
-1, 5
Let y(n) be the first derivative of -2*n**3/9 - 26*n**2/3 - 338*n/3 + 47. Determine r so that y(r) = 0.
-13
Suppose -4/3*a**3 + 2/3 - 20/9*a + 2/9*a**4 + 8/3*a**2 = 0. What is a?
1, 3
Let c(v) be the first derivative of 2/45*v**5 + 0*v + 1 - 2/9*v**3 + 2/9*v**2 + 0*v**4. Find m, given that c(m) = 0.
-2, 0, 1
Let f(n) be the third derivative of n**5/600 - 7*n**4/120 + 49*n**3/60 - 78*n**2. Find l, given that f(l) = 0.
7
Solve 3*w**2 - 21*w + 24 + 3/4*w**3 = 0 for w.
-8, 2
Let n(h) = -6*h + 3 + 3*h + 4*h. Let b be n(-3). Solve -7*l**2 + 6*l**2 + b + 1 = 0.
-1, 1
Let k be (-3)/(-15)*(-360)/(-32). Suppose 3 + 6*c - k*c**3 + 3/4*c**2 = 0. What is c?
-1, -2/3, 2
Let p(j) be the second derivative of 1/10*j**5 + 9*j - 1/3*j**3 - j**2 + 0 + 1/6*j**4. Determine m so that p(m) = 0.
-1, 1
Suppose 5*f + 3*r - 12 = r, -5*f - 5*r = 0. Suppose -3*v + f = -v. Factor -28 + v*c + 28 + c**2.
c*(c + 2)
Let g be (8/20)/((-4)/(-80)). Suppose 0 = -b - g + 10. Suppose -4/7 - 1/7*t**5 - 11/7*t**b + 1/7*t**3 + 12/7*t + 3/7*t**4 = 0. What is t?
-2, 1, 2
Let u(z) = z**3 - 5*z**2 + z + 4. Let r be u(5). Suppose -5 = h - r. Determine n, given that 9*n**2 - 12 - 5*n**4 + 9*n**3 - 3*n**3 - 12*n + 2*n**h = 0.
-1, 2
Let m(t) be the second derivative of t**7/28 - 7*t**6/20 - 123*t**5/40 + 215*t**4/8 + 154*t**3 - 588*t**2 - 371*t. Determine p so that m(p) = 0.
-4, 1, 7
Let a(y) = -9*y**3 + 8*y**2 - 9*y - 5. Let z(n) = n**3 + n + 1. Let l(p) = a(p) + 5*z(p). Factor l(j).
-4*j*(j - 1)**2
Let z(p) be the second derivative of 8*p**6/5 - 43*p**5/5 + 46*p**4/3 - 34*p**3/3 + 4*p**2 - 2*p - 35. Determine y, given that z(y) = 0.
1/4, 1/3, 1, 2
Let w = -55 + 90. Factor -w*x**2 - 17*x**2 + 8 + 5*x + 39*x.
-4*(x - 1)*(13*x + 2)
Let -1/2*y**5 + 2*y - 4*y**2 + 3/2*y**3 + 0 + y**4 = 0. Calculate y.
-2, 0, 1, 2
Let i = -53 - -66. Suppose 0 = -2*u - 3*u + 3*a + i, -3*u = 5*a - 1. Factor 2/9*l**u - 2/9*l**3 + 2/9*l - 2/9.
-2*(l - 1)**2*(l + 1)/9
Let c(q) = -4*q + q + 2*q - q**2. Let k be c(-1). Suppose k + 3/7*g**3 + 3/7*g**4 - 3/7*g - 3/7*g**2 = 0. What is g?
-1, 0, 1
Let k be (-8)/(-6) - (-110)/120. Suppose 2*w + 4*g = 4*w - 12, -5*g = -4*w + 18. Let 3/4*v**4 - 15/4*v**3 + 27/4*v + 0 + k*v**w = 0. What is v?
-1, 0, 3
Suppose -15 - 95 = 5*j. Let l be (-4)/(-22) - 40/j. Solve l*g + 0*g**2 + 0*g**4 + 3*g**2 - g**4 = 0.
-1, 0, 2
Let d = -21979/10 - -2198. Let y(a) be the second derivative of -1/3*a**3 - 1/30*a**6 + 7*a + d*a**5 + 0 + 0*a**2 + 1/12*a**4. Factor y(c).
-c*(c - 2)*(c - 1)*(c + 1)
Let c(g) be the second derivative of g**4/36 + 5*g**3/18 + g**2 - 2*g - 33. Find i such that c(i) = 0.
-3, -2
Let k(c) be the second derivative of 0*c**4 + 0*c**3 + 0*c**5 + 0*c**2 + 13*c - 1/28*c**7 + 0 + 1/20*c**6. Let k(y) = 0. Calculate y.
