
-1
Let k(f) = -f**3 + 2*f + 2. Let n be k(-3). Let z = n + -20. Solve -8/5*h**4 + 0 + 2/5*h**2 - 2/5*h + 8/5*h**z = 0 for h.
-1/2, 0, 1/2, 1
Let y(t) be the third derivative of t**7/3780 + t**6/1080 - t**5/90 + 13*t**4/12 - 28*t**2. Let g(o) be the second derivative of y(o). Solve g(i) = 0.
-2, 1
Solve 3*b**3 + b**2 + 54*b**2 + 57*b**3 + 5*b**4 = 0 for b.
-11, -1, 0
Suppose -5*n = -2*z - 3*z - 25, -3*n = 5*z + 1. What is d in -3*d - 1291*d**n - 10 + 10*d**2 - 2*d + 1296*d**3 = 0?
-2, -1, 1
Let s(w) = 2*w**2 + 14*w - 13. Let i be (-3 + 2)*(10 - 1) + 1. Let o be s(i). Let 1/2*v**o + 0 - v + 1/2*v**2 = 0. What is v?
-2, 0, 1
Let o(l) be the third derivative of -1/180*l**6 + 0*l**5 + 0*l + 0*l**3 + 1/72*l**4 + 0*l**7 + 0 + 7*l**2 + 1/1008*l**8. Let o(v) = 0. What is v?
-1, 0, 1
Factor 0 + 22/5*h**2 + 12/5*h + 12/5*h**3 + 2/5*h**4.
2*h*(h + 1)*(h + 2)*(h + 3)/5
Let y(x) be the first derivative of 4*x**3/3 - 19*x**2 + 102*x + 6. Let l(a) = -20*a**2 + 189*a - 511. Let h(q) = 2*l(q) + 11*y(q). Solve h(j) = 0.
5
Let p(w) be the second derivative of 0*w**3 + 0 - 7/108*w**4 + 10*w + 1/90*w**6 + 1/378*w**7 - 1/180*w**5 + 2/9*w**2. Suppose p(r) = 0. Calculate r.
-2, -1, 1
Suppose 3982 - 3938 = 22*n. Solve -3/4*u + 1/4*u**5 + 0 + 0*u**4 - 3/2*u**3 - n*u**2 = 0.
-1, 0, 3
Let q(t) be the third derivative of -t**5/120 - t**4/48 + t**3/6 - 25*t**2 + 2*t. Solve q(r) = 0 for r.
-2, 1
Let t = 24617 - 24614. Factor 12/7 + 16/7*b**2 - 2/7*b**t - 26/7*b.
-2*(b - 6)*(b - 1)**2/7
Suppose -2*h + 2 = -6, 0 = 2*w - h. Let q(c) be the third derivative of -1/60*c**6 + 0*c - 5*c**w + 8/3*c**3 + 1/5*c**5 - c**4 + 0. Find r, given that q(r) = 0.
2
Let c(u) = 11*u**2 + 338*u + 9743. Let f(a) = -57*a**2 - 1689*a - 48714. Let t(w) = -21*c(w) - 4*f(w). Let t(q) = 0. Calculate q.
-57
Factor y**4 - 3*y**3 - y**4 + 2090*y**2 - 2082*y**2 + 4*y**5 - 9*y**3.
4*y**2*(y - 1)**2*(y + 2)
Let c(z) be the first derivative of 0*z - 2/25*z**5 - 27 + 1/2*z**4 + 3/5*z**2 - 14/15*z**3. What is m in c(m) = 0?
0, 1, 3
Let o = -231/4 - -58. Let o*i**2 + 4 - 2*i = 0. Calculate i.
4
Let z(t) be the third derivative of t**6/600 - t**5/100 + 4*t**2 - 4*t. Suppose z(m) = 0. Calculate m.
0, 3
Let s(f) = f**3 - 9*f**2 - 10*f + 3. Let g be -2 + 12 - (-9 - -9). Let o be s(g). Suppose 2*w**2 + 2*w**4 + 1/2*w**5 + 0 + o*w**3 + 1/2*w = 0. What is w?
-1, 0
Let h(q) be the first derivative of 7/2*q**3 - 14 - 15/4*q**2 - 3*q. Solve h(g) = 0 for g.
-2/7, 1
Let m(g) be the third derivative of -g**7/21 + 23*g**6/120 - 4*g**5/15 + g**4/8 - 50*g**2. Factor m(c).
-c*(c - 1)**2*(10*c - 3)
Let x(c) be the first derivative of -1/3*c**6 + 28/3*c**3 + 7 + 16*c - 8/5*c**5 + 20*c**2 - 1/2*c**4. Solve x(g) = 0.
-2, -1, 2
Let l(w) = -3*w**2 + 216*w. Let c(x) = 3*x. Let u(o) = -6*c(o) + l(o). Factor u(m).
