that -15 + 20*r + 6*r**2 + 5*r**4 + 15*r**x - 10*r**2 - r**2 - 20*r**3 = 0.
-1, 1, 3
Suppose -53 = 4*i - 205. Let h = i - 38. Suppose 0*x + 0 - 1/5*x**4 + 0*x**3 - 1/5*x**5 + h*x**2 = 0. Calculate x.
-1, 0
Let x(r) be the second derivative of -r**7/189 - 4*r**6/135 - r**5/30 + 426*r. What is s in x(s) = 0?
-3, -1, 0
Let y(q) be the second derivative of 0 + 1/20*q**4 + 3/5*q**3 - 2*q + 27/10*q**2. Determine u, given that y(u) = 0.
-3
Let f(j) be the third derivative of -j**6/540 - 2*j**5/225 + j**4/45 - j**3/3 + 9*j**2. Let b(y) be the first derivative of f(y). Let b(p) = 0. What is p?
-2, 2/5
Let j(a) be the first derivative of 2*a**3/3 - 2*a**2 - 6*a - 154. Solve j(x) = 0 for x.
-1, 3
Let b(q) be the second derivative of 3*q**7/280 + q**6/30 + q**5/40 + q**3/6 - 6*q. Let w(m) be the second derivative of b(m). Factor w(o).
3*o*(o + 1)*(3*o + 1)
Factor -26/9 - 8*c**2 + 20/9*c**3 + 76/9*c + 2/9*c**4.
2*(c - 1)**3*(c + 13)/9
Let d = -13 + 18. Suppose -10 = 5*x, 4*b + d*x - 26 = -4. Solve t**2 - 4*t**2 - b*t + 4*t**2 + t**2 = 0.
0, 4
Factor -5/4*p + p**2 + 1/2 - 1/4*p**3.
-(p - 2)*(p - 1)**2/4
Let w(t) = 43*t**2 + 62*t + 16. Let u(c) = -515*c**2 - 745*c - 190. Let r(o) = 2*u(o) + 25*w(o). Determine g, given that r(g) = 0.
-2/3
Let l(i) be the third derivative of 0 + 51*i**2 + 0*i - 1/210*i**5 - 1/7*i**3 + 1/21*i**4. What is f in l(f) = 0?
1, 3
Let k(v) be the third derivative of -v**8/10080 + v**7/630 - v**6/120 + 3*v**5/5 - 3*v**2. Let q(o) be the third derivative of k(o). Solve q(y) = 0 for y.
1, 3
Let w(s) be the third derivative of -s**8/5040 + s**7/70 - 9*s**6/20 + 13*s**5/60 + 2*s**2. Let k(l) be the third derivative of w(l). Factor k(t).
-4*(t - 9)**2
Let p be -2*(2/(-8) - -8*5/480). Determine q so that 0 + 1/3*q**2 + p*q = 0.
-1, 0
Let z be (-183)/366 + (-1)/(-2). Determine x so that 4/3*x**3 + 2*x**4 + 7/9*x**5 + z - 1/3*x - 2/9*x**2 = 0.
-1, 0, 3/7
Let s(c) be the third derivative of -c**6/960 - 13*c**5/480 - 5*c**4/24 - 3*c**3/4 + 113*c**2. Factor s(x).
-(x + 2)**2*(x + 9)/8
Let q(s) be the third derivative of s**8/420 + 13*s**7/525 + 9*s**6/100 + s**5/15 - 7*s**4/15 - 8*s**3/5 + 5*s**2 - 2*s. Find v, given that q(v) = 0.
-2, -3/2, 1
Let l(a) be the second derivative of 1/12*a**4 + 0*a**3 + 1/20*a**5 - 6*a + 0 + 0*a**2. What is o in l(o) = 0?
-1, 0
Let o(z) be the first derivative of 3*z**4/5 + z**3 - 42*z**2/5 - 132*z/5 - 504. Find l such that o(l) = 0.
-2, 11/4
Find b such that 12*b**4 + 84*b - 21*b**3 - 39*b**2 + 416 - 878 + 426 = 0.
-2, 3/4, 1, 2
Let r be (-2)/(-3)*(1 + 0 - -5). Factor -l**2 - r*l**2 + 3*l**2 - 11*l + 4 - l**2.
-(l + 4)*(3*l - 1)
Let m = -50881 + 50884. Find q, given that 0*q**4 - 1/6*q**5 + 0*q + 1/2*q**m + 0 - 1/3*q**2 = 0.
-2, 0, 1
Determine u so that -2/9*u**2 + 0 - 16/9*u = 0.
