 10/3*r**m.
2*r*(r + 1)*(r + 2)**2/3
Let o be 10*(999/(-195) - -5). Let m = 61/39 + o. What is d in m*d**2 - 1/3*d - 2/3 = 0?
-1, 2
Solve 0 + 16/9*p - 4/9*p**5 - 16/9*p**4 + 16/9*p**2 - 4/3*p**3 = 0 for p.
-2, -1, 0, 1
Let t = -270 - -280. Let q be 4 + t + -16 - (-88)/42. Let -q*n**2 + 0 - 8/21*n = 0. Calculate n.
-4, 0
Let d be -8 + 55/11 + 7. Let o(s) be the second derivative of 0*s**3 + 0*s**2 + 0 - 1/24*s**4 - d*s. Factor o(t).
-t**2/2
Let h = -1558 + 1558. Let w(x) be the first derivative of 0*x**5 + 0*x**4 + 0*x + h*x**2 + 0*x**3 + 8 + 1/15*x**6. Factor w(d).
2*d**5/5
Let h(p) be the second derivative of 4205*p**4/12 + 145*p**3/3 + 5*p**2/2 + 2*p + 74. Factor h(y).
5*(29*y + 1)**2
Let a = -37 - -39. Factor -f**a + 2 + 3*f + 3*f - 6*f + f.
-(f - 2)*(f + 1)
Let t(y) be the third derivative of 0*y**3 - 25*y**2 + 1/90*y**5 + 1/180*y**6 + 0*y**4 + 0 + 0*y. Suppose t(g) = 0. Calculate g.
-1, 0
Let p(u) be the second derivative of -1/24*u**4 - 19*u + 0*u**3 + 1/12*u**6 + 0*u**2 + 1/28*u**7 + 0 + 1/40*u**5. Suppose p(z) = 0. Calculate z.
-1, 0, 1/3
Suppose 5*p = 3*z - 20, -5*z + p - 2 = -6. Let j(v) be the third derivative of 0 + 1/140*v**5 + z*v + 4*v**2 + 1/14*v**3 - 1/28*v**4. Factor j(b).
3*(b - 1)**2/7
Let x(a) be the first derivative of -a**3/7 - 153*a**2/7 - 7803*a/7 - 292. Solve x(o) = 0.
-51
Let h(z) be the first derivative of 15*z**4/4 + 100*z**3/3 + 30*z**2 + 100. Find y, given that h(y) = 0.
-6, -2/3, 0
Factor 84*w**3 - 12*w - 27*w**2 + 4*w**5 - 17*w**2 - 36*w**4 - 26*w**2 + 36*w - 6*w**2.
4*w*(w - 6)*(w - 1)**3
Let t = 2583 - 5155/2. Factor 3/2*m**4 + 9/2*m + 15/2*m**2 + 1 + t*m**3.
(m + 1)**3*(3*m + 2)/2
Factor -86/13*o**3 - 2/13*o**4 + 0 + 968/13*o - 880/13*o**2.
-2*o*(o - 1)*(o + 22)**2/13
Let f(u) be the first derivative of -u**6/2520 + u**5/60 - 7*u**4/24 + 4*u**3/3 - 6. Let b(p) be the third derivative of f(p). Solve b(k) = 0 for k.
7
Let a(h) be the first derivative of -h**5/90 + 2*h**4/9 - 19*h**2 - 24. Let o(x) be the second derivative of a(x). Factor o(p).
-2*p*(p - 8)/3
Let p(q) = q**2 + 13*q - 227. Let j be p(-23). Factor 24/11*d**2 + 2/11*d**j + 128/11 + 96/11*d.
2*(d + 4)**3/11
Let u(n) be the first derivative of n**3/3 + 5*n**2 - 7*n - 1. Let k be u(-11). Factor o**3 - k*o**3 - 2*o**3 + o**3 + 2*o + 2*o**5.
2*o*(o - 1)**2*(o + 1)**2
Suppose -2*v - 108 = 26. Let q = -64 - v. Factor 21/5*s + 3/5*s**4 + 3*s**q + 6/5 + 27/5*s**2.
3*(s + 1)**3*(s + 2)/5
Let v = 300 + -300. Let r(l) be the third derivative of -1/30*l**5 + 0*l**4 + l**2 + v*l**3 + 0*l + 0. Factor r(a).
-2*a**2
Let a = 6 - 7. Let r = a - -3. Factor -4*b**2 - 4*b**r + 6*b**2 + 2*b.
-2*b*(b - 1)
Let f(s) = 4*s - 28. Suppose -83 = -4*t - 55. Let p be f(t). Factor p + 1/2*n + 5/4*n**2 - 1/2*n**4 + 1/4*n**3.