-3*m*(m - 66)
Let -64*x**4 + 8*x**5 + 4*x**5 + 16*x**5 - 44*x - 7*x**3 + 8 + 23*x**3 + 56*x**2 = 0. Calculate x.
-1, 2/7, 1
Suppose 4*g - 4*i - 32 = 0, 2*g = -g + 2*i + 29. Let j(u) = 66*u - 647. Let l be j(10). Let -l + o**2 - o**4 + 0*o**4 + g = 0. Calculate o.
-1, 0, 1
Factor 66*m**2 + 79 + 123*m + 1771*m**3 - 19 - 1768*m**3.
3*(m + 1)**2*(m + 20)
Let t be 17/(170/15)*(-1)/(2/(-4)). Find j such that 0*j**t + 9/4*j**2 - 3/8*j**4 - 3*j + 9/8 = 0.
-3, 1
Let w(y) be the second derivative of -21*y - 1/60*y**6 - 1/6*y**3 + 0 - 5/24*y**4 - 1/10*y**5 + 0*y**2. Solve w(t) = 0 for t.
-2, -1, 0
Let k = -159/28 - -1487/252. Let 0*q + 0 + k*q**3 - 2/9*q**2 = 0. What is q?
0, 1
Let g(l) be the first derivative of 45*l**6/4 + 393*l**5/5 + 1329*l**4/8 + 79*l**3 - 69*l**2 - 36*l + 399. What is i in g(i) = 0?
-3, -2, -1, -2/9, 2/5
Let q(s) = -s**2 + 2*s + 101. Let h be q(11). Factor 0 + 9/4*f**h + 3/2*f.
3*f*(3*f + 2)/4
Let w(l) = -29*l**4 + 29*l**3 + 51*l**2 - 91*l + 49. Let m(p) = 7*p**4 - 7*p**3 - 13*p**2 + 23*p - 12. Let t(a) = -9*m(a) - 2*w(a). Factor t(n).
-5*(n - 1)**3*(n + 2)
Suppose 3*q = 5*q - 6. Suppose -5*y - 5*z = 5, 0 = y + 3*z - 5*z - 14. Let -f + q*f**2 - y + 1 + f = 0. What is f?
-1, 1
Let y(j) be the third derivative of j**7/210 - j**6/15 - 2*j**5/15 + 4*j**4 + 24*j**3 + 28*j**2 + 4. Suppose y(w) = 0. What is w?
-2, 6
Let o(s) = 4*s**2 - 206*s + 2911. Let n(i) = -6*i**2 + 308*i - 4366. Let z(t) = -5*n(t) - 8*o(t). Let z(b) = 0. What is b?
27
Suppose -7*p = -181 + 146. Factor 3/4*y**4 + 3/4*y**3 + 0 + 1/4*y**2 + 0*y + 1/4*y**p.
y**2*(y + 1)**3/4
Let a(q) be the first derivative of 0*q - 3/5*q**5 - 3/2*q**2 + q**3 + 21 + 3/4*q**4. Suppose a(r) = 0. What is r?
-1, 0, 1
Let g be (-3 + 0)/(((-792)/48)/11). Let d(l) be the third derivative of -g*l**3 - 7*l**2 + 1/20*l**5 + 0*l**4 + 0 + 0*l. Suppose d(f) = 0. What is f?
-2, 2
Suppose -12*d + 21 = -5*d. Let h(l) be the first derivative of 3/2*l - 3/2*l**d - 5 - 3/2*l**2. Factor h(i).
-3*(i + 1)*(3*i - 1)/2
Let z(p) = 13*p**3 - 353*p**2 + 4*p. Let i(v) = -11*v**3 + 351*v**2 - 3*v. Let u(g) = 4*i(g) + 3*z(g). Factor u(r).
-5*r**2*(r - 69)
Let n(o) be the second derivative of 2*o**7/105 - 4*o**5/25 + 2*o**4/15 + 2*o**3/5 - 4*o**2/5 - 77*o + 3. Suppose n(x) = 0. Calculate x.
-2, -1, 1
Find n, given that 5*n - 11/2 + 1/2*n**2 = 0.
-11, 1
Let h = 183/11410 + -2/1141. Let x(r) be the second derivative of -9*r + 0*r**2 - 1/42*r**4 - 1/21*r**3 + 0 + h*r**5 + 1/105*r**6. Let x(j) = 0. Calculate j.
-1, 0, 1
Let y = 145 + -142. Let m(h) be the third derivative of 0*h - h**2 + 1/210*h**5 + 0*h**y + 0 + 1/42*h**4 - 1/420*h**6. Factor m(u).
-2*u*(u - 2)*(u + 1)/7
Suppose 4*s = 9*s. Suppose f = -s*f + 5. Factor -3*a**f + 6*a**4 + 4*a**4 - 17*a**4 + a**4.
