 2
Let x be (-27)/60*325/(-39). Factor 0 - 3*t**4 + 3/4*t**5 - 3/2*t**2 + x*t**3 + 0*t.
3*t**2*(t - 2)*(t - 1)**2/4
Let o(u) be the second derivative of -u**7/630 - u**6/360 + u**5/180 + u**4/72 + 3*u**2/2 + 3*u. Let y(n) be the first derivative of o(n). Solve y(f) = 0.
-1, 0, 1
Let k(h) be the second derivative of 3*h**5/190 + 29*h**4/114 + 65*h**3/57 - 25*h**2/19 + h. Suppose k(z) = 0. Calculate z.
-5, 1/3
Let v = 17 - 3. Let u be (v/(-5))/(-1) - 2. Suppose 2/5 - 8/5*f**5 - 18/5*f**4 + 16/5*f**2 - u*f**3 + 12/5*f = 0. Calculate f.
-1, -1/4, 1
Let j be (-71)/23 + -3 + 6. Let z = 27/46 + j. Factor 1/2*i**2 + 0 + 0*i - z*i**3.
-i**2*(i - 1)/2
Let h(c) be the first derivative of -c**3/3 + 7*c**2/2 - 6*c + 28. Factor h(k).
-(k - 6)*(k - 1)
Suppose -132 = 18*o - 84*o. Suppose 0 + 0*a**o + 0*a**4 + 0*a**3 + 0*a - 4/7*a**5 = 0. Calculate a.
0
Let u(t) = 4 + 0 - 4*t - 6*t + 52*t**2 + 36*t**3. Let s(q) = 12*q**3 + 17*q**2 - 3*q + 1. Let x(p) = -10*s(p) + 3*u(p). Factor x(b).
-2*(b + 1)*(2*b + 1)*(3*b - 1)
Let z = -34 - -37. Factor 9/2*x**5 + 8*x**z - 21/2*x**4 + 0*x - 2*x**2 + 0.
x**2*(x - 1)*(3*x - 2)**2/2
Let h(c) = -7*c**4 - 36*c**2 - 35*c - 5. Let b(f) = f**4 + 6*f**2 + 6*f + 1. Let x(d) = 39*b(d) + 6*h(d). Factor x(z).
-3*(z - 3)*(z + 1)**3
Let c be (0/2)/(15/(-5)). Let v(f) be the third derivative of c*f + 1/6*f**3 + f**2 - 1/60*f**5 + 0 + 1/16*f**4. Determine j, given that v(j) = 0.
-1/2, 2
Let l(g) be the second derivative of g**7/18 - g**6/18 - g**5/30 - 3*g. Suppose l(q) = 0. Calculate q.
-2/7, 0, 1
Let o(v) be the second derivative of -v**5/30 - v**4/6 + 3*v**2/2 - v. Let x(a) be the first derivative of o(a). Suppose x(l) = 0. What is l?
-2, 0
Let a(p) = -p**2 + 7*p + 11. Let k be a(8). Suppose -x - k*y + 13 = -7*y, -5*x + 2*y = -11. Factor -x + 1/2*q**2 + 1/2*q.
(q - 1)*(q + 2)/2
What is d in 5*d - 10*d**3 + 15*d**2 - 30*d**5 + 50*d**5 - 15*d**3 - 15*d**4 = 0?
-1, -1/4, 0, 1
Let c(t) = t**3 + 11*t - 5 + 6*t**2 - 8*t + 0*t**3. Let y be c(-5). Solve 5/4*h**4 + 5/2*h**3 + 1/4 + 5/2*h**2 + 1/4*h**y + 5/4*h = 0.
-1
Let d(z) be the second derivative of -1/3*z**4 + 0 - 1/10*z**5 + 3*z + 0*z**2 + 1/3*z**3 + 2/15*z**6. Factor d(n).
2*n*(n - 1)*(n + 1)*(2*n - 1)
Let r be -6*-1*3/9. Let i(p) be the first derivative of 0*p**4 - 1 - 2*p**3 - p**r + 8/5*p**5 + 0*p. Suppose i(c) = 0. Calculate c.
-1/2, 0, 1
Let a be 0/2*(0 - -1) - -42. Let p be (-338)/(-8) - (-2)/(-8). Factor g**3 + p - a.
g**3
Let b(d) be the third derivative of d**6/40 + 3*d**5/20 - 11*d**2. Factor b(i).
3*i**2*(i + 3)
Factor 2/9*a - 2/9 - 2/9*a**3 + 2/9*a**2.
-2*(a - 1)**2*(a + 1)/9
Let c(k) = -6*k**5 + 23*k**4 - 8*k**3 - 6*k**2 + 10*k + 5. Let q(n) = -6*n**5 + 22*n**4 - 9*n**3 - 5*n**2 + 9*n + 4. Let a(l) = 5*c(l) - 6*q(l). Factor a(z).
