9*h**3 - 61 + 88*h**2 - 77 - 139*h**2 + 32*h - 371*h.
3*(h - 23)*(h + 1)*(3*h + 2)
Let i(q) be the first derivative of 10/3*q**3 + 15*q + 25/2*q**2 - 53. Let i(p) = 0. What is p?
-3/2, -1
Suppose -9*h = -0*h. Let f(b) be the first derivative of -2/25*b**5 + 2 + 2/5*b**2 + h*b**3 - 1/5*b**4 + 2/5*b. Let f(l) = 0. Calculate l.
-1, 1
Let v(k) = k**3 + k**2 - 4*k - 2. Let g be v(-3). Let z = g - -8. Suppose -6*h**2 + z*h**3 - 30*h**4 + 3*h**3 + 33*h**4 = 0. Calculate h.
-2, 0, 1
Factor -16/5 - 2/5*v**3 - 4/5*v + 2*v**2.
-2*(v - 4)*(v - 2)*(v + 1)/5
Let g be (-36)/414 - 1768/(-1288). Let 0 + g*k**3 - 15/7*k**2 + 6/7*k = 0. Calculate k.
0, 2/3, 1
Suppose 7*y - y + 24 = 0. Let p be y/((-4)/4) - 1. Solve -3*v**3 - 13*v**p - 8 - 4*v**5 + 0*v**2 + 20*v - 8*v**2 + 16*v**4 = 0 for v.
-1, 1, 2
Suppose -115*u - 23*u = 0. Factor -1/2*r**2 + 0 - 1/4*r**3 + u*r + 1/4*r**4.
r**2*(r - 2)*(r + 1)/4
Factor -4/3*a**2 - 32/3 - 8*a.
-4*(a + 2)*(a + 4)/3
Suppose 8*r - r = -287. Let x = 124/3 + r. Suppose v**5 - v**3 + x*v**4 + 0*v - 1/3*v**2 + 0 = 0. What is v?
-1, -1/3, 0, 1
Let x(n) be the first derivative of 2*n**5/5 + n**4/2 - 12*n**3 - 52*n**2 - 80*n - 56. Suppose x(o) = 0. What is o?
-2, 5
Suppose -2/19*w**2 + 92/19 + 90/19*w = 0. Calculate w.
-1, 46
Let g be 145/7 + (-24)/(-84). Let v(o) = -3*o**2 + 12. Let j(u) = -15*u**2 + 60. Let p(a) = g*v(a) - 4*j(a). Let p(i) = 0. What is i?
-2, 2
Solve -10*j**3 - 16*j**4 - 4*j**5 - 4*j - 16*j**2 - 16*j**3 - 4*j**3 + 6*j**3 = 0 for j.
-1, 0
Let s = -164 + 284. Let 144 - 8*q - s + 4*q**2 - 12*q = 0. What is q?
2, 3
Let a(u) = -15*u**3 + 35*u**2 + 115*u - 5. Let t(f) = -7*f**3 + 18*f**2 + 58*f - 2. Let g(h) = -2*a(h) + 5*t(h). Factor g(s).
-5*s*(s - 6)*(s + 2)
Let c(x) = 3*x**5 - 2*x**4 + 2*x**3 + 32*x**2 + 23*x + 14. Let k(r) = -2*r**5 + 3*r**4 - r**3 - 29*r**2 - 24*r - 13. Let z(g) = -3*c(g) - 4*k(g). Factor z(m).
-(m - 2)*(m + 1)**3*(m + 5)
Let j(r) = r - 1. Let q be j(3). Suppose a = q + 2. Let 2*l**4 + 2 - a*l**3 - 2*l - 4 + 6*l = 0. Calculate l.
-1, 1
Let g(u) be the third derivative of u**6/540 - 7*u**5/90 + 11*u**4/12 + 121*u**3/27 - 2*u**2 + 11*u. Let g(w) = 0. Calculate w.
-1, 11
Suppose -v = -3*b - 17, -1 = -2*b - 3. Suppose -4 + v = 5*d. Factor 0 + 1/2*i**3 + 1/2*i**d + 0*i.
i**2*(i + 1)/2
Let u(r) be the second derivative of -r**4/21 + 10*r**3/21 - 8*r**2/7 - 7*r + 3. Determine j so that u(j) = 0.
1, 4
Let h(k) be the third derivative of -5*k**8/336 - 5*k**7/42 - k**6/6 + 3*k**2 + 45. Find x, given that h(x) = 0.
-4, -1, 0
Determine x so that -1/4*x**2 - 71/2*x - 5041/4 = 0.
-71
Suppose -6*r = -10*r. Suppose r = -0*d - 2*d + 4. Find q such that -d*q**2 + 2 + q**3 + 6*q - 8*q**3 + 0*q**3 + q**3 = 0.
