-2, 0
Let g(l) be the third derivative of l**8/1008 - l**7/90 + 7*l**6/360 + l**5/12 + 432*l**2. What is s in g(s) = 0?
-1, 0, 3, 5
Let i(l) = l**2 - 361*l + 2482. Let w be i(7). Factor 3*q**3 + 0 + 10/3*q**2 - 4/3*q**w - q.
-q*(q - 3)*(q + 1)*(4*q - 1)/3
Let i(w) be the third derivative of w**8/4032 - w**6/36 - 7*w**5/30 - 18*w**2. Let u(m) be the third derivative of i(m). Let u(j) = 0. What is j?
-2, 2
Let b(k) be the first derivative of k**6/150 + k**5/50 - k**3/15 - k**2/10 - 7*k - 4. Let a(f) be the first derivative of b(f). Factor a(q).
(q - 1)*(q + 1)**3/5
Let p(c) be the third derivative of c**7/1260 + c**6/36 + 5*c**5/12 - 5*c**4/12 - 12*c**2. Let k(f) be the second derivative of p(f). Factor k(l).
2*(l + 5)**2
Determine j, given that -55*j**2 + 3*j + 118*j**2 + 3*j**4 - j**4 + 24 - 11*j - 81*j**2 = 0.
-2, 1, 3
Suppose 5*t + 3*m = -0*t + 10, t - 2*m = 2. Let u = t + 2. Let -3*b**3 + 3*b**3 + b**u - b**2 - b**3 - b + 2*b**3 = 0. What is b?
-1, 0, 1
Let t = -21100 + 21103. Factor 2*w**4 + 10*w**2 + 0 + 2*w + 17/2*w**t.
w*(w + 2)**2*(4*w + 1)/2
Let z be (-3 - (-975)/(-10)) + -4. Let g = z + 117. Factor -2*f + g*f**4 + 0 + 12*f**2 - 45/2*f**3.
f*(f - 1)*(5*f - 2)**2/2
Let o = 3269021/18335830 - 2/79721. Let z = o + 1/46. Factor 0 - z*l - 2/5*l**3 - 3/5*l**2.
-l*(l + 1)*(2*l + 1)/5
Factor 15 - 28 + 9 + 4*p - p**2.
-(p - 2)**2
Let n = -310/11 - -8546/297. Let v(z) be the first derivative of 10 - 4/9*z - n*z**3 + 1/27*z**6 - 1/9*z**4 + 4/45*z**5 - 7/9*z**2. Let v(f) = 0. Calculate f.
-1, 2
Let k(a) = -44*a**2 + 32*a + 428. Let g(y) = -4*y**2 + 3*y + 39. Let m(p) = 32*g(p) - 3*k(p). Let m(o) = 0. Calculate o.
-3, 3
Let c(m) be the first derivative of -m**4/78 - 8*m**3/39 - 7*m**2/13 - 40*m + 10. Let h(v) be the first derivative of c(v). Factor h(t).
-2*(t + 1)*(t + 7)/13
Let w be 17*13/221 - (-2)/6. Let w - 4/3*t**3 + 16/3*t**2 - 4/3*t**4 + 2/3*t**5 - 14/3*t = 0. Calculate t.
-2, 1
Let -74/9*t + 4/3*t**3 - 2/9*t**5 - 10/3 + 10/9*t**4 - 44/9*t**2 = 0. Calculate t.
-1, 3, 5
Factor 4*u**3 + 8*u**2 + 251*u**4 - 253*u**4 + 2*u**3.
-2*u**2*(u - 4)*(u + 1)
Suppose 10 = r + 2*i, 5*i - 3 = 22. Determine d, given that d - d**3 - 4*d**2 + 3*d**3 + r*d + d = 0.
0, 1
Let a(j) = -j**2 - 2*j + 1. Let v(u) = 14*u**4 + 38*u**3 - 27*u**2 - 40*u + 13. Let x(g) = a(g) - v(g). Let x(t) = 0. Calculate t.
-3, -1, 2/7, 1
Let h = -61 + 66. Let u(c) be the third derivative of 1/16*c**4 + 0 + 1/6*c**3 + 0*c - 3*c**2 - 1/24*c**h. Suppose u(t) = 0. What is t?
-2/5, 1
Let m(g) be the third derivative of -g**9/5040 - g**8/2240 - 11*g**4/12 - 7*g**2. Let o(l) be the second derivative of m(l). Factor o(k).
-3*k**3*(k + 1)
Let i = -436/3 + 440/3. Solve 1/3*v**3 + 0*v - 1/3*v**5 + 7/3*v**2 - v**4 - i = 0.
-2, -1, 1
Suppose -3*v - 10 = 8. Let j = -3 - v. Factor -5*y**2 + 3*y**j - y - 2*y**3 + 4*y**2 + 1.