(z - 1)**3*(2*z + 1)*(3*z - 1)
Let q(a) be the first derivative of 1/4*a - 1/12*a**3 + 1/8*a**2 + 3 - 1/16*a**4. What is n in q(n) = 0?
-1, 1
Suppose -25*r + 37*r = 24. Let -1/2*n**3 - 1/2*n**r + 0 + 0*n = 0. What is n?
-1, 0
Let l(c) = -4*c**5 - 2*c**4 - 9*c**3 - 7*c**2 - 2*c + 3. Let j(t) = 15*t**5 + 9*t**4 + 36*t**3 + 28*t**2 + 8*t - 11. Let y(k) = 6*j(k) + 22*l(k). Factor y(s).
2*s*(s + 1)**3*(s + 2)
Let u = -45 - -50. Let q(n) be the third derivative of 0*n**6 + 0*n**4 + 0 - n**2 + 0*n + 1/1155*n**7 - 1/165*n**u + 1/33*n**3. Solve q(w) = 0 for w.
-1, 1
Factor -32/11 + 16/11*h - 2/11*h**2.
-2*(h - 4)**2/11
Suppose -2*d + 5 = 1. Let f be -4 + 84/8 + d. Factor -11*q**2 + 4*q - 1/2 + 14*q**3 - f*q**4 + 2*q**5.
(q - 1)**4*(4*q - 1)/2
Let h(c) = c**4 - c**3 + c**2 - c - 1. Let v(t) = 19*t**4 + 62*t**3 + 43*t**2 - 88*t - 40. Let g(k) = 4*h(k) - v(k). What is d in g(d) = 0?
-3, -2, -2/5, 1
Solve -40/3*q - 16/3 - 1/3*q**4 - 11*q**2 - 10/3*q**3 = 0.
-4, -1
What is h in -2/3*h**4 + 8/3*h**3 - 2*h**2 + 8/3 - 8/3*h = 0?
-1, 1, 2
Let g(u) = u**5 + 2*u**4 + 5*u**3 + 4*u**2. Let c(d) = d**5 + 3*d**4 + 5*d**3 + 5*d**2. Let x(l) = -6*c(l) + 7*g(l). Suppose x(y) = 0. Calculate y.
0, 1, 2
Suppose -2*d + 4 = 0, 9*u - 2*d = 4*u + 11. Suppose -u*g + 8 = 2. Solve g*k - 52/3*k**3 + 2/3 - 4*k**2 - 6*k**5 - 18*k**4 = 0.
-1, -1/3, 1/3
Let r(g) be the third derivative of -g**9/20160 - g**8/3360 - g**7/1680 + g**5/30 - 2*g**2. Let y(h) be the third derivative of r(h). Let y(c) = 0. What is c?
-1, 0
Let c(n) be the first derivative of -n**5/300 + n**3/30 - n**2 - 2. Let w(h) be the second derivative of c(h). Factor w(f).
-(f - 1)*(f + 1)/5
Let v(u) be the second derivative of -u**10/6048 + u**9/5040 + u**8/3360 - u**4/6 + 5*u. Let q(z) be the third derivative of v(z). Suppose q(r) = 0. What is r?
-2/5, 0, 1
Let q = 22/45 - -1/90. Factor 1/4*b**2 + 0 + q*b - 7/4*b**5 - 15/4*b**3 + 19/4*b**4.
-b*(b - 1)**3*(7*b + 2)/4
Let s(r) = r - 3. Let z be s(6). Let u(o) be the third derivative of 0*o + 1/30*o**5 + 2*o**2 + 0 + 1/6*o**4 + 1/3*o**z. Factor u(p).
2*(p + 1)**2
Suppose 0 = -0*q - 4*q + 7*q. Suppose 2/3*i - 2/9*i**2 + q = 0. What is i?
0, 3
Let g(z) be the third derivative of 0 + 9*z**2 + 1/8*z**4 + 1/120*z**6 - 1/20*z**5 - 1/6*z**3 + 0*z. Let g(i) = 0. What is i?
1
Let i(x) = 2*x - 1. Let d be i(-2). Let m(y) = -y**3 - 5*y**2 - 3*y - 12. Let b be m(d). Let 1/3*p - 1/3*p**b - 1/3*p**4 + 0 + 1/3*p**2 = 0. Calculate p.
-1, 0, 1
Let h(s) be the second derivative of -3*s + 0 + 0*s**3 + 0*s**5 + 1/120*s**6 - 1/48*s**4 + 0*s**2. Factor h(l).
l**2*(l - 1)*(l + 1)/4
Let m(f) be the first derivative of f**6/36 - f**4/12 + f**2/12 + 19. Solve m(r) = 0.
-1, 0, 1
Let l be 3/(-10)*4/(-3). Suppose -m = -3*p - 15, 198 = -m + 4*p + 217. Factor 1/5*y - l + 2/5*y**2 - 1/5*y**m.
