+ c**4/60 - 3*c**2. Suppose b(m) = 0. Calculate m.
0, 1
Let m(n) be the second derivative of n**3/6 - 3*n**2/2 + 11*n. Let x be m(5). What is h in 0*h**3 + 0*h + 0 + 1/2*h**x - 1/2*h**4 = 0?
-1, 0, 1
Let j = 0 - -2. Solve 2*m - 3*m - m**3 - j*m**3 - 4*m**2 = 0.
-1, -1/3, 0
Factor -6*s**5 + s**5 - 6*s**3 - 12*s**4 + s**3 + 2*s**4.
-5*s**3*(s + 1)**2
Determine q so that 12*q**3 - 2 - 11*q - 18*q**2 - 1 + 23*q - 3*q**4 = 0.
1
Let x(i) be the third derivative of 1/3*i**3 + 0*i**4 + 0*i + 1/240*i**6 - i**2 + 1/40*i**5 + 0. Let o(v) be the first derivative of x(v). Factor o(u).
3*u*(u + 2)/2
Let o(m) be the third derivative of 0 + 1/108*m**4 + 0*m + 1/27*m**3 - 1/540*m**6 - 1/270*m**5 - m**2. Factor o(i).
-2*(i - 1)*(i + 1)**2/9
Let c(x) be the second derivative of 11/6*x**4 - 29/20*x**5 + 2*x - 1/21*x**7 + 0 + 2/3*x**3 - 4*x**2 + 13/30*x**6. Find t such that c(t) = 0.
-1/2, 1, 2
Suppose 1/6*n**2 + 0*n + 0 = 0. Calculate n.
0
Let c(l) = l**5 - l**4 - l**3 + l + 1. Let a(r) = -9*r**5 + r**4 - 10*r**3 - 22*r**2 - 21*r - 11. Let f(s) = -5*a(s) - 40*c(s). Let f(y) = 0. Calculate y.
-3, -1
Let p(o) = -o**3 + 7*o**2 + 2*o - 10. Let t be p(7). Let g be t/18 - (-12)/27. Factor -g - 2/3*v**2 - 4/3*v.
-2*(v + 1)**2/3
Let r be ((-1)/(-6))/((-52)/(-16) - 3). Solve -2/3*l**2 + 0*l + 0 + 0*l**3 + r*l**4 = 0.
-1, 0, 1
Let x(h) = 3*h - 11. Let c be x(5). Let g(o) be the second derivative of -1/42*o**c + 1/70*o**5 + 1/7*o**2 + 0 + 2*o - 1/21*o**3. Factor g(s).
2*(s - 1)**2*(s + 1)/7
Let m = 191 + -1340/7. Let s = 13/14 + m. Determine k so that 1/4*k**4 + s*k**3 + 0*k + 0 + 1/4*k**2 = 0.
-1, 0
Suppose 0 = -5*p - 4*w + 9, p + 2*p + 5*w - 8 = 0. Suppose p = 3*d - 11. Suppose -q**5 - q**3 - q**d + q**2 + 0*q**3 + 2*q**3 = 0. What is q?
-1, 0, 1
Let w(s) = 15*s**3 - 15*s**2 - 18*s + 3. Let k(v) = v**3 + v - 1. Let t(l) = -3*k(l) + w(l). Suppose t(n) = 0. What is n?
-1, 1/4, 2
Suppose 5*q = 38 + 172. Let n be 1131/q - (-1)/2. Factor 240/7*i**3 + 32/7 + 368/7*i**2 + n*i + 50/7*i**4.
2*(i + 2)**2*(5*i + 2)**2/7
Suppose -3*n + 3*y + 27 = 0, -4*n - n = -2*y - 30. Suppose 0*h + 2*g = h, -n*h = g. Factor -2/3*z - 2/3*z**2 + h.
-2*z*(z + 1)/3
Let x(s) = s**3 + s**2 - 9. Let l(t) be the first derivative of 2*t + 4. Let k(v) = 9*l(v) + 2*x(v). Factor k(n).
2*n**2*(n + 1)
Determine v, given that 16/3 + 8*v**2 + 4/3*v**3 + 12*v = 0.
-4, -1
Let a(n) be the second derivative of 0 + 3/4*n**2 + 7/8*n**3 + 5/16*n**4 + n. Factor a(m).
3*(m + 1)*(5*m + 2)/4
Let z be 175/28 + 3/4. Let u = 10 - z. Determine p, given that 3*p + 1 + 6*p**2 + p**3 + 3*p**3 - u*p**2 - 3*p**3 = 0.
-1
Suppose -5*j - 3*k + 6 = 0, -4*k + 2 = 4*j - 6. Let m(d) be the first derivative of j*d**3 + 0*d**4 + 0*d + 0*d**2 - 1/25*d**5 - 1 - 1/30*d**6. Factor m(q).
