t u(x) be the first derivative of x**6/16 - 3*x**5/40 - 9*x**4/16 - x**3/4 + 15*x**2/16 + 9*x/8 - 36. Factor u(n).
3*(n - 3)*(n - 1)*(n + 1)**3/8
Let j(f) be the third derivative of -f**8/1120 + f**7/336 - f**6/360 + f**3 + 4*f**2. Let m(z) be the first derivative of j(z). Factor m(w).
-w**2*(w - 1)*(3*w - 2)/2
Let s(j) = -3*j**2 + 3*j - 2. Let f be (3/(-2))/(1/6). Let h be (-6)/4 - (-1)/(-2). Let c(m) = 13*m**2 - 13*m + 9. Let x(g) = f*s(g) + h*c(g). Factor x(b).
b*(b - 1)
Suppose 0*m + 2/9*m**3 - 2/9*m**2 + 0 = 0. What is m?
0, 1
Suppose 5*w**2 - 37*w**3 + 9*w**4 - 2*w**2 + 25*w**3 = 0. What is w?
0, 1/3, 1
Let l(t) be the third derivative of -t**6/320 - 3*t**5/80 - 9*t**4/64 - t**3/4 + 34*t**2. Factor l(h).
-3*(h + 1)**2*(h + 4)/8
Let q(f) be the second derivative of -1/40*f**5 + 1/6*f**4 + 0 - 5/12*f**3 - f + 1/2*f**2. Solve q(t) = 0 for t.
1, 2
Let s(q) be the second derivative of -1/90*q**6 + 0*q**3 + 3*q + 0 + 0*q**4 + 1/30*q**5 + 0*q**2. Factor s(b).
-b**3*(b - 2)/3
Let j be ((-94)/(-18))/((-6)/(-36)). Let s = j + -31. What is o in -s*o**2 + 0*o + 1/3*o**3 + 0 = 0?
0, 1
Let t(k) be the third derivative of -k**7/35 + 29*k**6/60 - 3*k**5 + 8*k**4 - 32*k**3/3 - 2*k**2. Determine c, given that t(c) = 0.
2/3, 1, 4
Let 6*v**3 - 4*v**2 - 18*v**3 - 7*v**4 - 5*v**4 - 4*v**5 = 0. What is v?
-1, 0
Let l(t) be the second derivative of -4*t**2 - 5/6*t**4 - 8*t + 0 + 8/3*t**3 + 1/10*t**5. Solve l(q) = 0.
1, 2
Let c(u) be the second derivative of 2*u**7/63 + u**6/10 + u**5/10 + u**4/36 + 4*u. Let c(m) = 0. What is m?
-1, -1/4, 0
Let s(z) be the first derivative of -z**5/40 + z**4/32 + z**3/24 - z**2/16 + 57. Factor s(q).
-q*(q - 1)**2*(q + 1)/8
Find q, given that 3/2*q**2 + 9 - 15/2*q = 0.
2, 3
Suppose 3*o = 7*o. Let g(q) be the first derivative of 2/5*q**5 + 1/6*q**6 + 0*q + 1/4*q**4 + 0*q**2 - 2 + o*q**3. Suppose g(s) = 0. Calculate s.
-1, 0
Let q(o) be the first derivative of -3*o**4/16 + 5*o**3/12 + o**2/2 - o + 14. Find x such that q(x) = 0.
-1, 2/3, 2
Let v = 27 + -22. Let h(i) be the third derivative of 1/36*i**4 + 0 + 0*i**3 + 0*i + 1/90*i**v + 2*i**2. Suppose h(p) = 0. What is p?
-1, 0
Let m(i) be the second derivative of -1/30*i**5 + 0 + 2/3*i**2 - 3*i - 5/9*i**3 + 2/9*i**4. Factor m(h).
-2*(h - 2)*(h - 1)**2/3
Let g(s) = -s**3 + 6*s**2 + 2*s - 6. Let t be g(6). Suppose -4*o + t = -o. Factor -12/5*h**3 + 2/5*h**4 + 26/5*h**o + 8/5 - 24/5*h.
2*(h - 2)**2*(h - 1)**2/5
Suppose -3*b + 4 = -4*m, -5*m + 4*b - 14 = -4*m. Suppose 2*q = 5*q - 6. Find v such that 4*v**q - v**m - 2*v**2 = 0.
0
Suppose -14 = 2*a - 4. Let j(f) = -f - 3. Let q be j(a). Let -h**q + 6 - 5*h + 4*h - 4 = 0. What is h?
-2, 1
Let m(u) = -u**2 + 14*u - 13. Let q be m(13). Let q + 0*j**2 + 1/3*j**3 + j**4 + 0*j + 2/3*j**5 = 0. Calculate j.