-8, 0
Let y(x) be the first derivative of x**4/96 - x**3/12 - 20*x + 21. Let p(s) be the first derivative of y(s). Determine k, given that p(k) = 0.
0, 4
Let v(a) be the second derivative of 3/80*a**5 + 0 + 1/4*a**3 + 0*a**2 - 9/32*a**4 - 57*a. Factor v(g).
3*g*(g - 4)*(2*g - 1)/8
Let a = 401/665 - 3/95. Factor a - 1/7*q**2 + 0*q.
-(q - 2)*(q + 2)/7
Let u = 3/209 - 871/75240. Let y(k) be the third derivative of 0*k + 0 - 2*k**2 - 1/1260*k**7 + 0*k**4 + 0*k**3 + u*k**6 - 1/360*k**5. Factor y(d).
-d**2*(d - 1)**2/6
Factor -1/3*p**2 - 2/3 - p.
-(p + 1)*(p + 2)/3
Solve 20*m**3 - 14*m**2 - m**4 + 64*m - m**4 - 50*m**2 = 0.
0, 2, 4
Let k(q) = 29*q**2 - 56*q + 27. Let w(t) = 260*t**2 - 505*t + 245. Let g(a) = -35*k(a) + 4*w(a). Solve g(f) = 0.
1, 7/5
Let s(x) be the second derivative of -x**9/3024 + x**8/1344 + x**7/504 - x**6/144 + x**4/6 + x. Let r(c) be the third derivative of s(c). Factor r(d).
-5*d*(d - 1)**2*(d + 1)
Let d(t) be the third derivative of -t**5/12 - 55*t**4/24 - 25*t**3/3 - 645*t**2. Solve d(q) = 0.
-10, -1
Let a(y) = -8*y + 52. Let p be a(6). Suppose 2*o - 2*n = -o - 2, p*o = 5*n - 5. Factor 2/5*c + o + 2/5*c**2.
2*c*(c + 1)/5
Let j(h) = h**3 + 5*h**2 - 18*h - 24. Let s be j(-7). Suppose 5*t + 5*p = 10, 2*t - 4*p - s = -p. Let 2/7*g - 2/7*g**4 + 2/7*g**t + 0 - 2/7*g**3 = 0. What is g?
-1, 0, 1
Let n(x) = -x**3 - 36*x**2 - 2*x - 37. Let z be n(-36). Let v be 1 + 21/(-9)*10/z. Solve 4/9*l**3 - 1/3*l**4 + 14/9*l**2 + 4/9*l - v = 0 for l.
-1, 1/3, 3
Solve -768/11*h**2 - 32/11 - 670/11*h**4 - 150/11*h**5 - 256/11*h - 1064/11*h**3 = 0.
-2, -1, -2/3, -2/5
Let o(k) = 5*k**2 + 33*k + 20. Let j = 323 + -329. Let q be o(j). Find a such that -33/8*a**3 + 0 + 3/4*a - 9/8*a**5 - 3/8*a**q - 33/8*a**4 = 0.
-2, -1, 0, 1/3
Factor -10*j**2 + 26*j**3 - 20*j - 2*j**3 + 15 + j**2 - 5*j**4 - 4*j**3 - j**2.
-5*(j - 3)*(j - 1)**2*(j + 1)
Let h(u) be the third derivative of 1/240*u**6 + 0*u**3 + 0 + 0*u - 1/120*u**5 + 1/420*u**7 - 38*u**2 - 1/48*u**4. Suppose h(w) = 0. Calculate w.
-1, 0, 1
Let q(s) = 7*s**3 - 2*s**2 - 3*s + 3. Let r be q(-2). Let a be (-15)/(-6)*(-33)/r. Suppose -a*x**2 + 9/2*x - 3 = 0. What is x?
1, 2
Factor -3/7*t**3 - 24/7*t**2 - 57/7*t - 36/7.
-3*(t + 1)*(t + 3)*(t + 4)/7
Let s be 4942/(-378) + 13 - 152/(-594). Let s - 2/11*g**3 + 2/11*g - 2/11*g**2 = 0. What is g?
-1, 1
Let k(o) be the second derivative of -o**5/110 + 7*o**4/66 - o**3/3 + 5*o**2/11 + 92*o. Factor k(x).
-2*(x - 5)*(x - 1)**2/11
Let u be (-216)/(-45) + -5 + 1. Solve -u*t - 4/5*t**2 + 8/5 = 0.
-2, 1
Find l, given that 0 - 4/3*l**4 + 24*l + 44/3*l**2 - 32/3*l**3 = 0.
-9, -1, 0, 2
Let g(k) be the first derivative of 6 + 0*k - 3/4*k**2 + 0*k**4 - 3/20*k**5 + 3/4*k**3. Suppose g(m) = 0. Calculate m.
