o**6/72 - 5*o**4/24 - 5*o**3/9 + 33*o**2/2 + 31*o. Let g(b) be the first derivative of j(b). Solve g(n) = 0.
-1, 2
Let l(x) be the first derivative of -3/25*x**5 + 0*x + 0*x**4 + 0*x**2 + 24 + 4/5*x**3. Solve l(r) = 0.
-2, 0, 2
Let x(v) be the second derivative of 5*v**5/4 - 35*v**4/12 + 5*v**3/3 - 13*v + 1. Factor x(l).
5*l*(l - 1)*(5*l - 2)
Factor 60/7*u - 117/7*u**2 + 3/7*u**4 + 0 + 54/7*u**3.
3*u*(u - 1)**2*(u + 20)/7
Let k = 9881/3654 + -16/261. Let u = k - 11/28. Determine f so that -3*f - 3/2*f**2 + u - 3/4*f**4 + 3*f**3 = 0.
-1, 1, 3
Let i(a) = -9*a**4 - 2*a**3 - 5*a**2 + 16*a. Let s(q) = -4*q**4 - 2*q**3 - 2*q**2 + 8*q. Let f(m) = 2*i(m) - 5*s(m). Solve f(l) = 0.
-2, 0, 1
Let r(q) = -9*q**2 + 2*q - 1. Let p be r(-2). Let n be p/(-13) - (-8)/(-52). Factor 2*c**3 + 13*c**3 - 8*c**n - 9*c**2 + 2*c.
c*(c - 1)*(7*c - 2)
Let q(w) = 3*w**3 - 25*w**2 + 20*w + 52. Let i(d) = -3*d**3 + 24*d**2 - 21*d - 51. Let g(j) = -4*i(j) - 3*q(j). Find f, given that g(f) = 0.
-1, 4
Let k(w) = -9*w**2 + 14*w. Let c = 92 + -52. Let n(v) = -v**2 + v. Let b(s) = c*n(s) - 5*k(s). Solve b(o) = 0.
0, 6
Let l = 4 - 2. Suppose -2 = l*j - 3*j. Factor -4*w**2 - 6*w**j + 3*w**3 + 14*w - 2 - 5*w + 0*w**2.
(w - 2)*(w - 1)*(3*w - 1)
Let j = -318 - -318. Let w(p) be the third derivative of 0 + j*p + 2/21*p**3 - 5*p**2 - 1/210*p**5 + 1/84*p**4. Factor w(g).
-2*(g - 2)*(g + 1)/7
Let k(b) be the third derivative of 9*b**8/112 - 3*b**7/70 - b**6/5 + b**5/5 - 21*b**2 - 16. Factor k(h).
3*h**2*(h + 1)*(3*h - 2)**2
Suppose 0 = 62*b - 84 - 40. Factor 4/13 + 2/13*w - 2/13*w**b.
-2*(w - 2)*(w + 1)/13
Let m = 1/2791 + 22317/30701. Find v such that m - 14/11*v**2 + 0*v + 6/11*v**3 = 0.
-2/3, 1, 2
Let z(f) be the first derivative of f**4/5 + 28*f**3/15 + 22*f**2/5 + 4*f + 31. Find n such that z(n) = 0.
-5, -1
Let n be ((-11)/(-4))/(33/22). Let d = 5/2 - n. Determine m so that 0*m - 2/3*m**2 + 2/3*m**5 + 0 + d*m**4 - 2/3*m**3 = 0.
-1, 0, 1
Let z(s) = s**3 - 4*s**2 + 3. Let c be z(4). Let p(i) be the first derivative of -4*i**c + 15/2*i**2 - 5 - 3*i. Factor p(f).
-3*(f - 1)*(4*f - 1)
Let m = -11 - -13. Suppose -3 = -m*x + x. Determine l so that x*l + 2*l**2 - 3*l**2 - 15*l + 10*l = 0.
-2, 0
Let z(w) be the third derivative of w**6/32 - 31*w**5/240 + 17*w**4/96 - w**3/24 + 784*w**2. Determine y, given that z(y) = 0.
1/15, 1
Let g(r) = -30*r**2 - 34*r - 24. Let l(n) = 30*n**2 + 34*n + 20. Let c(a) = -4*g(a) - 5*l(a). Factor c(w).
-2*(w + 1)*(15*w + 2)
Let x = -917 + 917. Let l(j) be the third derivative of 0 - 1/6*j**4 + 1/5*j**5 - 1/10*j**6 + x*j**3 - 8*j**2 + 0*j + 2/105*j**7. Solve l(f) = 0 for f.
0, 1
Suppose 3*s + 518 = -2*w, 0*w - 4 = w. Let t = 170 + s. Find x such that 0*x + t*x**2 + 0 + 2/19*x**3 = 0.