-1, -1/2, 0
Factor 3*m**4 + 8*m**4 + m**5 - 16*m**4 - 5*m**3 + 6*m**2 + 3*m**4.
m**2*(m - 3)*(m - 1)*(m + 2)
Let y(n) be the second derivative of -n**5/40 + n**4/6 - 5*n**3/12 + n**2/2 - 50*n - 2. Solve y(u) = 0.
1, 2
Let v = 386 + -1924/5. Let 0 - 4/5*t**3 + 0*t**2 - 2/5*t**5 + 0*t - v*t**4 = 0. What is t?
-2, -1, 0
Factor -7/3*u + 3*u**2 + 2/3 + 1/3*u**4 - 5/3*u**3.
(u - 2)*(u - 1)**3/3
Let -60 - 26*j**3 - 18*j**2 + 80*j - 23*j**3 + 44*j**3 + 3*j**2 = 0. What is j?
-6, 1, 2
Suppose 7*z - 50 = 2*z - 4*u, u = -4*z + 51. Solve -z*c**3 - 7*c**4 - 10*c**3 - 10*c + 2*c**3 + 0*c**3 - 24*c**2 - 1 = 0.
-1, -1/7
Let d(q) = -2*q - 1 + 5*q - 2*q. Let i be d(3). Factor -2*c + 4*c**3 - 10*c**i + 10*c**2 - 2*c**5.
-2*c*(c - 1)**2*(c + 1)**2
Let d(j) be the third derivative of j**8/13440 - j**6/1440 - j**4/24 - 2*j**2. Let k(n) be the second derivative of d(n). Find a such that k(a) = 0.
-1, 0, 1
Let z(j) be the first derivative of -j**3/3 - 13*j**2/4 - 3*j + 31. Factor z(g).
-(g + 6)*(2*g + 1)/2
Let r be 1/(-1)*-2*3. Let n(y) = y**3 + 2*y**2 + 3*y + 3. Let x(k) = k**2 + k + 1. Let p(f) = r*x(f) - 2*n(f). Factor p(a).
-2*a**2*(a - 1)
Let f(h) be the first derivative of 1/16*h**4 - 1/2*h + 1/20*h**5 - 1 - 1/4*h**3 - 5/8*h**2. Let f(p) = 0. Calculate p.
-1, 2
Let t(w) = -7*w**2 + 2*w**3 + 3*w**2 - 3*w**2 + w**3 + 5*w**4 - w. Let i(l) = l**3 - l**2. Let j(u) = -2*i(u) + t(u). Find b such that j(b) = 0.
-1, -1/5, 0, 1
Let r be (1 - 2) + 10/(1020/138). Factor -6/17*q + 2/17 + r*q**2 - 2/17*q**3.
-2*(q - 1)**3/17
Let d(n) = -n**2 - 6*n + 2. Suppose 2*q = -4*f - 0*q - 14, -5*q = -2*f - 37. Let v be d(f). Determine m, given that -4/3*m**v - 2/3*m**3 - 2/3*m + 0 = 0.
-1, 0
Suppose -q = 31 - 33. Factor 0*w - 2/7 + 2/7*w**q.
2*(w - 1)*(w + 1)/7
Let m = 93 - 91. Factor -1/3*u**m - 1/3 - 2/3*u.
-(u + 1)**2/3
Suppose 0 = 162*l - 160*l. Factor 0 - 4/3*g**2 + l*g.
-4*g**2/3
Let m(o) be the third derivative of 0 - 1/36*o**6 + 3*o**2 + 0*o - 1/1008*o**8 - 1/90*o**7 + 3/8*o**4 - 3/2*o**3 + 1/10*o**5. Factor m(b).
-(b - 1)**2*(b + 3)**3/3
Let w(g) be the second derivative of -8*g**7/21 - 2*g**6/3 + 11*g**5/5 + 23*g**4/3 + 26*g**3/3 + 4*g**2 + 5*g. Let w(r) = 0. Calculate r.
-1, -1/4, 2
Let k(h) be the third derivative of h**6/72 - h**5/30 - h**4/24 + 2*h**3/9 - h**2. Suppose k(m) = 0. What is m?
-4/5, 1
Suppose 8*v**2 - 12*v**4 + 5*v - 4*v**5 + 3*v**2 - 4*v**3 + v**2 + 3*v = 0. Calculate v.
-2, -1, 0, 1
Let j(d) be the second derivative of -d**7/84 - d**6/60 + 3*d**5/20 + d**4/6 - 2*d**3/3 + 10*d. Let j(m) = 0. What is m?
-2, 0, 1, 2
Let h(j) be the third derivative of 0*j**3 + 1/540*j**6 - 1/108*j**4 - j**2 + 0 + 1/270*j**5 + 0*j - 1/945*j**7. Factor h(b).