0, 1
Let c = 17 - 14. Suppose -c*k - 6 + 6 = 0. Find v, given that k + 2/5*v**2 + 0*v - 2/5*v**3 = 0.
0, 1
Factor 0 - 2/5*b**3 - 54/5*b + 56/5*b**2.
-2*b*(b - 27)*(b - 1)/5
Let m(p) be the first derivative of 0*p + 19/6*p**4 - 16/3*p**2 + 1/3*p**5 + 64/9*p**3 + 3. Factor m(t).
t*(t + 4)**2*(5*t - 2)/3
Let t be 1/2*(-11)/((-22)/24). Solve t*l**3 + 3*l**5 + 212*l**2 - 15*l**3 - 266*l**2 + 12*l**4 = 0 for l.
-3, 0, 2
Let y be ((-7)/2 + 2)*(3 + -5). Let l be (-45)/220 + y/4. Factor 2/11*r + 0 + 6/11*r**3 + l*r**2 + 2/11*r**4.
2*r*(r + 1)**3/11
Let 6*j**4 - 2*j**3 - 18/7*j**5 + 32/7*j - 34/7*j**2 - 8/7 = 0. What is j?
-1, 2/3, 1
Let h be (-4069)/(-1144) + 0 + (-2)/11. Factor 15/8*k**5 + 0*k - 3/4*k**2 - 9/2*k**4 + 0 + h*k**3.
3*k**2*(k - 1)**2*(5*k - 2)/8
Let y(s) be the third derivative of s**10/15120 + s**9/7560 - s**8/840 - s**7/315 - s**4/24 - 29*s**2. Let k(h) be the second derivative of y(h). Factor k(j).
2*j**2*(j - 2)*(j + 1)*(j + 2)
Let l be (3/(-14))/(2916/(-126)). Let a(s) be the third derivative of 0*s**4 + 0 - 9*s**2 + 0*s + l*s**6 + 0*s**3 + 1/315*s**7 + 1/135*s**5. Factor a(m).
2*m**2*(m + 1)*(3*m + 2)/9
Let l = 599/5 - 3589/30. Let z(c) be the first derivative of -2/15*c**5 + 0*c + 2/9*c**3 - 1/3*c**2 + l*c**4 + 3. Factor z(g).
-2*g*(g - 1)**2*(g + 1)/3
Suppose 0*v - 2*v + 6 = 0. Suppose -4*g = -v*s - 8, -g + 3 - 1 = -3*s. Factor 1/3*l**3 + 1/3 + l**g + l.
(l + 1)**3/3
Let f(j) = -j**3 + 3*j**2. Let n(w) = -w**3 - 2*w**2. Let y(d) = -3*f(d) - 2*n(d). Factor y(c).
5*c**2*(c - 1)
Let d be (-40)/(-15)*((-62)/(-16) - 2). What is m in -d*m + 25 + 1/4*m**2 = 0?
10
Let z = 50051/143 - 350. Let f = 3866/715 - z. Find i, given that 21/5*i + f*i**2 - 6/5 = 0.
-1, 2/9
Find l such that -18/19*l**5 - 32/19*l**3 + 4*l**2 + 50/19*l + 8/19 - 84/19*l**4 = 0.
-4, -1, -1/3, 1
Suppose o + 1545 = 16*o. Let h = o - 103. Find x, given that -2/3*x**3 + 2*x**2 + h - 4/3*x = 0.
0, 1, 2
Let j(o) = 75*o**2 + 92*o + 22. Let i(s) = -38*s**2 - 46*s - 10. Let f(b) = 5*i(b) + 2*j(b). Let f(p) = 0. What is p?
-1, -3/20
Let n = -324 + 1299/4. Let r(j) be the second derivative of 5*j + 1/4*j**4 + 5/8*j**3 + n*j**2 + 3/80*j**5 + 0. Factor r(m).
3*(m + 1)**2*(m + 2)/4
Let b(k) be the second derivative of 2*k**7/21 - 2*k**6/15 + 2*k - 222. Determine d so that b(d) = 0.
0, 1
Let q = 3/59 - -109/177. Let w(g) be the first derivative of 2/9*g**3 - 1/6*g**2 - 4 + 1/12*g**4 - q*g. Find d such that w(d) = 0.
-2, -1, 1
Let b(p) be the first derivative of -p**4/10 + 18*p**3/5 + 333. What is g in b(g) = 0?
0, 27
Let v(k) be the third derivative of -18*k**2 + 1/180*k**5 + 0 + 0*k - 1/36*k**4 - 1/6*k**3. Let v(m) = 0. Calculate m.
-1, 3
Let d = -6 + 8. Let v = -26 + 29. Factor -m + v*m**2 - 5*m + m + d*m.