0
Let o(j) = j**3 + 14*j**2 + 59*j + 601. Let x be o(-13). Factor 2/7*f**x + 10/7*f - 4/7 - 8/7*f**2.
2*(f - 2)*(f - 1)**2/7
Factor 0*k + 3/2*k**4 + 0*k**3 + 0 - 3/2*k**2.
3*k**2*(k - 1)*(k + 1)/2
Let b(u) be the second derivative of 3*u**5/10 - 11*u**4/8 + 5*u**3/4 + 3*u**2/2 - u + 9. Find g, given that b(g) = 0.
-1/4, 1, 2
Let j(d) be the first derivative of 3*d**4/4 + 729*d**3/5 + 79497*d**2/10 - 15987*d/5 - 273. Factor j(p).
3*(p + 73)**2*(5*p - 1)/5
Let y(x) be the first derivative of 4*x**5/5 - 7*x**4/2 - 10*x**3/3 + 4*x**2 - 320. Factor y(m).
2*m*(m - 4)*(m + 1)*(2*m - 1)
Let x**3 - 8*x + 8*x**2 - 6*x**3 + x**3 + 2*x**3 = 0. What is x?
0, 2
Let a be (-1)/6*(-27)/(-15). Let l = a + 4/5. Factor 0*p - l + 1/2*p**2.
(p - 1)*(p + 1)/2
Let y(u) be the third derivative of -11*u**2 + 0*u + 3/56*u**4 - 1/140*u**5 - 1/7*u**3 + 0. Factor y(g).
-3*(g - 2)*(g - 1)/7
Let l(d) be the third derivative of d**5/80 - d**4/32 - 5*d**3/2 - 34*d**2 + d. Let l(z) = 0. Calculate z.
-4, 5
Let t be -1*4/(-16)*0. Let l be 8/(-6)*(1 - t)/(-2). Factor -2/3*n**3 + l*n**2 - 2/3 + 2/3*n.
-2*(n - 1)**2*(n + 1)/3
Let i(d) = -21*d**3 - 3*d**2 - 8*d + 13. Let q(w) = 10*w**3 + 2*w**2 + 4*w - 6. Suppose -7*k + 43 = 1. Let h(z) = k*i(z) + 13*q(z). Factor h(c).
4*c*(c + 1)**2
Let t = 60 - 58. Factor -14*r**t + 11*r**2 + 4*r + 5*r - 6*r.
-3*r*(r - 1)
Let f(h) = -h**2 + 15*h + 18. Let c be f(16). Let k(t) be the second derivative of 4*t + 0 - 2/15*t**3 + 1/30*t**4 + 1/5*t**c. Factor k(i).
2*(i - 1)**2/5
Let i(j) be the first derivative of j**5/450 + j**4/90 + j**3/45 + 11*j**2 - 50. Let p(c) be the second derivative of i(c). Factor p(f).
2*(f + 1)**2/15
Let q(o) be the third derivative of -3*o**5/20 + 11*o**4/16 + o**3/2 - 67*o**2 - 3*o. Factor q(c).
-3*(c - 2)*(6*c + 1)/2
Suppose -16 = -2*r - 4*u, 2*r + 16 = 4*r - 4*u. Let t = r + -6. Solve -2*l**3 + l**3 + 4*l**3 - 3*l**t = 0 for l.
0, 1
Let z(s) be the first derivative of s**3/12 + 3*s**2/2 + 9*s - 28. Factor z(o).
(o + 6)**2/4
Let r(w) be the second derivative of -w**7/14 + 3*w**6/10 - 9*w**5/20 + w**4/4 - 174*w. Determine l, given that r(l) = 0.
0, 1
Let x(z) be the second derivative of z**6/20 + 21*z**5/40 + 5*z**4/4 - 202*z. Solve x(u) = 0 for u.
-5, -2, 0
Let r(o) = o**3 + 5*o**2 + 26*o + 40. Let i be r(-2). Factor 4/3*t - t**3 + 0*t**2 - 1/3*t**4 + i.
-t*(t - 1)*(t + 2)**2/3
Let v be 1 - ((-12)/(-2) - 1428/210). Factor -2/5 + 3*l**3 - 4/5*l**2 - v*l.
(l - 1)*(3*l + 1)*(5*l + 2)/5
Let u(q) = -2*q**2 + 164. Let d be u(-9). Let -4/15*f**5 + 2/5*f**d - 4/15*f + 8/15*f**3 + 0 - 2/5*f**4 = 0. What is f?
-2, -1, 0, 1/2, 1
Let d = 18428/5529 + 2/5529. Solve 5/6*m**2 - d + 0*m = 0 for m.
-2, 2
Suppose w + 11 = 9. Let h be ((-94)/(-329))/(1/(-14)*w). Solve -8/5*m + 38/5*m**3 + 16/5*m**h + 0 + 14/5*m**4 = 0.