-1, -1/3, 1
Let d = -483 + 490. Let f(r) be the third derivative of 0*r**3 + 1/105*r**d + 0 - 1/20*r**6 - 1/12*r**4 + 0*r + 1/10*r**5 + r**2. Factor f(v).
2*v*(v - 1)**3
Let l be ((-2)/(-16))/(3/84*(-630)/(-360)). Find a, given that 144*a**l + 1248/7*a**3 - 366*a**4 - 96*a + 96/7 + 126*a**5 = 0.
-2/3, 2/7, 1, 2
Let i(n) be the first derivative of n**3 - 33*n**2/2 - 36*n + 9. Factor i(g).
3*(g - 12)*(g + 1)
Let u(k) be the third derivative of k**7/2520 - k**6/360 + k**4/18 - 5*k**3/6 - 23*k**2. Let z(l) be the first derivative of u(l). Find a, given that z(a) = 0.
-1, 2
Let m(l) be the third derivative of 9*l**8/616 - 81*l**7/385 + 69*l**6/110 - 26*l**5/33 + 14*l**4/33 + 3*l**2 - 52*l. Suppose m(x) = 0. What is x?
0, 2/3, 7
Suppose 28 = 3*d + 1. Factor -14*c + 20*c - 5*c**2 + d*c - 10.
-5*(c - 2)*(c - 1)
Let 15/4 - 17*s - 7*s**3 + 39/2*s**2 + 3/4*s**4 = 0. Calculate s.
1/3, 1, 3, 5
Suppose 4*m - 7*l + 4*l + 93 = 0, -25 = m + l. Let g = m + 21. Let w(p) = -p**2 + p - 4. Let t(d) = -3*d**2 + 2*d - 11. Let j(y) = g*t(y) + 8*w(y). Factor j(n).
(n + 1)**2
Let f = -49/2 - -25. Suppose 5*r - 26 = 4*c - 0, -c = -5*r + 14. Factor 0 + 1/2*j**r - f*j.
j*(j - 1)/2
Let o(j) = 8*j**3 - j**2 - 21*j - 7. Let w(v) = -9*v**3 + 21*v + 6. Let p(y) = -6*o(y) - 5*w(y). Factor p(k).
-3*(k - 4)*(k + 1)**2
Let x(k) be the second derivative of 2*k**7/147 - 6*k**6/35 + 4*k**5/7 + 20*k**4/21 - 64*k**3/7 + 128*k**2/7 + 58*k. Solve x(m) = 0.
-2, 1, 2, 4
Let q(n) = -5*n + 2. Let r be q(3). Let m be r/(-3) - 1/3. Factor 3*u**4 + 2 - 8*u**3 - 2*u**m + 12*u**2 + u**4 - 8*u.
2*(u - 1)**4
Let o(l) be the first derivative of l**7/70 + l**6/20 - 3*l**5/20 - l**4/2 + 2*l**3 - 7*l**2/2 + 3. Let r(z) be the second derivative of o(z). Solve r(s) = 0.
-2, 1
Let z(k) be the second derivative of k**4/6 + 16*k**3/3 - 17*k**2 - 22*k. Factor z(y).
2*(y - 1)*(y + 17)
Find c such that 0 - 2/3*c**4 + 0*c + 0*c**2 + 26/3*c**3 = 0.
0, 13
Let w = 1288865/1795156 - -115/7418. Let x = w - -2/121. Factor 3/4*y + 9/2*y**3 + 3*y**4 + x*y**5 + 0 + 3*y**2.
3*y*(y + 1)**4/4
Let c(h) be the second derivative of 15*h + h**2 + 1/10*h**5 + 0 - 1/6*h**4 - 1/3*h**3. Factor c(l).
2*(l - 1)**2*(l + 1)
Factor 5 + 5 + d - 16*d + 5*d**3.
5*(d - 1)**2*(d + 2)
Let a(z) = 5*z**3 - 5*z**2 + 2. Let c(r) = 10*r**3 - 10*r**2 + 5. Let n(u) = 5*a(u) - 2*c(u). Solve n(k) = 0 for k.
0, 1
Suppose -6 = -15*b + 1 + 23. Factor 1/3*h**3 + 0*h**b - 1/3*h + 0.
h*(h - 1)*(h + 1)/3
Let w(y) be the first derivative of -1/9*y**3 - 2/15*y**5 + 1/36*y**6 + 5/24*y**4 + 0*y**2 - 2 + 0*y. Determine s so that w(s) = 0.
0, 1, 2
Suppose 0 = 3*f + 9, -12 = -2*c + 2*f - 2. Determine l so that -8*l**c + 1 + 12*l**3 + 8*l**3 - 16*l**4 - 1 + 4*l**5 = 0.
0, 1, 2
Let q(r) be the third derivative of -r**7/5040 + r**6/180 - r**5/15 - r**4/8 - 5*r**2. Let p(j) be the second derivative of q(j). Find i such that p(i) = 0.