-n*(n - 2)*(n + 1)*(2*n + 1)/4
Let t be (-20)/832*-18*36/10. Let n = -4/13 + t. Suppose -1/4 + n*w**2 - 3/4*w**3 + 3/4*w - w**4 = 0. What is w?
-1, 1/4, 1
Suppose 6*c - 4*c - 88 = 0. Let r = -42 + c. Factor 0*h - 1/3*h**3 - 1/3*h**4 + 0 + 0*h**r.
-h**3*(h + 1)/3
Determine d so that -75/2*d + 3/4*d**2 + 1875/4 = 0.
25
Suppose 3*v - v = 12. Let a be 3/(-6) + v/4. Find x such that 6*x + a - x**2 + 0*x**2 - 5 - x**2 = 0.
1, 2
Let g = -7 + 16. Let m be ((-15)/(-10))/((-3)/(-72)*4). Factor -5*z**5 - 2*z**5 - m*z**4 - g*z**3 - 3*z**2 + 4*z**5.
-3*z**2*(z + 1)**3
Let q(h) be the second derivative of h**7/42 - h**6/12 + 5*h**4/12 - 5*h**3/6 - h**2 - 7*h. Let v(m) be the first derivative of q(m). What is d in v(d) = 0?
-1, 1
Let k(t) = t**3 + 16*t**2 - 16*t + 19. Let b be k(-17). Factor -102 - 3*f**2 - f**2 + f**b - 9*f + 114.
-3*(f - 1)*(f + 4)
Let u(g) be the second derivative of g**7/10 - 8*g**6/25 - 27*g**5/20 - 7*g**4/10 + 4*g**3/5 - 4*g. Determine q, given that u(q) = 0.
-1, 0, 2/7, 4
Factor 0 - 1/3*l**4 - 1/3*l - l**2 - l**3.
-l*(l + 1)**3/3
Suppose 0 = -2*d - 2*d. Let y = 323/354 + -73/177. Suppose 0 + y*p**3 + d*p - p**2 = 0. Calculate p.
0, 2
Let f = 701 + -3503/5. Factor -6/5*i - 6/5*i**2 - 2/5 - f*i**3.
-2*(i + 1)**3/5
Suppose 3*m = 3*p - 15, 2*p + 3*m + 8 = -m. Factor -8*q**3 + 36*q + 27*q**p + 4*q**4 + q**4 - 33*q**2 - 3*q**4.
2*q*(q - 3)**2*(q + 2)
Let o(d) = 4*d**4 - 5*d**3 + 3*d**2 - 3. Let v(a) = a**4 - a**3 + a**2 - 1. Let z = -15 - -18. Let y(t) = z*v(t) - o(t). Factor y(m).
-m**3*(m - 2)
Factor 3*w**2 + 3/2*w**5 - 9/2*w**4 + 3*w**3 - 9/2*w + 3/2.
3*(w - 1)**4*(w + 1)/2
Suppose 0 = 5*q + 3*m - 14 - 2, 4*q + 5*m - 5 = 0. Let z be 60/225 + 4/30. Factor -2/5*p**2 - 2/5*p**q + 2/5*p**4 + 0 + 0*p + z*p**3.
-2*p**2*(p - 1)**2*(p + 1)/5
Let u = 0 + 2. Let t be u/(-3)*(-8 - -2). Factor -2*j**2 + t*j**2 + 4*j**2 - 2*j**2 - 2 - 2*j**4.
-2*(j - 1)**2*(j + 1)**2
Let l(w) be the first derivative of -w**7/14 + w**6/10 + 17*w - 21. Let j(n) be the first derivative of l(n). Factor j(g).
-3*g**4*(g - 1)
Suppose 5*i - 4*b = 24, 5*b - 2*b = -4*i + 44. Let s be i/15*2/(-16)*-6. Let 2/5*t - 2/5 + 2/5*t**2 - s*t**3 = 0. What is t?
-1, 1
Let l(q) be the second derivative of -q**6/630 + q**5/105 - 2*q**3 - 2*q. Let b(x) be the second derivative of l(x). Suppose b(k) = 0. Calculate k.
0, 2
Let z = -406 + 2031/5. Let k(s) be the first derivative of 4 - 1/20*s**4 - 1/15*s**3 + z*s**2 + 0*s. Factor k(y).
-y*(y - 1)*(y + 2)/5
Suppose 2*a - 3 = a. Let v = 65 + -63. Find o, given that 61*o**v + 12 + 74*o**2 - 91*o**4 + 84*o - 84*o**a - 56*o**4 = 0.
-1, -2/7, 1
Let p(q) be the third derivative of -q**10/90720 + q**8/20160 - 13*q**4/12 + 3*q**2. Let l(c) be the second derivative of p(c). Solve l(f) = 0.
