w + 0 + 1/3*w**4 + 0*w**y + w**3 = 0.
-3, 0
Let b(n) be the first derivative of -n**5/45 + n**4/6 - n**3/9 - 5*n**2/9 - 690. Factor b(w).
-w*(w - 5)*(w - 2)*(w + 1)/9
Let x(j) be the first derivative of 0*j - 5/2*j**2 + 1/12*j**4 + 1/35*j**5 + 4 + 2/21*j**3. Let g(q) be the second derivative of x(q). Let g(r) = 0. What is r?
-2/3, -1/2
Let x(s) be the second derivative of s**7/273 + 203*s**6/195 + 6834*s**5/65 + 11560*s**4/3 - 314432*s**3/39 - 3*s + 94. Solve x(k) = 0.
-68, 0, 1
Let z(o) = 44*o**3 + 845*o**2 + 43253*o - 89883. Let q(l) = -52*l**3 - 846*l**2 - 43254*l + 89882. Let a(n) = -5*q(n) - 6*z(n). Factor a(v).
-4*(v - 2)*(v + 106)**2
Let y = -28 - -48. Factor 5*w - y*w**2 - 22*w + 15*w**3 - 3*w.
5*w*(w - 2)*(3*w + 2)
Let x(z) = -3*z - 13. Let h be x(-10). Suppose -1 - h*b**3 + 2*b**2 - b**4 + 17*b**3 = 0. Calculate b.
-1, 1
Find z, given that 3299*z - 6102*z + 3070*z - 3*z**2 = 0.
0, 89
Let q(n) = n**3 - 5*n**2 + 6*n - 2. Let j be q(4). Let l(x) = x + 4. Let v be l(j). Solve -4*r**3 + 2*r**3 + 4*r**2 - v*r**2 = 0 for r.
-3, 0
Let i = -1733 - -1735. Factor -1/3*f**i + 2/3*f - 1/3.
-(f - 1)**2/3
Let m = 84 + -112. Let h = -25 - m. Factor 0 + 12/5*v**4 + 0*v + 6/5*v**2 + 3*v**h + 3/5*v**5.
3*v**2*(v + 1)**2*(v + 2)/5
Let w(q) be the second derivative of -q**5/4 - 5*q**4/4 + 25*q**3/3 + 11*q - 7. Suppose w(f) = 0. Calculate f.
-5, 0, 2
Let h(q) be the third derivative of q**5/160 - q**4/2 + 31*q**3/16 + 95*q**2. Factor h(m).
3*(m - 31)*(m - 1)/8
Let k(p) be the second derivative of 0 - 7/30*p**5 + 3*p - 5/6*p**4 - 1/45*p**6 - p**3 + 0*p**2. Suppose k(c) = 0. Calculate c.
-3, -1, 0
Suppose 3*w + 0 - 6 = -3*q, w - 4*q - 2 = 0. Factor -54*d + 5*d**2 - 24*d**3 - 373*d**4 + 58*d**w + 376*d**4.
3*d*(d - 3)**2*(d - 2)
Suppose -16/5*o**3 - 54/5 - 72/5*o**2 - 108/5*o = 0. What is o?
-3/2
Let d(z) be the second derivative of 7*z**5/4 - 95*z**4/12 - 85*z**3/3 - 20*z**2 - 618*z. Let d(c) = 0. What is c?
-1, -2/7, 4
Let l = -8/55 - -6/11. Let c be (-1)/((-3)/(-6)) - -5. Factor 0*j + l*j**4 - 2/5*j**c + 0*j**2 + 0.
2*j**3*(j - 1)/5
Factor 1/4*l**4 + 0 - 25/4*l**2 - 11/4*l**3 - 13/4*l.
l*(l - 13)*(l + 1)**2/4
Let b(q) be the third derivative of 19*q**2 + 1/18*q**5 + 0 - 25/36*q**4 - 1/540*q**6 + 125/27*q**3 + 0*q. Factor b(i).
-2*(i - 5)**3/9
Find v such that -16*v + 108/5*v**3 + 14/5*v**4 - 2/5*v**5 + 152/5*v**2 - 192/5 = 0.
-2, 1, 12
Solve 3*y**3 + 3*y**3 - 8*y**2 - 2*y**3 - 5*y - 27*y = 0.
-2, 0, 4
Let f(o) be the third derivative of -o**5/15 + o**4 - 10*o**3/3 - 22*o**2 - 8*o. Let f(m) = 0. What is m?
1, 5
Let l = -5655 - -5658. Suppose u - 3/4*u**l + 0 - u**2 + u**4 - 1/4*u**5 = 0. Calculate u.
-1, 0, 1, 2
Let 104/15*y + 112/15*y**2 + 0 + 34/15*y**3 + 2/15*y**4 = 0. What is y?