-2*b*(b - 1)**2*(b + 1)/9
Let y = -5 - -14. Let m be (6/(-4))/(y/(-3)). Suppose -m*f**3 + 0 + 1/2*f**2 + 1/2*f - 1/2*f**4 = 0. Calculate f.
-1, 0, 1
Let z(c) be the third derivative of c**8/42 + 3*c**7/35 + c**6/10 + c**5/30 + 3*c**2. Let z(f) = 0. Calculate f.
-1, -1/4, 0
Let q(m) be the second derivative of 5*m**4/3 + 25*m**3/6 - 4*m. Factor q(d).
5*d*(4*d + 5)
Let h(r) be the first derivative of -9/10*r**4 - 2/5*r**3 + 2 - 2/5*r + r**2. Determine o, given that h(o) = 0.
-1, 1/3
Factor 45/8*r + 3/8*r**3 - 21/8 - 27/8*r**2.
3*(r - 7)*(r - 1)**2/8
Let m be 1*(-3 - 68/(-20)). Factor 0*l - m*l**4 + 0 + 0*l**2 + 0*l**3.
-2*l**4/5
Let b be 4/(-2)*(-6)/12. Let p be (2 - b)*1/3. Factor -2/3*i**2 - p*i**3 + 0*i + 0.
-i**2*(i + 2)/3
Let w(y) = y**4 - y**3 + y**2 - y + 1. Let g(j) = 3*j**4 + j**3 + j**2 - j + 1. Let b(s) = g(s) - w(s). Suppose b(r) = 0. Calculate r.
-1, 0
Suppose -3*y + 6 = -0. Let a = -121/4 - -32. What is w in 1/2*w + w**3 - 1/4 + a*w**y = 0?
-1, 1/4
Let l(z) be the third derivative of -z**7/210 + z**5/60 - 39*z**2. Let l(m) = 0. What is m?
-1, 0, 1
Determine r so that -10 - 50*r**2 + 37*r + 25*r**3 - 5*r**4 - 2*r + 5*r**2 + 0*r**4 = 0.
1, 2
Let v be (4/(-3))/(3/(-27)). Let b = -4 + v. Suppose 4 - 3*k - 3*k - b + 10*k**2 = 0. What is k?
-2/5, 1
Let d(b) be the third derivative of -b**6/120 - b**5/20 - b**4/6 - 2*b**3/3 - 3*b**2. Let l be d(-3). Factor 2*r**2 + 12 - r**2 - l - 4*r.
(r - 2)**2
Let g(o) be the second derivative of -o**5/30 + 5*o**4/18 + o**3/9 - 5*o**2/3 + 39*o. Factor g(j).
-2*(j - 5)*(j - 1)*(j + 1)/3
Factor 2/5*y**2 + 4/5*y + 2/5.
2*(y + 1)**2/5
Let t(k) be the second derivative of k**5/40 + k**4/24 + 5*k. What is z in t(z) = 0?
-1, 0
Let q(b) be the first derivative of b**3/7 + 27*b**2/14 + 6*b + 50. Suppose q(n) = 0. What is n?
-7, -2
Let h = 13 - 5. Let m = h - 6. Factor 6*l**3 + 4 - 2*l - 3*l**3 - 4*l**m - l**3.
2*(l - 2)*(l - 1)*(l + 1)
Suppose 4*i + i = 10. Find d such that 4*d**i - 2*d**3 - 4*d**2 + 2*d = 0.
-1, 0, 1
Let a(u) be the second derivative of 1/4*u**3 + 0 + 0*u**2 + 2*u - 1/16*u**4 - 3/40*u**5 + 1/40*u**6. Factor a(f).
3*f*(f - 2)*(f - 1)*(f + 1)/4
Let o(i) be the second derivative of -1/12*i**4 + 0*i**2 + 1/30*i**6 + 0*i**3 + 0 - 1/40*i**5 - 5*i + 1/84*i**7. What is d in o(d) = 0?
-2, -1, 0, 1
Let t = 3 + 1. Determine m so that 32*m**2 - 3*m**t - 3*m**3 - 32*m**2 = 0.
-1, 0
Suppose -5*a**4 + 214*a**2 - 199*a**2 + 4*a**3 - 5*a - 10 + a**3 = 0. What is a?
-1, 1, 2
Let w be 910/75 - 9 - (-2)/(-6). Solve -w*k**3 + 38/5*k**2 - 16/5*k - 8/5 = 0 for k.
-2/7, 1, 2
Let t = 12 + -6. Let h(g) = 17*g**3 + 9*g**2 + 2*g + 5. Let u(o) = -o**4 + 18*o**3 + 9*o**2 + 2*o + 6. Let c(v) = t*h(v) - 5*u(v). Determine x so that c(x) = 0.
-1, -2/5, 0
Let m = -244/3 - -82. Factor 0 + 2*c**2 - m*c.
2