-2, 0, 1
What is k in 9/4*k + 0 - 3*k**2 + 3/4*k**3 = 0?
0, 1, 3
Determine f so that 24/13 + 38/13*f + 16/13*f**2 + 2/13*f**3 = 0.
-4, -3, -1
Suppose 17 - 11 = 18*n - 48. Let -1/2*o**2 + 0 + 0*o + 0*o**n + 1/2*o**4 = 0. What is o?
-1, 0, 1
Factor 9/4*k**3 + 33*k + 75/4*k**2 + 9.
3*(k + 2)*(k + 6)*(3*k + 1)/4
Let r(b) be the first derivative of b**4/9 - 20*b**3/27 - 8*b**2/9 + 80*b/9 + 69. Determine g, given that r(g) = 0.
-2, 2, 5
Let h(x) be the first derivative of -5*x**6/6 + 2*x**5 + 45*x**4/4 - 70*x**3/3 - 50*x**2 + 120*x + 348. Solve h(s) = 0.
-2, 1, 2, 3
Let a(f) be the first derivative of -1/12*f**3 + 4*f + 0*f**2 + 5 - 1/16*f**5 + 7/48*f**4. Let g(j) be the first derivative of a(j). Factor g(l).
-l*(l - 1)*(5*l - 2)/4
Let c(f) be the second derivative of 4/3*f**2 + 14/15*f**5 - 11*f + 5/2*f**4 + 0 - 49/45*f**6 - 28/9*f**3. Suppose c(b) = 0. Calculate b.
-1, 2/7, 1
Let i = 69 + 41. Let n = i - 986/9. Find o such that 0*o**3 - 4/9*o**2 + 2/9*o**5 - 2/9*o + n*o**4 + 0 = 0.
-1, 0, 1
Let b(t) be the third derivative of t**8/2688 + t**7/5040 - t**4/12 - t**3/2 + 34*t**2. Let p(u) be the second derivative of b(u). Factor p(n).
n**2*(5*n + 1)/2
Let t(w) be the third derivative of -7*w**2 + 1/24*w**6 + 0 + 0*w + 0*w**3 + 5/6*w**4 + 1/3*w**5. Find j such that t(j) = 0.
-2, 0
Let i(y) be the second derivative of y**7/3780 - y**5/180 + y**4/54 - 7*y**3/2 - 15*y. Let o(j) be the second derivative of i(j). Factor o(s).
2*(s - 1)**2*(s + 2)/9
Suppose 25*t - 35*t = -60. Let w(p) be the first derivative of 4 + t*p - 3/2*p**2 - p**3. Factor w(v).
-3*(v - 1)*(v + 2)
Let y = 281/68810 + 2/2949. Let v(i) be the third derivative of 0*i**6 + 0*i + 0*i**4 + 0*i**3 + 0*i**5 - y*i**7 - 2*i**2 + 0. Factor v(x).
-x**4
Factor 0*x - 1/6*x**3 + x**2 - 16/3.
-(x - 4)**2*(x + 2)/6
Let x be (-45)/(-70)*168/80. Let n(a) be the second derivative of -17/2*a**4 + 8*a - x*a**5 - 14*a**3 + 0 + 12*a**2. Let n(s) = 0. What is s?
-2, 2/9
Let h = 49 - 53. Let l be 3/(h/((-16)/18)). Let -5/3*z + 4/3*z**2 + l - 1/3*z**3 = 0. Calculate z.
1, 2
Let s(i) be the third derivative of -i**7/1400 - i**6/180 - i**5/150 + i**4/15 - i**3/3 + 10*i**2. Let n(l) be the first derivative of s(l). Factor n(r).
-(r + 2)**2*(3*r - 2)/5
What is k in 11*k**3 - 5*k**4 + 29*k**2 - 10*k**3 - 5*k - 15*k + 19*k**3 - 24*k**2 = 0?
-1, 0, 1, 4
What is c in 2/5*c**3 - 48/5 - 4/5*c + 2*c**2 = 0?
-4, -3, 2
Let i(j) be the first derivative of 2*j**5/35 - 3*j**4/14 - 2*j**3/3 + 15*j**2/7 + 36*j/7 - 191. Factor i(t).
2*(t - 3)**2*(t + 1)*(t + 2)/7
Let v(i) be the second derivative of i**6/20 - 7*i**5/40 + i**4/8 - i**3 - 6*i. Let l(a) be the second derivative of v(a). Determine u so that l(u) = 0.
1/6, 1
Find k, given that -40*k**3 + 85*k**