3*m*(m - 1)
Let k(a) be the second derivative of 21*a**6/40 + 33*a**5/80 - 9*a**4/16 + a**3/8 - a + 61. What is u in k(u) = 0?
-1, 0, 1/7, 1/3
Let h = 693 - 10391/15. Suppose -11*i - 30*i = 7*i. Factor -2/15*u**3 + h*u + 2/15*u**2 + i.
-2*u*(u - 2)*(u + 1)/15
Let q(i) = i**2 - 27*i + 56. Let d be q(25). Suppose -14*g = -d*g. Factor 1/2*k + g + 1/2*k**2.
k*(k + 1)/2
Let l(o) be the second derivative of 3*o**5/40 + 33*o**4/16 + 23*o**3/4 + 45*o**2/8 - 479*o. Suppose l(h) = 0. Calculate h.
-15, -1, -1/2
Factor 1444 + p**2 - 20*p - 5*p**2 + 8*p**2 + 13*p + 159*p.
4*(p + 19)**2
Let a(m) be the first derivative of 4*m**3/9 - 14*m**2/3 + 8*m - 276. Determine d, given that a(d) = 0.
1, 6
Let n(t) be the third derivative of t**7/2016 + 5*t**4/24 - 2*t**2. Let h(k) be the second derivative of n(k). Let h(r) = 0. What is r?
0
Determine w, given that 80*w + 256*w - 484*w**3 + 2 + 349*w**2 + 30 + 443*w**2 = 0.
-2/11, 2
Let d(m) be the third derivative of -5*m**9/3024 - m**8/84 - 5*m**7/168 - m**6/36 - 10*m**3/3 - 21*m**2. Let k(q) be the first derivative of d(q). Factor k(i).
-5*i**2*(i + 1)**2*(i + 2)
Find j such that 16*j**2 - 8/5*j**4 + 28/5*j**5 - 16/5*j + 0 - 84/5*j**3 = 0.
-2, 0, 2/7, 1
Let l = 116 - 114. Let z be (12 + -24)/(l*-11). Factor -z*x + 4/11 + 2/11*x**2.
2*(x - 2)*(x - 1)/11
Factor 24/7*c + 18/7*c**3 - 8/7 + 50/7*c**2.
2*(c + 1)*(c + 2)*(9*c - 2)/7
Let q be (-16)/48 - (-3)/207*527. Factor -122/23*t**2 - 28/23*t**3 - q*t - 2/23*t**4 - 72/23.
-2*(t + 1)**2*(t + 6)**2/23
Suppose 5*u - 3*h - 52 = 0, 20 = 41*u - 40*u - 3*h. Let b(g) be the first derivative of 26*g**2 - 8 - 70/3*g**3 - 49/4*g**4 - u*g. Let b(s) = 0. Calculate s.
-2, 2/7
Let g(y) be the third derivative of y**9/7560 - y**8/3360 + y**4/3 + 6*y**2. Let f(k) be the second derivative of g(k). Solve f(c) = 0.
0, 1
Let k(c) = -3*c**4 - 15*c**3 + 4*c**2 - 7. Let a(i) = -i**4 - 7*i**3 + 2*i**2 - 3. Suppose -4*s + 2*s + 6 = 0. Let x(r) = s*k(r) - 7*a(r). Factor x(q).
-2*q**2*(q - 1)**2
Suppose -14*m = -11*m - 201. Suppose -55*p - 111 + 208 + 15*p**2 - m = 0. What is p?
2/3, 3
Suppose -2*h = -6*h - 5*s + 644, -s + 483 = 3*h. Factor -3 - 1 + 16*y**3 + 12*y**2 + 153*y - h*y - 16*y**4.
-4*(y - 1)**2*(2*y + 1)**2
Let a be ((-121)/(-99))/1 - (-8)/(-18). Let m(v) be the first derivative of 0*v - 16/9*v**3 - 4 - 8/9*v**2 + a*v**4. Factor m(w).
4*w*(w - 2)*(7*w + 2)/9
Factor 12/7 + 2/7*n**2 - 2*n.
2*(n - 6)*(n - 1)/7
Let i(z) be the first derivative of -3*z**5/5 + z**4/4 + z**3 - z**2/2 + 47. Find o, given that i(o) = 0.
-1, 0, 1/3, 1
Let g = -6724/3 + 26905/12. Factor g*b**2 + 3 + 5*b.
(b + 6)*(3*b + 2)/4
Let k(u) = -u - 18. Let r(l) = l**2 + 32*l + 12. Let p(m) = 6*k(m) - 2*r(m). Factor p(y).
-2*(y + 2)*(y + 33)
Let j(k) = 5*k**2 - 2*k + 1. Let s be