7
Let n(k) be the first derivative of 2*k**5/35 + k**4/7 + 2*k**3/21 - 59. Find z, given that n(z) = 0.
-1, 0
Let w(u) = -11*u**2 - u. Let b be w(1). Let d = b - -86/7. Factor d*a**3 - 4/7 - 6/7*a + 0*a**2.
2*(a - 2)*(a + 1)**2/7
Let f(c) = -1 + 0*c**3 + 10*c**2 + 5*c + 16*c + 4 + 7*c**3. Let t(n) = -3*n**3 - 5*n**2 - 10*n - 2. Let i(b) = -2*f(b) - 5*t(b). What is v in i(v) = 0?
-2, -1
Let x = 881 + -1759/2. Suppose x*z**4 + 3/2*z**2 + 9/2*z**3 - 3 - 9/2*z = 0. What is z?
-2, -1, 1
Let 49/4 + 1/4*y**2 - 7/2*y = 0. Calculate y.
7
Let r(c) be the first derivative of -c**6/30 - 2*c**5/15 + c**4/2 + c**2 - 37. Let h(m) be the second derivative of r(m). Factor h(w).
-4*w*(w - 1)*(w + 3)
Let u(i) be the second derivative of -i**5/100 + i**4/3 - 77*i**3/30 - 121*i**2/5 - i + 55. Factor u(v).
-(v - 11)**2*(v + 2)/5
Let r be ((-24)/(-9))/((-58)/(-12)*4). Let u = 30/203 + r. Find i, given that -u*i**2 - 6/7*i - 4/7 = 0.
-2, -1
Suppose 0*r - 5*r = 2*w, 54 = 5*w - r. Solve 93*i**4 - 57*i**3 - 523*i**4 + 25*i**2 + 192*i**3 + 280*i**5 - w*i = 0 for i.
-1/4, 0, 2/7, 1/2, 1
Let f(g) be the first derivative of 2*g**5/5 - 23*g**4 + 1058*g**3/3 - 127. Factor f(o).
2*o**2*(o - 23)**2
Let q(h) be the second derivative of 7*h + 0*h**3 + 0*h**4 - 1/50*h**5 + 0*h**2 + 1/105*h**7 + 0*h**6 + 0. Factor q(p).
2*p**3*(p - 1)*(p + 1)/5
Let f = 200 + -2399/12. Let x(n) be the first derivative of 2/9*n**3 - 3 - f*n**4 + 0*n**2 + 0*n. Suppose x(d) = 0. What is d?
0, 2
Let u = 84 + -1507/18. Let l(p) be the first derivative of -2/27*p**3 + 0*p + 0*p**2 - 4 + u*p**4 - 8/45*p**5. Solve l(b) = 0.
0, 1/4, 1
Let b(h) = h**2 - 5*h - 1. Let a be b(5). Let o(r) = 9*r**4 + 23*r**3 + 35*r**2 - 4*r. Let s(y) = -y**4 - y**2 - y. Let n(m) = a*o(m) - 5*s(m). Factor n(i).
-i*(i + 3)**2*(4*i - 1)
Let q be 2*10 + -405 + 389. Solve -6/11*n - 4/11 + 2/11*n**q + 2/11*n**2 + 6/11*n**3 = 0.
-2, -1, 1
Let c be (2044/(-126) - -16) + (-4)/(-9). Let r(z) be the first derivative of 4/3*z + 5 + 1/3*z**2 - c*z**3. What is p in r(p) = 0?
-1, 2
Suppose -4*f + 5*n + 16 = 0, 0 = -f + 3*n - 1 + 5. Let g = f + -15/4. What is c in 1/4*c + g*c**2 - 1/2 = 0?
-2, 1
Let h(a) be the second derivative of -9*a**5/20 + 17*a**4/4 - 5*a**3/2 - 75*a**2/2 - 353*a. Determine k so that h(k) = 0.
-1, 5/3, 5
Let k(a) be the first derivative of a**5 + 10*a**4 + 110*a**3/3 + 60*a**2 + 45*a - 84. Factor k(r).
5*(r + 1)**2*(r + 3)**2
What is c in 0 + 0*c + 1/2*c**3 - 5/2*c**2 = 0?
0, 5
Let o(y) be the third derivative of y**10/37800 + y**9/15120 - 11*y**5/60 + 7*y**2. Let m(f) be the third derivative of o(f). Factor m(p).
4*p**3*(p + 1)
Suppose -4*l - 11 = -3*p, 0 = -2*p + 2*l - 5*l - 4. Let x be p/3*(-4 - -4). What is g in 3/4*g**3 + 0*g**2 - 3/2*g**4 + x*g + 0 + 3/4*g**5 = 0?
0, 1
Suppose -64 = -16*p + 41 - 25. Suppose 0 = -5*h + 13 - 3. Factor 0*g + 0 - 7*g**4 - 13/4*g**3 - 5*g**p - 1/2*g**h.
-g**2*(2*g + 1)**2*(5*g + 2)/4
Let a(z) = 3*z**2 - 26*z + 28. Let t(u) = u**2 - 12*u + 13. Let i(r) = -2*a(r) + 5*t(r). Suppose i(c) = 0. Calculate c.