(y - 1)**2*(y + 1)
Suppose 9*q + 450 = 12*q. Find r such that 10*r**2 + 264*r - 84*r**2 - 82*r**2 + 15*r**3 + 171*r - q = 0.
2/5, 5
Let v(l) be the second derivative of l**7/210 + l**6/150 - 7*l**5/100 - l**4/60 + l**3/5 + 32*l - 2. Let v(z) = 0. Calculate z.
-3, -1, 0, 1, 2
Let z(f) be the second derivative of -2/7*f**3 + 0 + 0*f**2 - 11*f + 1/42*f**4 + 1/70*f**5. Find h, given that z(h) = 0.
-3, 0, 2
Suppose 0 = 2*s - 8. Let t = s - 2. Let -2*h**5 + 4*h**3 - 2*h + 0*h**2 + 4*h**4 - 15*h**2 + 7*h**t + 4 = 0. Calculate h.
-1, 1, 2
Let s be 36/66*176/64. Solve -2 + 3*m + 1/4*m**3 - s*m**2 = 0 for m.
2
Let n(s) be the first derivative of 9 + 0*s - 3/4*s**4 - 2*s**3 - 3/2*s**2. Factor n(m).
-3*m*(m + 1)**2
Let a(t) = t**3 - 10*t**2 - 11*t + 3. Let f be a(11). Let r(m) be the first derivative of 1/6*m**2 + 1/9*m**f - 2/3*m + 3. What is p in r(p) = 0?
-2, 1
Let q(o) be the first derivative of 5*o**4/4 - 35*o**3/3 - 5*o**2/2 + 35*o + 137. Factor q(u).
5*(u - 7)*(u - 1)*(u + 1)
Suppose 2*o - 17 = -d, -2*d + o + 4*o = 29. Factor -1/5*y**d - 1/5 - 3/5*y - 3/5*y**2.
-(y + 1)**3/5
Let r be ((-74)/6 - -2) + (-6)/(-18). Let m = -10 - r. Solve m + 3/4*o + 9/4*o**2 = 0.
-1/3, 0
Let l(q) = -3*q**3 + 2*q**2 + 5*q - 5. Let n(k) = 2*k**3 - k**2 - 3*k + 3. Let r(w) = -3*l(w) - 5*n(w). Factor r(v).
-v**2*(v + 1)
Determine h, given that 1/2*h**2 + 4 - 3*h = 0.
2, 4
Let i(h) be the third derivative of 0 - 2*h + 0*h**3 - 1/210*h**5 - 1/84*h**4 - 45*h**2. Determine d so that i(d) = 0.
-1, 0
Suppose 120*u**2 - u**4 - 56*u + 39 + 2 - 66*u - 38*u**3 = 0. Calculate u.
-41, 1
Let y(m) = -2*m**3 - 65*m**2 - 118*m - 58. Let j(a) = a**3 - a - 1. Let p(t) = -3*j(t) + y(t). Factor p(k).
-5*(k + 1)**2*(k + 11)
Let d = -1829/3 + 610. Let w(v) be the second derivative of 0*v**3 + 0*v**2 + d*v**4 + 1/10*v**5 - 7*v + 0. Find f such that w(f) = 0.
-2, 0
Let h = 5504 + -5500. Factor 0 + 3/5*t + 1/5*t**h + 1/5*t**3 - t**2.
t*(t - 1)**2*(t + 3)/5
Let p(o) = -7*o**2 - 6*o - 35. Let v(h) = -4*h**2 - 2*h - 18. Let a(u) = 3*p(u) - 5*v(u). Find g, given that a(g) = 0.
-5, -3
Let a(o) be the first derivative of -3*o**5/25 - 33*o**4 - 16206*o**3/5 - 607506*o**2/5 - 1167051*o/5 - 216. Factor a(u).
-3*(u + 1)*(u + 73)**3/5
Let s be (66/30)/(15/(-18)*16/(-40)). Factor 6/5*r**2 + 0*r - s*r**3 + 9*r**4 + 0.
3*r**2*(3*r - 1)*(5*r - 2)/5
Let c(s) be the first derivative of -17 - 1/24*s**4 + 1/9*s**3 + 0*s - 1/12*s**2. Factor c(z).
-z*(z - 1)**2/6
Factor 3*b**4 - 86453*b**2 - 2*b**4 + 86452*b**2.
b**2*(b - 1)*(b + 1)
Let z(k) be the second derivative of -k**6/10 - 13*k**5/10 + 29*k**4/9 - 20*k**3/9 - k - 255. Factor z(r).