-13, -2, 0
Suppose -36 = 4*j - 2*v, 0 = -4*j + j + 4*v - 27. Let o be 2/5 + j/((-270)/(-12)). What is n in o*n + 0 - 4/7*n**4 + 2/7*n**3 + 2/7*n**2 = 0?
-1/2, 0, 1
Let s be 3/(-5)*(-5 + 30/7). Suppose -12/7*j - s*j**2 + 15/7 = 0. Calculate j.
-5, 1
Let m(o) be the third derivative of -o**6/60 - 3*o**5/5 - 5*o**4 - 56*o**3/3 + 14*o**2. Let m(k) = 0. Calculate k.
-14, -2
Factor -54*f**3 - 78*f + 56*f**3 + 76*f.
2*f*(f - 1)*(f + 1)
Let d(q) be the first derivative of q**6/18 + q**5/3 - 17*q**4/12 - 17*q**3/9 + 16*q**2/3 + 28*q/3 - 136. Find s such that d(s) = 0.
-7, -1, 2
Let f(a) be the third derivative of -a**6/1260 - 13*a**5/210 - 169*a**4/84 - a**3/6 - 8*a**2. Let x(l) be the first derivative of f(l). Let x(p) = 0. What is p?
-13
Let p(q) be the third derivative of q**9/6720 - q**8/6720 - q**5/60 + 3*q**2. Let g(o) be the third derivative of p(o). Suppose g(l) = 0. What is l?
0, 1/3
Suppose 4*t - 4 - 7 = 5*r, -3*t - 2*r = -14. Let d be ((-12)/t)/(3 - (-18)/(-5)). Solve -1/3*q**d - 2*q**3 - 1/3*q + 4/3*q**2 + 4/3*q**4 + 0 = 0 for q.
0, 1
Let u(o) be the first derivative of 3*o**5/35 - 6*o**4/7 + 136. Factor u(a).
3*a**3*(a - 8)/7
Let z(g) = -3*g**2 + g. Let j(y) = -14*y**2 + 12*y. Let k(i) = -j(i) + 5*z(i). What is w in k(w) = 0?
-7, 0
Let i(d) be the first derivative of 0*d + 49/2*d**2 - 26 + 1/4*d**4 + 14/3*d**3. Find y, given that i(y) = 0.
-7, 0
Let j(c) be the third derivative of c**9/15120 + c**8/4200 - c**6/900 - c**5/600 + 7*c**3/6 - 8*c**2. Let s(d) be the first derivative of j(d). Factor s(y).
y*(y - 1)*(y + 1)**3/5
Let t = 86 - 65. Suppose 5*x - t = -2*f, -9 = -5*x + 7*f - 5*f. Factor -3/5*d**2 - 3/5*d**4 - 6/5*d**x + 0 + 0*d.
-3*d**2*(d + 1)**2/5
Let a = -21 + -115. Let z = a + 410/3. Factor -2 - 4/3*d + z*d**2.
2*(d - 3)*(d + 1)/3
Let t(r) be the first derivative of -1/120*r**6 - 1/8*r**4 + 0*r + 1/20*r**5 - 6 + 0*r**2 - 3*r**3. Let j(q) be the third derivative of t(q). Factor j(u).
-3*(u - 1)**2
Let s(o) be the third derivative of -1/420*o**5 - 1/56*o**4 - 1/21*o**3 + 0 + 0*o + 6*o**2. Suppose s(v) = 0. What is v?
-2, -1
Suppose 0 = 7*j - 5*j. Let o = 2 - j. Suppose -2*s**4 - 11*s**o + 3*s**3 + 3*s**5 + 11*s**2 - 4*s**4 = 0. Calculate s.
0, 1
Let l(d) be the second derivative of -25/2*d**2 + 8*d + 1/4*d**5 - 5/4*d**4 - 15/2*d**3 + 0. Determine o so that l(o) = 0.
-1, 5
Suppose 11*k + 3*k = -84. Let s be (-23 + -1)/k*(-2)/(-2). Factor d**3 - d - 1/2*d**s + 1/2 + 0*d**2.
-(d - 1)**3*(d + 1)/2
Let k = 10 + -17. Let b be (2/k)/(1/(-7)). Factor b*a**2 - 9 - 2*a**5 - a**4 + 3*a**5 - 2*a**3 + 10 + a - 2.
(a - 1)**3*(a + 1)**2
Let u(l) be the third derivative of 1/245*l**7 + 0 + 0*l + 1/1176*l**8 + 0*l**4 + 0*l**5 - 1/105*l**6 - 26*l**2 + 0*l**3. Factor u(c).
2*c**3*(c - 1)*(c + 4)/7
Suppose 0 = -27*u - 9*u + 4*u. Factor -1/3*i**2 + 0*i + u.
