2*k**6/15 - 54*k**2. Suppose j(r) = 0. Calculate r.
-8/7, 0
Let k be 11*(0 - (-13 + 423/33)). Find d such that 0*d**k + 0*d**4 + 1/4*d**5 + 1/4*d - 1/2*d**3 + 0 = 0.
-1, 0, 1
Find p such that -2/15*p**2 + 4/15 - 2/15*p = 0.
-2, 1
Find x, given that -3*x**2 + 23*x - 67*x - 5*x**2 + 29*x + 0*x**2 - x**3 = 0.
-5, -3, 0
Factor 2/3*f**2 - 6/5 - 2/5*f - 2/15*f**3.
-2*(f - 3)**2*(f + 1)/15
Let k be (-2358)/(-99) - 4/(-22). Factor -m + 16*m - 35*m - k + 4*m**2.
4*(m - 6)*(m + 1)
Factor 1/3*r - 1/9*r**2 - 2/9.
-(r - 2)*(r - 1)/9
Let t(p) = 8*p**3 + p**2 - 3*p + 1. Let m be t(2). Let j be 140/m - 8/12*3. Factor -2/9*y**2 + 2/9*y + 2/9 - j*y**3.
-2*(y - 1)*(y + 1)**2/9
Let c be 5*(2 - 1/1). Suppose 30 = 5*i + c. Suppose 8*f**4 + 5*f**5 + 4*f**i + 4*f**3 - 13*f**5 - 8*f**2 = 0. Calculate f.
-1, 0, 1, 2
Find a, given that -4/3*a**2 - 8*a - 12 = 0.
-3
Let c(b) = 3*b**2 - 43*b + 77. Let w be c(2). Let -2/9*f**4 + 4/9*f**2 + 8/9*f**5 + 8/9*f - 2/9 - 16/9*f**w = 0. What is f?
-1, 1/4, 1
Suppose 0 = -10*z + 3 - 3. Suppose -7*o + 14 + z = 0. Factor -72/5*r - 3/5*r**3 - 27/5*r**o - 48/5.
-3*(r + 1)*(r + 4)**2/5
Factor -64/11*t**2 + 0 - 52/11*t**4 - 6/11*t - 10*t**3.
-2*t*(t + 1)**2*(26*t + 3)/11
Determine u so that 8/7*u**2 + 2*u**3 - 6/7*u + 0 = 0.
-1, 0, 3/7
Let s be ((-24)/20)/3*25*(-28)/210. Suppose -4/3*n**2 + 0 - s*n - 1/3*n**3 = 0. What is n?
-2, 0
Let q = 1053/7 - 150. Suppose -3*v + 2*o = -o - 12, 5*v = 4*o + 19. Factor 0 + 3/7*p**v + 6/7*p**2 + q*p.
3*p*(p + 1)**2/7
Let c = 1937 + -27115/14. Let d(b) be the first derivative of -c*b**4 - 3/7*b**3 + 0*b**2 + 3/7*b + 11. Find x, given that d(x) = 0.
-1, 1/2
Factor 0 - 6/5*n**3 + 4/5*n + 2/5*n**2.
-2*n*(n - 1)*(3*n + 2)/5
Let g(b) = 6*b**4 + 7*b**3 - 4*b**2 - 8*b - 1. Let v(k) = k**4 - k**2 - k + 1. Let z(u) = 3*g(u) - 3*v(u). Factor z(h).
3*(h - 1)*(h + 1)**2*(5*h + 2)
Suppose 108 + 22*i**4 + 899*i**2 - 34*i**4 + 10*i**4 + 4*i**2 + 792*i + 20*i**4 + 237*i**3 = 0. What is i?
-6, -1, -1/6
Let g(d) be the first derivative of -d**6/480 + d**5/120 + d**4/32 - 17*d**2/2 - 9. Let v(b) be the second derivative of g(b). Factor v(f).
-f*(f - 3)*(f + 1)/4
Suppose 4*g - 26 = 6. Suppose 5*k - 7 = -b, -4*k + 3*b - 5*b + 2 = 0. Find s such that 27*s**3 + g*s - 13*s + 15*s**4 + 5*s**2 - k*s**3 = 0.
-1, 0, 1/3
Factor -392/3*u**2 - 952/3*u - 578/3.
-2*(14*u + 17)**2/3
Let p(b) = -15*b**3 + 25*b**2 + 20*b - 10. Let n(m) = m**3 - 2*m**2 - 1. Let f(q) = 10*n(q) + p(q). Factor f(t).
-5*(t - 2)*(t - 1)*(t + 2)
Let g = -747 - -2248/3. Suppose -4*o = -3*o - 3. Determine s so that -2/3 + 11/3*s + g*s**o - 16/3*s**2 = 0.
2/7, 1
What is b in 3/4*b**3 + 6*b**2 + 21/4*b + 0 = 0?
