
Let g(p) be the third derivative of -p**6/1080 - p**5/40 - p**4/9 - 2*p**3/3 - 14*p**2. Let z(f) be the first derivative of g(f). Factor z(s).
-(s + 1)*(s + 8)/3
Let y = 351 + -349. Let o(t) be the second derivative of -2/21*t**3 + 0*t**y + 3/35*t**5 - 2/21*t**4 - 6*t + 0. What is q in o(q) = 0?
-1/3, 0, 1
Let y = -38 + 8. Let p be (-1 - 2)*y/18. Factor -5*n**5 - 6*n**2 - n**p + 3*n**5 + 3*n**2 - 9*n**4 - 9*n**3.
-3*n**2*(n + 1)**3
Let 54/7 - 57/7*o + 3/7*o**2 = 0. Calculate o.
1, 18
Let v(a) = -a**2 - a + 2. Let k(l) = -72*l**2 + 57*l + 15. Let c(w) = k(w) - 6*v(w). Factor c(r).
-3*(r - 1)*(22*r + 1)
Let b(r) be the first derivative of r**4/14 - 4*r**3/21 + r**2/7 + 86. Factor b(h).
2*h*(h - 1)**2/7
Let l(y) be the third derivative of -y**6/200 - 17*y**5/100 - 3*y**4/4 - 2*y**2 + 49. Factor l(v).
-3*v*(v + 2)*(v + 15)/5
Let n(q) = -8*q + 5. Let r be n(0). Let x(f) be the third derivative of -7/24*f**4 + 0 + 0*f - 2/15*f**r - 1/40*f**6 + 4*f**2 - 1/3*f**3. Factor x(u).
-(u + 1)**2*(3*u + 2)
Let 4*p**5 + p**4 - 127*p**3 - 3*p**5 + 125*p**3 = 0. What is p?
-2, 0, 1
Let s(y) be the first derivative of -5/6*y**6 + 0*y**2 + 23 - 45/4*y**4 + 0*y**3 - 10*y**5 + 0*y. Factor s(o).
-5*o**3*(o + 1)*(o + 9)
Let g be 0/(5/5 + 1). Let o(t) be the second derivative of g*t**2 - 1/10*t**5 + 0*t**3 - 2*t + 0 + 1/3*t**4. Factor o(r).
-2*r**2*(r - 2)
Let i be (0/(-2))/(6/12*-2). Suppose 8*g - 5*g - 18 = i. Determine z so that 0*z - g*z**2 + 3/2 + 9/2*z**4 - 3*z**5 + 3*z**3 = 0.
-1, -1/2, 1
Let h be (1 + (-13)/15)/((-144)/(-27)). Let f(l) be the third derivative of 0*l + 2*l**2 + h*l**5 + 0 - 1/3*l**3 - 1/240*l**6 + 0*l**4. What is x in f(x) = 0?
-1, 2
Let o(a) be the third derivative of a**8/84 - 16*a**7/105 + 4*a**6/5 - 32*a**5/15 + 8*a**4/3 + a**2 - 111. Factor o(f).
4*f*(f - 2)**4
Let g(o) = -4*o**2 + 10*o - 8. Let t(z) = 2*z + 3. Let n be t(-6). Let b(l) = -17*l**2 + 40*l - 32. Let u(d) = n*g(d) + 2*b(d). Factor u(c).
2*(c - 4)*(c - 1)
Let z(k) = -6*k**3 + 21*k**2 + 6*k + 21. Let a(f) = -f**2 + 3*f + 7. Let s be a(7). Let q(d) = -d**3 + 4*d**2 + d + 4. Let r(l) = s*q(l) + 4*z(l). Factor r(u).
-3*u*(u - 1)*(u + 1)
Let 105*x - 33 + 4*x**2 + 7 - 14 - 93*x = 0. Calculate x.
-5, 2
Let j = -9701 + 145519/15. Determine c, given that -j*c - 2/15*c**2 + 0 = 0.
-2, 0
Suppose -4*u - 12 = l, -5*l + 5*u + 36 = -l. Find c, given that -12*c**4 - 33*c**3 + 21*c + 9 - 3*c**l + 6*c**2 + 15*c**3 - 3*c**5 = 0.
-3, -1, 1
Factor -134*t**2 - 36 + 267*t**2 - 39*t - 136*t**2.
-3*(t + 1)*(t + 12)
Suppose -3 = -3*x + 9. Solve 10*b + b**4 - 8*b**3 + 4*b**2 - 2*b**5 - 18*b**4 + 9*b**4 + x + 0*b**2 = 0.
-2, -1, 1
Let s(i) be the second derivative of -i**6/10 + i**5/5 + 7*i**4/2 + 10*i**3 + 25*i**2/2 + 162*i + 2. Determine p so that s(p) = 0.