-1, 0, 1
Let v(s) be the first derivative of -s**6/360 + s**5/180 + 3*s**2 + 6. Let x(z) be the second derivative of v(z). Factor x(u).
-u**2*(u - 1)/3
Let u(i) be the second derivative of -2/3*i**6 + 5/4*i**4 - 15*i - 5/3*i**3 + i**5 - 5/2*i**2 + 0. Factor u(k).
-5*(k - 1)**2*(2*k + 1)**2
Let a(s) be the second derivative of 0*s**4 - 1/6*s**3 + 1/3*s**2 + 0 - 12*s + 1/60*s**5. Determine x so that a(x) = 0.
-2, 1
Solve -81*j - 243 - 9*j**2 - 1/3*j**3 = 0.
-9
Let p = -96 + 99. Solve 15*a**p - 30*a + 25*a**2 + 81*a**4 - 106*a**4 + 5*a**5 + 10*a = 0 for a.
-1, 0, 1, 4
Let w be 8 + 1216/(-96)*(-3)/(-5). Factor 8/5 - w*g**2 - 6/5*g.
-2*(g - 1)*(g + 4)/5
Let w = 77 + -75. Let b be w - (5 + -3 + 3 + -3). Suppose 1/3*j**3 + 0*j + b - 1/3*j**5 - 2/3*j**2 + 2/3*j**4 = 0. Calculate j.
-1, 0, 1, 2
Factor -3/7*r**2 - 108/7 - 39/7*r.
-3*(r + 4)*(r + 9)/7
Let g(u) be the first derivative of -u**6/14 - 4*u**5/35 + 10*u**4/7 - 22*u**3/7 + 43*u**2/14 - 10*u/7 + 163. Find i such that g(i) = 0.
-5, 2/3, 1
Let g(n) be the first derivative of 1 - 1/60*n**5 - 1/24*n**4 + 11/2*n**2 + 0*n + 0*n**3 + 1/60*n**6. Let h(j) be the second derivative of g(j). Factor h(o).
o*(o - 1)*(2*o + 1)
Let t(b) be the first derivative of b**4 + 28*b**3/3 + 32*b**2 + 36*b + 10. Let y(g) = 1. Let a(f) = t(f) + 12*y(f). Suppose a(o) = 0. Calculate o.
-3, -2
Factor -15/2 + 3/4*y**3 + 15/2*y**2 - 3/4*y.
3*(y - 1)*(y + 1)*(y + 10)/4
Let q(i) = -i**2 - i - 2. Let w(v) = 8*v**2 - 88*v + 100. Let d(m) = -5*q(m) - w(m). Find x such that d(x) = 0.
1, 30
Let s be (-9170)/108*(-21)/70. Let r = -101/4 + s. Let 0*b**2 - 2/3*b + r*b**3 - 4/9 = 0. What is b?
-1, 2
Factor 1/2*o**2 + 16 - 6*o.
(o - 8)*(o - 4)/2
Let l = -3193/90 - -71/2. Let v(c) be the second derivative of 2/27*c**3 - 1/9*c**2 + 5*c + 1/54*c**4 - l*c**5 + 0. Let v(j) = 0. What is j?
-1, 1/2, 1
Let i(n) be the first derivative of -3 + 4/3*n**2 - 1/9*n**3 - 1/12*n**4 + 4*n. Factor i(j).
-(j - 3)*(j + 2)**2/3
Let c = 316 + -2840/9. Let l = 3/64 - -485/576. Suppose -2/9*m**4 + 8/9*m - l - c*m**3 + 2/3*m**2 = 0. What is m?
-2, 1
Let g be 7/((-21)/18)*(-10)/15. Factor 2 - 124*a**g + 128*a**4 + 0*a - 2*a - 6*a**2 + 2*a**3.
2*(a - 1)*(a + 1)**2*(2*a - 1)
Determine v so that 36*v + 2/3*v**3 + 10*v**2 + 80/3 = 0.
-10, -4, -1
Suppose -8*r**3 + 5*r**4 - 9*r + 735*r**2 + 374*r + 383*r**3 = 0. What is r?
-73, -1, 0
Factor 5*c**2 + 21 - 56 + 175 + 80*c + 0*c**2.
5*(c + 2)*(c + 14)
Let t(j) be the third derivative of 3*j**5/4 - 4*j**4 + 2*j**3 - 17*j**2 - 3*j. Let t(x) = 0. Calculate x.
2/15, 2
Factor -50 + 714*d**2 - 331*d**2 - 359*d**2 + d**3 - 19*d - 8*d.
(d - 2)*(d + 1)*(d + 25)
Let f be ((-4 - -5) + -5)/3*(-54)/24. Factor 0 - 1/4*z**f + z**2 - 1/4*z**4 + z.
-z*(z - 2)*(z + 1)*(z + 2)