-2, -1, 0, 2/7
Let s be (6/(-12))/1 + 31/2. Let t(w) = w**3 - 16*w**2 + 17*w - 27. Let a be t(s). Solve 9/5*z**2 - 6/5*z + 0*z**a - 3/5*z**4 + 0 = 0 for z.
-2, 0, 1
Suppose -3*o = -6*o - 3. Let t(x) = -4*x**2 - 25*x + 1. Let u(r) = r**2 + 1. Let b(c) = o*u(c) + t(c). Suppose b(h) = 0. Calculate h.
-5, 0
Suppose 5*f - 8 = 2*p + 1, 2*f + p - 9 = 0. Let u = 5 - 1. Find s such that 13*s + s**f - 17*s + 4*s**2 + s**3 - 4*s**u + 2*s**3 = 0.
-1, 0, 1
Suppose 4*i - 1 = 7. Suppose -3*j + j + 2*j - 8*j = 0. Solve -2/3*w**i + 0*w**3 + 0 + 2/3*w**4 + j*w = 0 for w.
-1, 0, 1
Suppose 3*d = -5*d - 464. Let s = d + 58. Factor -4/11*m**2 + 2/11*m + 2/11*m**3 + s.
2*m*(m - 1)**2/11
Factor 7*z - 9 - 2*z + z + 3*z**2.
3*(z - 1)*(z + 3)
Let g(c) = c**2 + 3*c**3 - 7*c**2 - 2*c**3 + 12 + 3*c. Let b be g(5). Determine u, given that -b + 6*u + 1 + 5 + 2*u**2 = 0.
-2, -1
Let q(a) be the third derivative of 0*a - 1/15*a**5 + 0 + 1/3*a**4 + 0*a**3 - 3*a**2. Determine t so that q(t) = 0.
0, 2
Let o(u) = -5*u**3 + 3*u**2 - u - 2. Let m be o(1). Let v be m/(-20)*20 + -1. Solve -3/8*c**v - 9/8*c**2 + 3/8*c + 0 + 9/8*c**3 = 0.
0, 1
Let u(r) be the first derivative of -r**6/66 + 8*r**5/55 - 3*r**4/22 - 40*r**3/33 - 25*r**2/22 - 225. Factor u(n).
-n*(n - 5)**2*(n + 1)**2/11
Factor 5/9 - 1/9*s**2 - 4/9*s.
-(s - 1)*(s + 5)/9
Let i(k) be the second derivative of -7*k**5/5 - 334*k**4/3 - 466*k**3/3 + 188*k**2 - 384*k. Solve i(u) = 0.
-47, -1, 2/7
Factor 8*k**4 + 105*k**5 + 84*k**5 - 177*k**5.
4*k**4*(3*k + 2)
Let v(a) be the third derivative of -a**7/280 - a**6/60 + a**5/10 + a**4 - a**3 - 18*a**2. Let o(f) be the first derivative of v(f). Let o(u) = 0. Calculate u.
-2, 2
Let m(q) = q**2 - 2*q. Let w(n) = -5*n**2 + 22*n + 8. Let k(f) = -14*m(f) - 2*w(f). Factor k(b).
-4*(b + 2)**2
Determine y, given that -5*y**2 + 12*y**2 - 2*y**2 + 26*y + y**2 - 5*y**2 = 0.
-26, 0
Let h(u) be the first derivative of -u**6/6 + 3*u**5/5 - u**4/2 - 315. Let h(w) = 0. Calculate w.
0, 1, 2
Let u(v) = 1 - 6 + 0 + 10*v**3 - 15*v**2 - 1 + 11*v. Let i(g) = -30*g**3 + 45*g**2 - 32*g + 17. Let l(q) = 6*i(q) + 17*u(q). Factor l(n).
-5*n*(n - 1)*(2*n - 1)
Let h(c) be the first derivative of -c**6/3 + 2*c**4 - 4*c**3/3 - 3*c**2 + 4*c - 316. Solve h(a) = 0 for a.
-2, -1, 1
Factor -6 - 3/2*t**2 + 15/2*t**3 + 3/2*t**4 - 12*t - 3/2*t**5.
-3*(t - 2)**2*(t + 1)**3/2
Let q(t) be the first derivative of 3*t**5/5 - 2*t**3 + 3*t + 52. Suppose q(c) = 0. What is c?
-1, 1
Let a = 3554/10653 + -1/3551. Find k, given that -1/3*k**3 - a - k**2 - k = 0.
-1
Let p = 61457/20 + -15358/5. Solve t + 1/4*t**4 + p*t**3 + 0 + 2*t**2 = 0.
-2, -1, 0
Let j(y) be the second derivative of y**4/4 + 3*y**3 - 6*y**2 + 14*y. Let r(n) = 8*n**2 + 53*n - 36. Let i(