-5/3, -1, 5
Let q = 1092 - 42586/39. Let g(f) be the first derivative of q*f**3 - 6/13*f + 1 - 2/13*f**2. Factor g(a).
2*(a - 3)*(a + 1)/13
Let j(y) be the first derivative of 0*y + 3 - 1/60*y**5 - 5/2*y**2 + 1/120*y**6 + 0*y**4 + 0*y**3. Let i(q) be the second derivative of j(q). Factor i(a).
a**2*(a - 1)
Let s(y) be the third derivative of y**7/3780 + y**6/1080 - 3*y**4/8 - 3*y**2. Let t(i) be the second derivative of s(i). Suppose t(h) = 0. What is h?
-1, 0
Let a be 8/((-128)/(-110)) + 1 - 7. Let p(t) be the first derivative of 0*t - 15/32*t**4 - a*t**3 - 3/8*t**2 + 8. Factor p(u).
-3*u*(u + 1)*(5*u + 2)/8
Find u such that 240/7*u + 32/21 + 1350/7*u**2 = 0.
-4/45
Let q(h) be the third derivative of -h**8/1512 + h**7/945 + h**6/270 - h**5/135 - h**4/108 + h**3/27 + 2*h**2 - 16. What is x in q(x) = 0?
-1, 1
Let z(c) be the third derivative of c**7/105 - 3*c**6/16 + 43*c**5/120 + 3*c**4/2 - 5*c**3/3 + 20*c**2. Suppose z(y) = 0. What is y?
-1, 1/4, 2, 10
Let s = -38/25 + 316/175. Let 6/7 + 4/7*z - s*z**2 = 0. Calculate z.
-1, 3
Let a be (6*5)/(-3) + 4. Let z be (-3)/a*-2 + 1. Solve -2 - 2*w**2 + z - 3*w - w + 0*w**2 = 0.
-1
Suppose 4*b + 2 + 2 = 0, -5*b = -3*s + 5. Let o(k) be the first derivative of k**2 - 1/2*k**4 + 3 + 2/3*k**3 - 2/5*k**5 + s*k. Factor o(h).
-2*h*(h - 1)*(h + 1)**2
Solve 48/5 + 14/5*t**2 - 8/5*t**3 + 68/5*t - 2/5*t**4 = 0 for t.
-4, -2, -1, 3
Suppose -11*m + m = -m. Let t(a) be the first derivative of 0*a + 0*a**3 + m*a**2 - 1/18*a**4 - 5. Factor t(r).
-2*r**3/9
Factor 0*z**2 + 237 + 1770*z - 1536*z - 3*z**2.
-3*(z - 79)*(z + 1)
Let c(t) = -t**3 - 7*t**2. Suppose 9*k + 14 = 7*k. Let r be c(k). Find i, given that -7/4*i**3 - 1/2*i - 9/4*i**2 + r = 0.
-1, -2/7, 0
Let h(y) be the second derivative of 3*y**5/140 - y**4/7 + 3*y**3/14 - 395*y. Let h(m) = 0. What is m?
0, 1, 3
What is m in -22/5*m**3 - 326/5*m**2 + 0 + 12*m = 0?
-15, 0, 2/11
Let w(n) = 3*n**2 + 28*n + 10. Let t be w(-8). Let h = t - -112/5. Solve h*r - 8/5*r**2 + 2/5*r**5 + 0 + 12/5*r**3 - 8/5*r**4 = 0 for r.
0, 1
Suppose -8/3 - 2/3*h**2 + 10/3*h = 0. Calculate h.
1, 4
Suppose -5*q + 20 = 0, 4*s + 4*q - 2*q = 28. Let d(c) be the second derivative of -2/15*c**3 - 1/60*c**4 + 5*c + 0 + 1/100*c**s + 2/5*c**2. Factor d(n).
(n - 2)*(n - 1)*(n + 2)/5
Suppose -1 = 2*a - 7. Suppose 8*v - a*v - 20 = 0. Let -22*j**5 + v - 4 + 24*j**5 - 2*j**3 = 0. Calculate j.
-1, 0, 1
Let w be (900/1100)/(6/32). Factor 288/11 + w*t + 2/11*t**2.
2*(t + 12)**2/11
Suppose -b = -m, 4*b + 3 - 28 = -m. Factor -3*q**2 - 5*q**b + 11*q**2 + 10*q**3 - 5*q - 8*q**2.
-5*q*(q - 1)**2*(q + 1)**2
Let l(x) = -x**2 + 1. Let q(j) = 18*j**2 + 45*j + 12. Let g = 61 - 60. Let s(b) = g*q(b) - 2*l(b). Factor s(h).