4
Let y(w) = 3*w**2 + 4*w + 13. Let c(a) = -5*a**2 - 4*a - 17. Let r(q) = -2*c(q) - 3*y(q). Solve r(h) = 0.
-1, 5
Let h be 10/15 + (-14)/(-6). Factor -5*b**h - 7 - 25*b**2 + 7*b - 8 - 9*b - 33*b.
-5*(b + 1)**2*(b + 3)
Let b = -4/435 + 592/1305. Let -b*r**3 + 8/9*r**2 + 0 + 4/3*r = 0. Calculate r.
-1, 0, 3
Let i = 4 - 0. Find m, given that 0*m - m**i - 2*m - 543*m**2 + 2*m**3 + 544*m**2 = 0.
-1, 0, 1, 2
Factor -104/11*u**3 + 0 + 2/11*u**4 + 0*u - 106/11*u**2.
2*u**2*(u - 53)*(u + 1)/11
Let s be (90895/(-84))/(-7) - (-1)/(-4). Let m = -154 + s. Solve 0 - m*p**4 + 2/3*p**3 + 0*p - 1/3*p**2 = 0 for p.
0, 1
Let a(c) be the second derivative of -c**5/150 + c**4/18 - 4*c**3/45 + 208*c. Determine t so that a(t) = 0.
0, 1, 4
Let k(z) be the third derivative of 2/3*z**3 - 7/12*z**4 + 0 + 2*z**2 + 0*z - 3/10*z**5. Factor k(d).
-2*(d + 1)*(9*d - 2)
Factor 8 - 8/3*m - 2/3*m**2.
-2*(m - 2)*(m + 6)/3
Let o be ((0 - -1)/(-12))/(10 + (-217)/21). Factor p**2 - o*p + 0.
p*(4*p - 1)/4
Suppose -4*l**2 - 7*l**2 - 27*l**2 + 3*l**3 + 22 + l**2 + 9*l**2 - 57*l = 0. Calculate l.
-2, 1/3, 11
Suppose -4*t**2 + 72 + 4*t**3 - 48*t + 1/2*t**4 = 0. What is t?
-6, 2
Let d = -2876 + 5755/2. Factor -d*u + 0*u**2 + 0 + 3/2*u**3.
3*u*(u - 1)*(u + 1)/2
Suppose 20*s - 6 = 23*s, 2*s + 4 = -3*v. Let l(h) be the second derivative of v*h**2 + 0 + 3*h - 7/20*h**5 + 1/48*h**4 + 1/12*h**3. Find w, given that l(w) = 0.
-1/4, 0, 2/7
Let f(k) be the second derivative of -k**4/66 + 290*k**3/33 - 21025*k**2/11 - k + 57. What is p in f(p) = 0?
145
Let r = 60/11 + 969/22. Let l = r + -49. Factor 1/2*y**2 - l + 1/4*y**3 - 1/4*y.
(y - 1)*(y + 1)*(y + 2)/4
Factor 44/7*u + 46/7*u**2 + 0 + 2/7*u**3.
2*u*(u + 1)*(u + 22)/7
Let m = 22515/4 + -5628. Factor 0*n + 0 - m*n**2 - 3/8*n**4 - 9/8*n**3.
-3*n**2*(n + 1)*(n + 2)/8
Suppose t - 6 = -4*r + 81, 2*r = 2*t + 36. Suppose 4*a = h + 18, -3*a + h = 8 - r. Determine d so that -1/2 - a*d**3 - 33/4*d**2 - 15/4*d = 0.
-1, -2/5, -1/4
Let q(k) be the third derivative of 1/8*k**3 - 1/240*k**5 + 0 + 0*k + 1/48*k**4 - 22*k**2. Let q(y) = 0. What is y?
-1, 3
Let o = -968 + 968. Let q(i) be the second derivative of 1/30*i**6 - 6*i + 1/42*i**7 - 1/3*i**3 - 3/20*i**5 + o + 0*i**2 - 5/12*i**4. Factor q(y).
y*(y - 2)*(y + 1)**3
Factor -10/3*y**3 + 0 + 6*y**2 + 2/9*y**4 - 26/9*y.
2*y*(y - 13)*(y - 1)**2/9
Let h(k) be the first derivative of -k**4/6 + k**2 + 8*k - 1. Let q(v) be the first derivative of h(v). Factor q(o).
-2*(o - 1)*(o + 1)
Factor -5314410 - 1215/2*y**2 - 5/4*y**3 - 98415*y.
-5*(y + 162)**3/4
Let y(g) = g**3 - 3*g**2 + 3. Let p be y(3). Suppose -5*b + 4*b + 0*b**2 + p*b - 4*b**2 = 0. Calculate b.
0, 1/2
Let t = -130 - -12