-7, -1, 0
Let q(r) be the second derivative of -r**7/21 + r**6/4 - 3*r**5/10 - r**4/6 - 4*r + 2. Factor q(z).
-z**2*(z - 2)**2*(4*z + 1)/2
Let r = -16/189 - -10/27. Let x = 1/2 - -1/14. Suppose -r*k**2 + 2/7*k + x = 0. What is k?
-1, 2
Let a = -13 + 17. Factor 0*b**a + 7*b**3 + 8*b**3 - 3*b - 17*b - 5*b**4.
-5*b*(b - 2)**2*(b + 1)
Let f = 27 + -23. Suppose g + 28 = 5*m, -3*g - 3 = -f*m + 26. Factor -j**2 - 6 - m*j - 4*j + 9*j**3 + 4*j**2 + 3*j**4.
3*(j - 1)*(j + 1)**2*(j + 2)
Let p(t) be the second derivative of t**8/1344 - t**7/840 - t**6/480 + t**5/240 + 9*t**2 - 29*t. Let w(c) be the first derivative of p(c). Solve w(a) = 0 for a.
-1, 0, 1
Let j(g) = -8*g**2 + 16*g - 4. Let p(f) = -5*f + f**3 + 10*f - f**2 - 6*f + 0*f**2 - 1. Let b = 5 + -4. Let l(k) = b*j(k) + 2*p(k). Factor l(x).
2*(x - 3)*(x - 1)**2
Factor -8*j**2 + 22*j**2 + 104*j - 10*j**2 + 1156 + 32*j.
4*(j + 17)**2
Factor 26/15*i**4 + 2*i**3 + 2/15*i + 14/15*i**2 + 0 + 8/15*i**5.
2*i*(i + 1)**3*(4*i + 1)/15
Let l(a) be the second derivative of -a**6/900 + a**4/60 - 2*a**3/45 + 2*a**2 + 9*a. Let h(c) be the first derivative of l(c). Factor h(z).
-2*(z - 1)**2*(z + 2)/15
Let -18*n**3 + 22*n**3 + 102*n**2 - 2*n**2 = 0. What is n?
-25, 0
Let o(a) = -6*a**2 - 6*a + 1. Let g(b) = -5*b**2 - 5*b + 2. Let x(z) = 5*g(z) - 4*o(z). Let t be x(0). Factor 3*h**2 - 3 - t - 6*h - 4*h**2.
-(h + 3)**2
Let w(q) be the first derivative of 3*q**4/16 + 3*q**3/4 - 3*q**2/8 - 9*q/4 - 241. Factor w(y).
3*(y - 1)*(y + 1)*(y + 3)/4
Let g(w) be the second derivative of -w**8/3360 + w**4/6 + 8*w. Let r(q) be the third derivative of g(q). Suppose r(v) = 0. Calculate v.
0
Let i = -32 + 35. Let a(k) = -k**5 + k**4 - 2*k**2 + k - 1. Let p(q) = 2*q**5 - q**4 - q**3 + 2*q**2 - q + 2. Let h(j) = i*a(j) + 2*p(j). Factor h(x).
(x - 1)**2*(x + 1)**3
Let y(m) = -2*m - 22. Suppose -5*x - 55 = -0*x. Let h be y(x). Factor -5*f**3 - 4*f + 5*f**4 - 4*f + 13*f - 5*f**2 + h*f**3.
5*f*(f - 1)**2*(f + 1)
Let y(s) be the second derivative of s**7/3780 + s**6/540 - s**5/60 + 5*s**4/12 - 13*s. Let g(x) be the third derivative of y(x). Suppose g(h) = 0. What is h?
-3, 1
Let c(b) be the third derivative of 0*b**4 - 16*b**2 + 0*b + 0 + 1/168*b**8 + 0*b**7 + 0*b**5 - 1/60*b**6 + 0*b**3. Factor c(k).
2*k**3*(k - 1)*(k + 1)
Let b be ((-9)/12)/((-13)/(39/90)). Let v(f) be the second derivative of 0*f**2 - b*f**5 + 1/60*f**6 + 3*f + 0 - 1/24*f**4 + 1/12*f**3. Factor v(j).
j*(j - 1)**2*(j + 1)/2
Let w(t) = -5 + 4 + 2*t - 4 + 1. Let s be w(3). What is g in g**2 + 2*g**s - 3*g + 0*g**2 = 0?
0, 1
Let a(d) be the second derivative of d**7/84 - d**6/30 + d**5/40 - 582*d. Find c, given that a(c) = 0.
0, 1
Let g(n) = -n**5 + n**4 - 21*n**3 + 21*n**2 + 11. Let t(m) = -m**5 + m**4 - 11*m**3 + 11*m**2 + 6. Let h(a) = -6*g(a) + 11*t(a). Suppose h(w) = 0. Calculate w.