-3*a**4*(a + 2)
Suppose 0 = 70*h - 142*h + 80*h - 24. Suppose 4*d = 2*g - 16, -4*d + 23 = 4*g - 9*d. Factor 2/7 - g*t - 26/7*t**h + 30/7*t**2 + 8/7*t**4.
2*(t - 1)**3*(4*t - 1)/7
Let n(g) be the third derivative of -g**5/12 + 35*g**4/8 - 245*g**3/3 - 5*g**2 - 42. Find o, given that n(o) = 0.
7, 14
Let k(j) = -j**3 - 7*j**2 - 6*j + 6. Let m(y) = -3*y. Let f be m(2). Let r be k(f). Let -r*b**2 + b**3 - 6 - 3*b + 12*b**2 + 2*b**3 = 0. What is b?
-2, -1, 1
Let v = -5643 - -5645. Factor -2/3 - 16/3*w**v + 6*w.
-2*(w - 1)*(8*w - 1)/3
Let c(d) = 8*d**2 - 5*d - 3. Let k(l) = 9*l**2 - 5*l - 4. Let b(i) = 4*c(i) - 3*k(i). Solve b(z) = 0.
0, 1
Suppose 189*m - 360 = 69*m. Let 0 + 1/4*r**m - 1/4*r**5 + 1/2*r**4 + 0*r - 1/2*r**2 = 0. Calculate r.
-1, 0, 1, 2
Let b = 0 - -2. Let i(v) be the first derivative of -8/9*v + 1 - 4/9*v**b - 2/27*v**3. Factor i(r).
-2*(r + 2)**2/9
What is y in -24*y**2 + 16/3*y + 32/3 - 8/3*y**4 + 44/3*y**3 = 0?
-1/2, 2
Let j(y) be the second derivative of 0 - 16*y + 3/8*y**4 - 1/2*y**3 - 3/40*y**5 + 0*y**2. Factor j(i).
-3*i*(i - 2)*(i - 1)/2
Solve 10*y**4 + 286/15*y**2 + 0 + 484/15*y - 112/3*y**3 = 0.
-2/3, 0, 11/5
Let c(m) be the third derivative of m**5/10 + 47*m**4/180 + 2*m**3/45 - 3*m**2 - 11*m. Factor c(x).
2*(x + 1)*(45*x + 2)/15
Determine c, given that 9/5*c**4 + 63/5*c + 99/5*c**2 + 12/5 + 57/5*c**3 = 0.
-4, -1, -1/3
Let j(w) be the second derivative of -3*w**5/20 - 7*w**4/4 - 7*w**3 - 12*w**2 + 4*w - 9. Factor j(a).
-3*(a + 1)*(a + 2)*(a + 4)
Suppose -3*o - 2*t = -11, 5*o - 2*t - 13 = -0*o. Let -3*r**5 - 231*r**4 + 225*r**4 + 0*r**5 + 6*r**2 + 3*r**o = 0. What is r?
-2, -1, 0, 1
Let b(n) be the second derivative of n**4/24 + 3*n**3/4 - 5*n**2/2 + 2*n + 10. Let b(a) = 0. What is a?
-10, 1
Let a(n) = -3*n + 15. Let l be a(4). Factor -10*s**3 + 7*s**3 - 5*s**l + 12*s**4 - 4*s**2.
4*s**2*(s - 1)*(3*s + 1)
Suppose 0 = 4*t + p - 49, -2*t + 21 = -0*p - 3*p. Suppose -4*n = -3*n - 6. Factor -t*k**3 - 2*k - n*k + 5*k - 15*k**2.
-3*k*(k + 1)*(4*k + 1)
Suppose 4*t - 3*o - 17 = 0, 2*o + 8 = -5*t + 6*t. Factor 0 - 8*v + 1 - 2 - t*v**2 - 5.
-2*(v + 1)*(v + 3)
Let m(u) be the first derivative of u**3/3 - 453*u**2/14 - 130*u/7 - 542. Solve m(g) = 0 for g.
-2/7, 65
Find b, given that -48/5 + 47/5*b**2 - 16/5*b**3 + 16/5*b + 1/5*b**4 = 0.
-1, 1, 4, 12
Let q(a) be the third derivative of -a**7/630 - 13*a**6/360 - 17*a**5/60 - 67*a**4/72 - 14*a**3/9 + 391*a**2 + 1. Factor q(f).
-(f + 1)**2*(f + 4)*(f + 7)/3
Factor -13*t**4 + 4*t**4 - 5*t**4 - 6*t**4 - 16*t**2 - 4*t**5 - 32*t**3.
-4*t**2*(t + 1)*(t + 2)**2
Let q(b) be the third derivative of 4/7*b**4 + 0*b + 0 + 32/21*b**3 + 25*b**2 + 13/105*b**5 + 1/70*b**6 + 1/1470*b**7. Determine j so that 