-q**4*(q + 1)/5
Let t(z) be the first derivative of -2/25*z**5 - 1 + 0*z**4 - 1/15*z**6 + 0*z**3 + 0*z + 0*z**2. Solve t(f) = 0 for f.
-1, 0
Let w(n) be the first derivative of -3 - 2/9*n - 2/27*n**3 - 2/9*n**2. Factor w(z).
-2*(z + 1)**2/9
Let q(r) = -7*r**3 - 5*r**2 - 4*r. Let c(j) = 20*j**3 + 16*j**2 + 12*j. Suppose 4*o - 12 = -2*a, 2*a - 9 = -3*o + 6*a. Let u(t) = o*c(t) + 8*q(t). Factor u(y).
4*y*(y + 1)**2
Let o(x) be the first derivative of -2*x**3/27 - x**2/9 + 10. Factor o(q).
-2*q*(q + 1)/9
Let f(w) be the third derivative of -w**6/60 - w**5/15 + w**4/12 + 2*w**3/3 + 2*w**2. Suppose f(p) = 0. What is p?
-2, -1, 1
Let c(f) be the third derivative of 1/140*f**6 - 3*f**2 - 1/28*f**4 + 0*f + 0*f**3 + 1/490*f**7 + 0 - 1/140*f**5. Factor c(p).
3*p*(p - 1)*(p + 1)*(p + 2)/7
Factor 36*h + 6*h**2 + 110 - h**2 - 2*h**2 - 2.
3*(h + 6)**2
Factor -1/5*y + 0 + 1/5*y**2.
y*(y - 1)/5
Suppose -51*d = -54*d + 6. Let b = -76 + 382/5. Find n, given that 2/5*n + 0 - b*n**d = 0.
0, 1
Let d(n) = 10 - 11 - 2*n - 18. Let v be d(-11). Factor -1/2 + 1/4*k**v - 3/4*k + 0*k**2.
(k - 2)*(k + 1)**2/4
Let k(v) be the first derivative of -v**5/5 - 5*v**4/4 - 7*v**3/3 - 3*v**2/2 + 23. Factor k(m).
-m*(m + 1)**2*(m + 3)
Let -v**3 + 2 - 4*v**3 + 3*v**3 + 2 + 6*v = 0. What is v?
-1, 2
Find t, given that 4/3 + 2/3*t**2 - 2*t = 0.
1, 2
Solve -7/3*z**2 - 5*z**3 - 4/3*z**5 - 1/3*z - 13/3*z**4 + 0 = 0.
-1, -1/4, 0
Let k(w) be the second derivative of -w**7/8820 + w**6/1260 - w**5/420 - w**4/12 - 2*w. Let z(x) be the third derivative of k(x). Factor z(d).
-2*(d - 1)**2/7
Let f(n) = -n**2 + 1. Let v(x) = 3*x**2 - 8*x - 11. Let h(m) = -4*f(m) - v(m). Let l be h(-7). Factor -1/5*o + l - 1/5*o**2.
-o*(o + 1)/5
Solve x**2 + x**4 - 20*x - 3*x**3 + x**5 - 2*x**4 + 22*x = 0.
-1, 0, 1, 2
Let w(y) be the third derivative of y**7/105 + 7*y**2. Factor w(b).
2*b**4
Suppose -3*n = -5*h, 0*h + 4*h = 4*n. Factor 3/2*y**3 + h*y + 1/2*y**4 + 0 + y**2.
y**2*(y + 1)*(y + 2)/2
Suppose -30 + 5 = -5*b. Determine g so that -4/5*g**3 + 8/5*g**2 + 6/5*g**b - 2/5*g - 8/5*g**4 + 0 = 0.
-1, 0, 1/3, 1
Let s = -141/152 - -20/19. Let j(p) be the first derivative of 2 + 1/12*p**3 - 1/16*p**4 - 1/4*p + s*p**2. Determine y so that j(y) = 0.
-1, 1
Let j(d) be the third derivative of -d**7/210 + d**5/60 + 5*d**2 + d. Find l, given that j(l) = 0.
-1, 0, 1
Let u be (-2)/(-4) + (-4)/8. Factor w + 0*w**2 - 2*w**2 + u*w**2 + w.
-2*w*(w - 1)
Solve 0 + 4/3*q**2 + 8/3*q = 0.
-2, 0
Let q(z) be the third derivative of 1/36*z**4 + 0*z + 0 - 2/9*z**3 - 4*z**2 + 1/90*z**5. Factor q(u).
2*(u - 1)*(u + 2)/3
Let j(u) be the third derivative of u**10/529200 - u**8/70560 - u**5/30 + 2*u**2. Let n(v) be the third derivative of j(v). Solve n(s) = 0 for s.