-i**2/3
Let x = -96 - -174. Factor 14*r + 16 + 2*r - x*r**2 + 82*r**2.
4*(r + 2)**2
Let j(b) be the third derivative of 0*b**3 + 0*b - 2/315*b**7 + 1/216*b**6 + 0 + 29*b**2 + 1/45*b**5 - 1/336*b**8 + 1/54*b**4. Find c such that j(c) = 0.
-1, -2/3, 0, 1
Find l such that -17/4*l**3 + 57/4*l**2 + 5/4 - 39/4*l - 3/2*l**4 = 0.
-5, 1/6, 1
Let f(p) be the first derivative of p**4/4 + 8*p**3/3 + 8*p**2 + 22. Factor f(r).
r*(r + 4)**2
Determine g, given that -2/3*g**3 - 16/3*g + 20/3*g**2 - 2/3*g**4 + 0 = 0.
-4, 0, 1, 2
Let o be (-1)/4 + (-34)/(-40). Suppose -32*g - 19*g = -36*g - 30. Factor -3/5*m**5 + 6/5*m**3 + 0*m**g + 0*m + 0 + o*m**4.
-3*m**3*(m - 2)*(m + 1)/5
Let h(q) = q**2 + 43*q + 52. Let c(r) = -2*r**2 - 64*r - 78. Let u(x) = 5*c(x) + 8*h(x). Factor u(k).
-2*(k - 13)*(k + 1)
Let t(x) be the first derivative of 1/18*x**6 + 2/9*x**3 - 6 + 0*x + 0*x**4 - 1/6*x**2 - 2/15*x**5. Find w such that t(w) = 0.
-1, 0, 1
Let c(y) = y**2 + 12*y + 24. Let v be c(-10). Let k(x) be the second derivative of 0*x**2 - 1/60*x**5 + 5*x + 0 + 1/9*x**3 - 1/36*x**v. Factor k(z).
-z*(z - 1)*(z + 2)/3
Let q(a) = -a**2 - 3*a**2 - 2*a**3 - 10 + 18*a - 2*a**2. Let x(t) = -t**3 - 3*t**2 + 9*t - 5. Let i(u) = 6*q(u) - 11*x(u). Determine c so that i(c) = 0.
-5, 1
Let d(l) be the second derivative of -2*l**7/147 - 8*l**6/105 + 36*l**5/35 - 74*l**4/21 + 122*l**3/21 - 36*l**2/7 - 238*l. Determine x so that d(x) = 0.
-9, 1, 2
Let n(z) be the third derivative of 1/24*z**4 - 9*z**2 + 0*z**3 - 1/840*z**7 + 0*z + 0*z**5 - 1/160*z**6 + 0. Factor n(c).
-c*(c - 1)*(c + 2)**2/4
Let b(i) = -142*i - 8. Let s be b(-4). Find d such that 2*d**3 - 2*d**2 - 3*d**2 - 559 + d**3 + s + d = 0.
-1/3, 1
Let -1/8*k**2 - 169/2 - 13/2*k = 0. Calculate k.
-26
Let b(i) be the first derivative of -5*i**4/12 - 8*i**3/9 + 2*i**2/3 + 817. Factor b(g).
-g*(g + 2)*(5*g - 2)/3
Suppose 5 = -f - 25. Let h = f - -32. Let 16*y + 20 + h*y + 8*y + 5*y**2 - 6*y = 0. What is y?
-2
Let c = 17/1057 + 16759/9513. Let 0*f + 4/9*f**2 - c = 0. Calculate f.
-2, 2
Let 32 + a + 3*a**2 - 4*a - 15*a - a**2 - 2*a = 0. What is a?
2, 8
Let l = -1128 - -1130. Factor 1/5 + 1/5*q**l + 2/5*q.
(q + 1)**2/5
Let t(a) = a**3 - 8*a**2 + 6*a + 9. Let i be t(7). Let u = 46 + -136/3. Factor -1/3 + w - u*w**i.
-(w - 1)*(2*w - 1)/3
Let p(j) be the third derivative of -5*j**2 + 0 + 0*j**4 - 1/420*j**7 + 0*j**3 + 0*j + 0*j**5 - 1/120*j**6. Factor p(m).
-m**3*(m + 2)/2
Suppose 9*z - 3*h + 35 = 4*z, 0 = 2*z - 4*h. Let c be ((-5)/z*(-1 + 1))/1. Factor 0 - 1/3*x**4 + 0*x**2 + c*x**3 + 0*x.
-x**4/3
Let u = 1139 + -4529/4. Let c = -25/4 + u. Factor c*q**3 + 0 + q**2 + 1/2*q.
q*(q + 1)**2/2
Let y(m) = -2*m - 6. Let k be y(-4). Let c = 39 - 