-r*(r + 10)*(3*r - 2)**2/3
Let p(o) be the first derivative of -o**3/18 - 17*o**2/12 + 19*o/3 + 83. Factor p(z).
-(z - 2)*(z + 19)/6
Let w(y) be the second derivative of -1/190*y**5 + 0 + 0*y**4 + 7*y + 0*y**2 + 0*y**3. Determine k so that w(k) = 0.
0
Let p be ((-6)/(-60))/(43/1290). Let -2 - 17/2*m**2 + 5/2*m**p + 8*m = 0. Calculate m.
2/5, 1, 2
Suppose 0 = 10*v - 3*v. Suppose 0 = -5*m + 5*p, v = 3*m - 6*m + 2*p. Factor 0*u**3 + m*u**2 + 0 + 2/5*u**5 + 0*u - 2/5*u**4.
2*u**4*(u - 1)/5
Let p(b) be the third derivative of b**6/540 - b**5/60 + b**4/18 + 16*b**3/3 + 19*b**2. Let y(m) be the first derivative of p(m). Let y(s) = 0. What is s?
1, 2
Let l = 52526 - 367632/7. Determine b, given that 32/7*b - 2*b**4 - 8/7 - l*b**2 + 2/7*b**5 + 38/7*b**3 = 0.
1, 2
Let -353919*k**4 - k**5 - 2*k**3 + 23*k**2 + 353912*k**4 - 16 + 8*k - 5*k**3 = 0. What is k?
-4, -1, 1
Let x(y) be the first derivative of y**3/6 + 11*y**2/2 + 20*y + 76. Factor x(o).
(o + 2)*(o + 20)/2
Let v(w) be the first derivative of 1/7*w - 4/21*w**3 + 3/14*w**2 + 13. Factor v(h).
-(h - 1)*(4*h + 1)/7
Let b(k) = -k**2 - 3*k + 4. Let h = 21 - 24. Let y be b(h). Find z, given that 6*z - 5*z + z - 2*z**2 + y*z**2 - 4 = 0.
-2, 1
Let p be (-1)/(-168)*(42 + -40). Let m(y) be the third derivative of -p*y**8 + 0*y + 13*y**2 + 0*y**5 + 1/15*y**6 + 0*y**7 + 0*y**3 + 0 - 1/6*y**4. Factor m(g).
-4*g*(g - 1)**2*(g + 1)**2
Suppose 0 = 47*v - 52*v + 10. Suppose m - 3 = 10*u - 7*u, -v*u = 2*m - 6. What is j in 2/5*j**3 + u*j + 0 + 0*j**2 = 0?
0
Let a be 260/(-35)*(-16)/104. Let a*x**4 + 0 + 0*x - 2/7*x**5 - 8/7*x**2 + 2/7*x**3 = 0. What is x?
-1, 0, 1, 4
Let d(b) be the third derivative of b**7/280 - 3*b**5/80 - b**4/16 - 3*b**2 - 10*b. Find m, given that d(m) = 0.
-1, 0, 2
Let i(h) = -h**3 + 10*h**2 + h - 6. Let b be i(10). Suppose -2*r**4 + 4*r**2 + 0*r**3 + 2*r + 0*r - 2 - b*r**3 + 2*r**5 = 0. Calculate r.
-1, 1
Let x(p) be the third derivative of -p**5/360 + 29*p**4/144 - 2*p**2 - 12. Factor x(d).
-d*(d - 29)/6
Let h(k) be the first derivative of -2*k**7/21 + 2*k**5/5 - 2*k**3/3 + 14*k + 5. Let i(c) be the first derivative of h(c). Factor i(y).
-4*y*(y - 1)**2*(y + 1)**2
Let l(z) = z**3 + 4*z**2 + z - 4. Let o be l(-3). Suppose 4*i - 7 = -3*t, 3*t = -i + o - 7. Solve -3*c**2 + c**4 + 4*c**4 - 2*c - 4*c**i + 0*c = 0 for c.
-1, 0, 2
Let -4/5*x**2 + 3/5*x**4 + 1/5 + 2/5*x**3 - 2/5*x = 0. Calculate x.
-1, 1/3, 1
Factor 13*p + 6 + 2*p**4 - 13*p - 6 - 30*p**3.
2*p**3*(p - 15)
Suppose -248/5*u - 2/5*u**2 - 7688/5 = 0. Calculate u.
-62
Let x(w) be the first derivative of 1/12*w**6 + 3/2*w**3 + 15/8*w**4 + 0*w + 0*w**2 + 44 + 7/10*w**5. Determine q so that x(q) = 0.
-3, -1, 0
Let o(l) = -155*l + 1089. Let t be o(7). Solve -3/4*x**2 - 1/4*x**5 + 5/4*x**3 + 0 + 0*x - 1/4*x**t = 0