-1, 0, 1
Let c(s) be the first derivative of -2*s**3/45 + s**2/5 - 4*s/15 - 12. Suppose c(j) = 0. Calculate j.
1, 2
Suppose 0 = -52*s + 62 + 42. Let -4/5*j**s - 4/5*j**3 + 8/5*j + 0 = 0. What is j?
-2, 0, 1
Solve 56/5*q**5 + 10*q**2 + 34*q**4 + 34*q**3 - 4/5 - 2*q = 0 for q.
-1, -2/7, 1/4
Let k = 8 + -8. Let j(m) be the second derivative of -1/12*m**4 + k - 1/6*m**3 + 0*m**2 - m. Find l such that j(l) = 0.
-1, 0
Let j = -236/7 + 34. Let a = 1 - -1. Factor 0 - 2/7*r**a - j*r.
-2*r*(r + 1)/7
Let g(r) be the second derivative of r**6/50 - 9*r**5/50 + 13*r**4/20 - 6*r**3/5 + 6*r**2/5 - 10*r. Find p such that g(p) = 0.
1, 2
Let a = -14 + 21. Let k(l) = -2*l**3 + 6*l**2 - 10*l - 2. Let f(d) = 4*d**3 - 12*d**2 + 19*d + 3. Let q(n) = a*k(n) + 4*f(n). Factor q(v).
2*(v - 1)**3
Let j(l) = -14*l**3 - 2*l - 5. Let o(w) be the second derivative of w**5/4 + w**3/6 + w**2 + 3*w. Let a(n) = -4*j(n) - 11*o(n). Let a(h) = 0. What is h?
-1, 2
Let u = 4 - 4. Let a = 47/2 - 23. Let u*j**2 + 1/2 - a*j**4 + j**3 - j = 0. What is j?
-1, 1
Let f = 22 + -18. Let g(h) be the first derivative of -4/7*h**2 + 2/7*h**f - 2/7*h**3 - 2 - 2/35*h**5 + 8/7*h. What is k in g(k) = 0?
-1, 1, 2
Let h be (-3 - (-81)/15) + (1 - 3). Factor 0*b + 0 - h*b**2.
-2*b**2/5
Let k(b) be the third derivative of -3*b**5/140 + b**4/56 + 7*b**2. Find w such that k(w) = 0.
0, 1/3
Let y = -5 - -10. Suppose c - y*c = -8. Solve 12 + 0*x - 9*x**c - 9*x - 3*x = 0.
-2, 2/3
Let l be (4 + 2)*(-9)/(-6). Suppose -4*k + l*k - 15 = 0. Let 4/9*v - 2*v**2 + 2*v**k + 0 = 0. What is v?
0, 1/3, 2/3
Let n = 290 + -288. Find y such that -2/3*y**3 + 10/3*y**n - 14/3*y + 2 = 0.
1, 3
Let p(k) be the first derivative of -k**3/3 + k + 2. Factor p(m).
-(m - 1)*(m + 1)
Let x = 236/363 - -2/121. Determine k, given that -x*k**4 - 2*k**3 + 0*k + 0 - 4/3*k**2 = 0.
-2, -1, 0
Let h(z) = 0 + 7 + 3*z**2 + 21*z - 4. Let m be h(-7). Factor 2/3*u**m - 2/3*u**4 + 0 + 2/3*u**2 - 2/3*u.
-2*u*(u - 1)**2*(u + 1)/3
Let -15/4 + 10*s + 5/4*s**4 + 0*s**3 - 15/2*s**2 = 0. What is s?
-3, 1
Let s(m) be the third derivative of -m**7/560 - m**6/320 + 3*m**5/160 + 5*m**4/64 + m**3/8 + 2*m**2. Suppose s(y) = 0. What is y?
-1, 2
Determine p, given that 24 - 4*p**3 - 12*p**2 - 7 - 2 + 1 = 0.
-2, 1
Let y = -138 + 141. Let m(j) be the first derivative of -1/20*j**4 + 0*j**2 + 0*j + 3 + 2/15*j**y - 3/25*j**5. Factor m(c).
-c**2*(c + 1)*(3*c - 2)/5
Let i(t) = -t + 20. Let g be i(18). Factor 3*y**g + 3/2 + 3/4*y**3 + 15/4*y.
3*(y + 1)**2*(y + 2)/4
Let a(f) = f**2. Let c(m) = -1. Let i(h) = -3*a(h) - 3*c(h). Factor i(x).
-3*(x - 1)*(x + 1)
Let s = -7 - -3. Let v = -2 - s. Determine p so that 0*p + 0 + 1/4*p**v - 1/4*p**3 = 0.
0, 1
Let a(w) be the first derivative of -w**4/4 + 2*w**3 - 53. Factor a(h).
-h**2*(h