-(y - 2)*(y - 1)*(y + 1)/5
Let y(v) be the first derivative of v**5/5 + v**4/4 - 4*v**3 - 41. Determine w so that y(w) = 0.
-4, 0, 3
Let s(u) be the first derivative of -u**6/3 - 2*u**5 - 7*u**4/2 + 2*u**3/3 + 8*u**2 + 8*u + 33. Solve s(h) = 0 for h.
-2, -1, 1
Find q such that 19*q**2 - 5*q - 17*q**2 - 13*q = 0.
0, 9
Let v be (-3)/(-6)*(96/(-18) - -6). Factor -1/3*b**4 + v*b**3 - 1/3*b + 1/3*b**2 + 0.
-b*(b - 1)**2*(b + 1)/3
Let u be (-1 - -1)*(40/(-5) + 9). Suppose 0*l**2 - 1/3*l**3 + 0*l + u = 0. What is l?
0
Suppose -5*x = -b - 20 + 8, 4*x - 14 = 3*b. Let a be 2/4*b/(-3). Factor a*d - 1/3*d**3 + 1/3 - 1/3*d**2.
-(d - 1)*(d + 1)**2/3
Let x = 174/13 - 18992/1417. Let a = 430/327 - x. Factor 2/3*v**4 + 0 - a*v**3 + 2/3*v**2 + 0*v.
2*v**2*(v - 1)**2/3
Let c(k) = -k**2. Let n be -2 + 2 + -3*2. Let t(i) = i**2 + 6*i + 1. Let l be t(n). Let b(q) = -q**3 - 2*q**2 - q. Let h(o) = l*b(o) - 4*c(o). Factor h(y).
-y*(y - 1)**2
Let i(h) = 6*h + 2. Let o(x) = -4*x**2 + 9*x - 13. Let g(l) = l**2 - 2*l + 3. Let r(p) = -9*g(p) - 2*o(p). Let z(d) = -i(d) + 2*r(d). Factor z(s).
-2*(s + 1)*(s + 2)
Let l(q) be the first derivative of 1 + q**3 + 1/2*q**2 - 2*q - 1/5*q**5 - 1/4*q**4. What is k in l(k) = 0?
-2, -1, 1
Let q = 1433/9 - 159. Let s be (2/5)/((-2)/(-20)). Factor -4/3*y + 32/9*y**s + 2/9 + q*y**2 + 16/3*y**3.
2*(y + 1)**2*(4*y - 1)**2/9
Suppose -4*u - 3*k + 27 = 0, 42 = 5*u + 4*k - 3*k. Solve q - 6*q + q**3 - q - u*q**2 - 4*q**3 = 0.
-2, -1, 0
Let t(u) be the third derivative of -u**7/42 - u**6/4 - 3*u**5/4 - 5*u**4/6 - 19*u**2. Factor t(l).
-5*l*(l + 1)**2*(l + 4)
Let s(y) = -7*y**2 + 2*y + 1. Let a(p) = 15*p**2 - 5*p. Let m(g) = 2*a(g) + 5*s(g). Find u such that m(u) = 0.
-1, 1
Suppose -4/5*b - 4/5*b**3 + 0 + 8/5*b**2 = 0. What is b?
0, 1
Let b = 123 + -2213/18. Let m(g) be the first derivative of 0*g**2 + 0*g**3 + b*g**4 + 2 + 0*g + 2/45*g**5. Factor m(s).
2*s**3*(s + 1)/9
Let t(b) = -b**2 - 9*b - 8. Let u be t(-8). Let g be (-2)/(-5) + (-2)/5. Factor -d**2 + g*d**2 + 3*d + u*d - 2*d.
-d*(d - 1)
Let m(c) be the third derivative of c**5/5 - 2*c**4/3 - 8*c**3/3 - 3*c**2. Factor m(a).
4*(a - 2)*(3*a + 2)
Let b(j) be the third derivative of -3*j**8/1120 + j**7/140 - j**6/240 + 4*j**3/3 - 10*j**2. Let x(i) be the first derivative of b(i). Factor x(p).
-3*p**2*(p - 1)*(3*p - 1)/2
Let t = -435 - -438. Factor 0*q + 3/4*q**5 + 0 + 9/4*q**t + 3/4*q**2 + 9/4*q**4.
3*q**2*(q + 1)**3/4
Let q(i) be the second derivative of -7/48*i**4 - 3/80*i**5 - 1/8*i**2 + 0 + 4*i - 5/24*i**3. Determine y so that q(y) = 0.
-1, -1/3
Let b(i) be the second derivative of 0*i**2 + 0 - 1/4*i**4 + 1/10*i**6 + 0*i**5 - 4*i + 0*i**3. Solve b(g) = 0.
-1, 0, 1
Fin