5*(h + 2)*(4*h + 1)
Factor -171*s**2 - 48*s**2 + 46*s**2 - 65*s**2 - 26*s**2 + 11616*s + 2*s**3 - 170368.
2*(s - 44)**3
Suppose 0*z = -6*z - 1836. Let a = 1552/5 + z. Factor 8/5 + 18/5*i**3 - 32/5*i - a*i**2.
2*(i - 2)*(i + 1)*(9*i - 2)/5
Let n be 0/(2 + -11 - -8). Let l(r) be the second derivative of 1/10*r**6 + 1/2*r**4 - 4*r + n + 0*r**2 + 0*r**3 - 9/20*r**5. Factor l(g).
3*g**2*(g - 2)*(g - 1)
Suppose 4 = 3*p - 2*n, 0*p + p = n + 1. Let u be (p + 32/(-20))*(0 + 10). Factor -36/7*b**2 - 2/7*b**u + 40/7*b + 2*b**3 - 16/7.
-2*(b - 2)**3*(b - 1)/7
Let t(z) be the first derivative of 4*z**2 - 4*z - 4/3*z**3 + 24. Let t(m) = 0. Calculate m.
1
Let g(a) be the second derivative of a**6/5 + 2*a**5/5 - 11*a**4/18 + 2*a**3/9 - 266*a. Let g(r) = 0. What is r?
-2, 0, 1/3
Let f = -4/19 + 267/95. Let a = f - 4/15. Factor a*o**2 + 2/3 + 2/3*o**3 + 7/3*o.
(o + 1)*(o + 2)*(2*o + 1)/3
Let b = 667/1374 - -10/687. Factor 5/2*s + 3/2 + b*s**2 - 1/2*s**3.
-(s - 3)*(s + 1)**2/2
Let m be 3/2 - 63/(-18). Let a = 310 + -306. Solve 3/2*n + n**2 + 0*n**a + 1/2*n**m - 2*n**3 - 1 = 0 for n.
-2, -1, 1
Let o(w) be the second derivative of -5*w**7/56 - w**6/20 + 9*w**5/4 + 13*w**4/2 + 4*w**3 - 19*w - 1. What is x in o(x) = 0?
-2, -2/5, 0, 4
Let q = 598/5 - 1784/15. Find h, given that -8/3*h + q*h**2 + 2 = 0.
1, 3
Let g be 0 + 111/(-45) - (-584)/219. Factor x**2 - 8/5*x - g*x**3 + 4/5.
-(x - 2)**2*(x - 1)/5
Let g(i) = -11*i**5 - 18*i**4 - 43*i**3 + 34*i**2 + 17. Let d(u) = 2*u**5 + 3*u**4 + 7*u**3 - 6*u**2 - 3. Let f(h) = -34*d(h) - 6*g(h). Factor f(q).
-2*q**3*(q - 5)*(q + 2)
Let k(a) be the second derivative of a**5/5 + 2*a**4/3 - 2*a**3/3 - 4*a**2 + 2*a + 28. Solve k(r) = 0.
-2, -1, 1
Suppose 4*y - 5*l = 328, 3*l + 16 = -l. Let a = y + -74. Let 3*i + 3/4*i**2 + a = 0. What is i?
-2
Let y(x) be the third derivative of -x**6/540 - x**5/54 + x**2 + 75. Factor y(t).
-2*t**2*(t + 5)/9
Suppose -4*m + 3*i = -6*m - 78, 143 = -3*m + 2*i. Let q be (0 + 12)*3/(m/(-5)). Let -2/3*c - 4/3*c**q + 0 + 2/3*c**3 + 4/3*c**2 = 0. Calculate c.
-1, 0, 1/2, 1
Let b(m) be the second derivative of -m**7/315 - m**6/75 - m**5/50 - m**4/90 - 12*m - 3. Suppose b(y) = 0. Calculate y.
-1, 0
Let j(c) be the second derivative of c**9/1890 - c**8/672 + c**7/1260 + 7*c**4/6 + 11*c. Let x(f) be the third derivative of j(f). What is q in x(q) = 0?
0, 1/4, 1
Find x, given that 4*x + 3/2*x**4 - 6 + 23/2*x**2 - 11*x**3 = 0.
-2/3, 1, 6
Let z = 4949710/2612367 + 2/137493. What is f in 36/19*f**3 + z*f**2 - 6/19*f**5 + 2/19*f**4 + 2/19*f - 6/19 = 0?
-1, 1/3, 3
Let q(l) = -9*l**3 - 5*l**2 - l + 2. Let s be q(-3). What is a in -106 - s*a - 133*a + 120*a - 326 - 36*a**2 - 2*a**3 = 0?
-6
Let l(f) = -f**2 + 4*f - 5. Let k(j) be the second derivative of j**4/6 - 2*j**3/3 + 5*j**2/