3*o**3 = 0. What is o?
-7, 1
Let j(b) be the second derivative of -11/2*b**3 + 1/12*b**4 + 0*b**2 - 1 - 4*b. Factor j(i).
i*(i - 33)
Let k be (7 - 1550/(-140)) + (-324)/(-1512). Factor 2/7*i**2 - k*i + 2048/7.
2*(i - 32)**2/7
Suppose 4*f + 2*y - 80 = 0, -5*f + 2*y = -5 - 104. Suppose -7*d + 28 = -f. Let -4*g**3 + d*g**2 + 1 - 8*g**2 + 4*g - 7*g**2 + 7 = 0. Calculate g.
-2, -1, 1
Factor 31650*d**2 + 560 + 1125/2*d**3 + 8410*d.
5*(d + 56)*(15*d + 2)**2/2
Suppose -950*w + 1/2*w**4 + 1500 - 33/2*w**3 + 195*w**2 = 0. Calculate w.
3, 10
Let w(m) be the first derivative of 14/3*m**4 + 0*m - 15/2*m**2 + 16/3*m**3 + 13 + 49/30*m**5. Let j(a) be the second derivative of w(a). Factor j(i).
2*(7*i + 4)**2
Let i be -1*(19515/(-30))/((-2)/4). Let w = 1303 + i. Factor -1/4*j**w - 1/2 + 3/4*j.
-(j - 2)*(j - 1)/4
Factor -5*l**2 - 551083 - 70274 - 377688 + 1440*l + 2420*l + 610*l.
-5*(l - 447)**2
Let v = -85 + 144. Suppose -2*r + 121 - v = 0. Find c such that c**3 - r*c**2 + 11*c - 5 + 24*c**2 + 0 = 0.
1, 5
Let l(u) be the third derivative of 0*u**4 + 30*u**2 + 0*u**3 + 23/90*u**5 + 1/180*u**6 + 0*u + 0. Factor l(k).
2*k**2*(k + 23)/3
Factor -1452/5 + 75*u - 3/5*u**2.
-3*(u - 121)*(u - 4)/5
Let r(v) = v**3 + 9*v**2 - 2*v - 15. Let a be r(-9). Factor -10*s**2 - 16*s**2 + s**5 - 3*s**4 - 4 - 15*s**2 - s**a + 48*s**2.
(s - 2)**2*(s - 1)*(s + 1)**2
Let m(t) be the second derivative of t**6/15 - 61*t**5/6 + 199*t**4/18 + 305*t**3/9 - 202*t**2/3 - 51*t - 14. What is x in m(x) = 0?
-1, 2/3, 1, 101
Suppose 24*f - 41 = 80 - 1. Let x(w) be the second derivative of -3/5*w**2 + 1/10*w**4 + 10*w - 1/15*w**3 + 0 + 1/50*w**f. Factor x(s).
2*(s - 1)*(s + 1)*(s + 3)/5
Let j(i) be the second derivative of i**6/300 + 11*i**5/150 + 13*i**4/20 + 3*i**3 + 75*i**2/2 + 42*i. Let h(n) be the first derivative of j(n). Factor h(k).
2*(k + 3)**2*(k + 5)/5
Let r be (-12)/(-8)*(4 - 72/27). Let s(g) be the first derivative of -g**3 - 1 + 0*g + 3/5*g**r + 3/5*g**4 - 3/25*g**5. Find a such that s(a) = 0.
0, 1, 2
Let n be 1990/(-1393)*(-9)/15. Determine s so that -2/7*s**2 - n*s + 8/7 = 0.
-4, 1
Let s be (-29)/(-84) + ((-8)/10)/((-42)/(-5)). Let w(o) be the first derivative of 1/3*o**3 - 1/8*o**4 - o + s*o**2 - 4. Factor w(a).
-(a - 2)*(a - 1)*(a + 1)/2
Let p(g) = 5*g**3 + 10*g**2 + 3*g - 3. Let j(i) = -5*i**3 + 19*i**3 + 1996*i - 8 - 1988*i + 30*i**2. Let v(n) = -3*j(n) + 8*p(n). Factor v(o).
-2*o**2*(o + 5)
Let k(u) be the second derivative of 19/13*u**2 - 33*u - 20/39*u**3 + 1/78*u**4 + 0. Factor k(n).
2*(n - 19)*(n - 1)/13
Let r(c) be the third derivative of -c**5/100 + 18*c**4/5 - 56*c**3 + 272*c**2 - 5*c. Solve r(g) = 0 for g.