-1, 0, 1
Let d(b) be the first derivative of 4*b**5/5 - 15*b**4 + 84*b**3 - 98*b**2 - 100. Factor d(y).
4*y*(y - 7)**2*(y - 1)
Determine u so that -1/4*u**3 + 0*u - 1/8*u**2 + 0 - 1/8*u**4 = 0.
-1, 0
Let b(g) be the first derivative of -g**6/1620 + g**5/270 + g**4/36 + 4*g**3/3 + 17. Let c(s) be the third derivative of b(s). Determine k, given that c(k) = 0.
-1, 3
Let r be ((-50)/(-15))/((-2)/3) + 5. Let h(y) be the first derivative of 0*y - 2/3*y**3 + 6 - y**4 - 2/5*y**5 + r*y**2. Factor h(u).
-2*u**2*(u + 1)**2
Let t = -71 + 87. Let o be ((120/14)/(-4))/(t/(-28)). Solve 3/4*x**4 + 0 + 9/4*x**5 - 3/4*x**2 - o*x**3 + 3/2*x = 0 for x.
-1, 0, 2/3, 1
Let i(d) be the first derivative of d**3 + 0*d + 1/120*d**6 + 3/40*d**5 + 0*d**2 + 11 + 1/4*d**4. Let c(r) be the third derivative of i(r). Factor c(n).
3*(n + 1)*(n + 2)
Let c = 1872 + -1870. Factor -1/3*k**4 + 0*k - 1/3 + 0*k**3 + 2/3*k**c.
-(k - 1)**2*(k + 1)**2/3
Let k be 16/(-14) + (-2542)/(-1722). Find z such that -k*z**3 + 1/3*z + 0 - 1/6*z**4 + 1/6*z**2 = 0.
-2, -1, 0, 1
Let p(l) = -13*l**2 + 338*l - 10097. Let s(k) = -15*k**2 + 336*k - 10098. Let z(j) = -6*p(j) + 5*s(j). Suppose z(r) = 0. What is r?
58
Find n such that -1560*n**2 - 36 + 471*n + 507/4*n**3 = 0.
2/13, 12
Suppose w + 3*u = 33, -58*w + 4*u - 31 = -55*w. Solve 9/4*m**2 - 5/4*m**w + 1/2 + 1/4*m**4 - 7/4*m = 0.
1, 2
Let x(s) be the first derivative of -2/7*s**2 + 1/7*s**4 - 9 - 2/35*s**5 + 0*s**3 + 2/7*s. Factor x(a).
-2*(a - 1)**3*(a + 1)/7
Let a be -2 + ((-48)/(-35))/(12/20). Factor a*j**4 - 12/7*j**3 + 26/7*j**2 - 24/7*j + 8/7.
2*(j - 2)**2*(j - 1)**2/7
Let t(d) be the first derivative of 1/9*d**3 + 256/3*d - 22 + 16/3*d**2. Find z, given that t(z) = 0.
-16
Let r(a) be the first derivative of -1/6*a**2 + 4/27*a**3 - 1/9*a + 10. Suppose r(h) = 0. Calculate h.
-1/4, 1
Let 8/5*j**2 - 2*j - 2/5*j**3 + 4/5 = 0. Calculate j.
1, 2
Factor 6*p**2 - p**2 + 28*p + 3*p + 29*p - 197 - 28.
5*(p - 3)*(p + 15)
Suppose -3*o = -2*c - 11, -3*c - 4*o + 31 = o. Let v(a) be the second derivative of 0 - 4*a**4 - 4*a**3 - 3/2*a**c - 10*a. Solve v(z) = 0 for z.
-1/4
Let b(v) be the third derivative of v**6/540 + v**5/45 - v**4/108 - 2*v**3/9 - 2*v**2 + 78. Factor b(g).
2*(g - 1)*(g + 1)*(g + 6)/9
Let m = 6071/1350 - -2/675. Factor 9/2*o - m*o**2 - 3/2 + 3/2*o**3.
3*(o - 1)**3/2
Let n(r) = 33*r - r + 14*r - 24 - 22*r**2. Let u(i) = 7*i**2 - 15*i + 8. Let o = 536 + -541. Let g(z) = o*n(z) - 16*u(z). Suppose g(a) = 0. Calculate a.
1, 4
Let h(j) = 35*j**2 - 15*j - 10. Let w(b) = 17*b**2 - 8*b - 6. Let q(z) = 3*h(z) - 5*w(z). Factor q(v).
5*v*(4*v - 1)
Let s(z) be the first derivative of 0*z**2 + 1/27*z**3 - 1 - 1/90*z**5 + z + 0*z**4. Let i(l) be the first derivative of s(l). Suppose i(d) = 0. Calculate d.
-1, 0, 1
L