4, 140
Let c(h) be the first derivative of -1/9*h**4 + 27*h - 13 - 4/3*h**2 - 2/3*h**3. Let y(d) be the first derivative of c(d). Suppose y(a) = 0. What is a?
-2, -1
Suppose 241*p - 247*p = 20538. Let j be p/(-45) + 77/(-33)*-1. Find d such that j + 2/5*d**2 + 56/5*d = 0.
-14
Let i(f) = -11*f**2 - 132*f + 60. Let k(q) = -20*q**2 - 264*q + 110. Let n(u) = -11*i(u) + 6*k(u). Solve n(r) = 0.
0, 132
Let r(f) be the first derivative of f**6/15 + 4*f**5/5 + 13*f**4/10 - 8*f**3 + 36*f**2/5 + 1192. Factor r(i).
2*i*(i - 1)**2*(i + 6)**2/5
Let k(l) = 7*l**5 + 25*l**4 + 56*l**3 - 34*l. Let n(t) = 2*t**5 + t**3 - t. Let u(r) = k(r) - 2*n(r). Factor u(v).
v*(v + 1)*(v + 4)**2*(3*v - 2)
Let p(q) = -q**2 + q. Let t(f) = 4*f**4 - 16*f**3 - 334*f**2 + 1462*f + 1764. Let o(b) = 6*p(b) - t(b). Let o(h) = 0. Calculate h.
-9, -1, 7
Let c(j) be the first derivative of 5*j**3/3 + 7105*j**2 + 10096205*j + 4429. Let c(u) = 0. Calculate u.
-1421
Let l = -9738 - -983530/101. Let n = l - -1268/707. Suppose 3/7*a**3 - 6/7 + 15/7*a - n*a**2 = 0. Calculate a.
1, 2
Let q be 8/48*(-2 + 55/11). Factor -q*j**3 + 1/4*j**5 + 0*j**4 + 0 + 0*j**2 + 1/4*j.
j*(j - 1)**2*(j + 1)**2/4
Factor 73*c + 12 - 93*c + 3*c**2 + 300*c**4 - 147*c**4 + 6*c**3 - 154*c**4.
-(c - 6)*(c - 1)**2*(c + 2)
Let o(i) be the second derivative of i**7/14 + 7*i**6/30 - 11*i**5/4 - 79*i**4/12 - 10*i**3/3 + 40*i + 9. Suppose o(s) = 0. Calculate s.
-5, -1, -1/3, 0, 4
What is m in -106 - 490*m + 242*m**2 + 131 + 221 + 4*m**3 - 2*m**3 = 0?
-123, 1
Find k such that 7*k**3 + 235*k**2 - 2105 + 624 - 679 - 2*k**3 - 1531*k - 399*k = 0.
-54, -1, 8
Let t be ((-15)/115725)/((-10)/(-25)). Let a = 12347/9258 + t. Suppose -a*w - 1/3*w**3 - 4/3*w**2 + 0 = 0. What is w?
-2, 0
Suppose 14*o = 20*o - 186. Let q = o + -401/13. Solve 0 - 16/13*a**2 + 8/13*a + 10/13*a**3 - q*a**4 = 0 for a.
0, 1, 2
Let n(a) be the first derivative of a**3/12 - 31*a**2/4 + 130*a + 3983. Factor n(o).
(o - 52)*(o - 10)/4
Let z(i) be the first derivative of i**4/4 - 1889*i**3/9 - 105*i**2 - 4572. Let z(j) = 0. Calculate j.
-1/3, 0, 630
Solve -333 - 69/2*a**3 - 1/2*a**4 - 231/2*a + 367/2*a**2 = 0 for a.
-74, -1, 3
Let f(j) be the third derivative of 3*j**7/175 - 31*j**6/300 - 11*j**5/150 + 59*j**4/60 + 2*j**3 + 1977*j**2. Find w, given that f(w) = 0.
-1, -5/9, 2, 3
Let f(u) be the first derivative of u**4/9 + 64*u**3/27 + 110*u**2/9 + 3419. Solve f(w) = 0 for w.
-11, -5, 0
Suppose 4*q - 2*q**2 - 8*q**2 + 5*q**3 + q + 6*q - 26*q = 0. Calculate q.
-1, 0, 3
Let m(s) be the third derivative of -s**5/15 - 1145*s**4/3 - 2622050*s**3/3 - 4*s**2 - 260*s + 2. Factor m(q).
-4*(q + 1145)**2
Let y(i) be the second derivative of 37*i + 28/3*i**3 - 65/3*i**4 + 58/5*i**5 + 0 + 0*i**2 - 14/15*