-9, 1
Let a(s) be the second derivative of -2*s**6/15 - 9*s**5/4 - 151*s**4/12 - 45*s**3/2 - 25*s**2/2 + 28*s. Factor a(j).
-(j + 1)*(j + 5)**2*(4*j + 1)
Let n(o) be the first derivative of -8*o**3/33 + 76*o**2/11 - 722*o/11 - 69. What is q in n(q) = 0?
19/2
Let m be (-4)/10*(-55)/88. Let p(q) = -3*q + 2. Let l be p(0). Solve 0 - 1/2*s - m*s**l = 0.
-2, 0
Let t = 68 + -68. Suppose -13*o = -55 + 3. Suppose 0 - 3/4*v**o + t*v + 0*v**3 + 3/4*v**2 = 0. Calculate v.
-1, 0, 1
Let c(n) be the third derivative of n**6/135 + 49*n**5/270 + 13*n**4/9 + 4*n**3/3 + 143*n**2. Factor c(q).
2*(q + 6)**2*(4*q + 1)/9
Let k be 1*6 - (-3 + 10 - 4). Let z be (-2)/(-4 + 4 - k). Let 1/3*n**2 - z + 1/3*n = 0. What is n?
-2, 1
Let v be (-6 - -7) + (-1 - 2)/(-3). Let -q - q**2 + 13*q**4 + 4*q**3 - 2*q**3 + 6*q**5 + 7*q**3 - v*q**3 = 0. What is q?
-1, -1/2, 0, 1/3
Suppose -28 = -2*v - 3*k + 4*k, 4*k - 42 = -3*v. Suppose 6 = 16*j - v*j. Factor 1/4*z + 1/2 - 1/2*z**2 - 1/4*z**j.
-(z - 1)*(z + 1)*(z + 2)/4
Let a(m) be the first derivative of m**3/15 - 18*m**2/5 + 324*m/5 - 57. Let a(f) = 0. Calculate f.
18
Suppose -1 + 16 = 3*a. Suppose a = -0*q + q. Suppose 12 - 57*d**3 + 6*d**2 - d**5 + 0*d + 21*d**4 + 69*d**2 - 2*d**q - 48*d = 0. Calculate d.
1, 2
Let q be -67*((-1)/(4/20) + 4). Let t = 69 - q. Determine m so that 0 + 0*m + 2/13*m**t = 0.
0
Let l(s) be the third derivative of -s**8/672 - s**7/35 + 7*s**6/120 + s**5/10 - 13*s**4/48 - 4*s**2 + 1. Solve l(t) = 0 for t.
-13, -1, 0, 1
Let a(q) be the first derivative of 51*q**4/28 + 7*q**3 + 6*q**2 - 12*q/7 - 274. Factor a(u).
3*(u + 1)*(u + 2)*(17*u - 2)/7
Factor -9/5*g + 12/5*g**2 - 3/5*g**3 + 0.
-3*g*(g - 3)*(g - 1)/5
Let h(f) be the third derivative of -1/10*f**7 - 1/4*f**4 + 3/40*f**6 + 0*f**3 + 2*f**2 + 3/112*f**8 + 0*f + 0 + 3/20*f**5. Determine c, given that h(c) = 0.
-2/3, 0, 1
Let u be -1*6 - 1 - -1. Let a be (u/(-9))/(1/3). Find i such that -i**2 + 0*i**2 + 2*i - 2*i**3 + 3*i**a - 2*i**4 = 0.
-1, 0, 1
Find d such that -2/3*d**3 - 8/3*d - 2/3 - 19/6*d**2 + 1/3*d**5 + 5/6*d**4 = 0.
-2, -1, -1/2, 2
Let g(x) be the third derivative of x**8/131040 + x**7/10920 + x**5/60 + 7*x**2. Let a(w) be the third derivative of g(w). Factor a(u).
2*u*(u + 3)/13
Let j(s) = -1. Let u(g) = -883*g**2 - 1 - 12*g + 886*g**2 + 1. Let w(h) = 9*j(h) - u(h). Suppose w(t) = 0. Calculate t.
1, 3
Let w = -15406 + 15421. Factor -10*c**2 - 5/3*c**3 - 20/3 - w*c.
-5*(c + 1)**2*(c + 4)/3
Let -2/11*w**2 - 4/11*w + 0 = 0. What is w?
-2, 0
Solve 384*t - 16*t**2 + 0 + 1/6*t**3 = 0 for t.
0, 48
Let d(a) = 2*a**2 - 8 - 3*a**4 + 8*a - 3*a**4 + 0*a + 4*a**3. Let i(q) = -q**4 + q - 1. Let s(p) = -d(p) + 8*i(p). Factor s(h).
-2*h**2*(h + 1)**2
Suppose -q + 28 = q - 3*i, 3*i - 52 = -2*q. Suppose 24 = 2*u - m + 5*m, q = 5*m. Solve -36*y**2 - 20*y - 27/4*y**u - 4 - 27*y**3 = 0 for y.
-2, -2/3
Let o(t) be the first derivative of -5/4*t**2 - 25/4*t + 15 - 1/12*t**3. Suppose o(n) = 0. What is n?
-5
Let -9/4*u - 1/4*u**2 - 9/2 = 0. Calculate u.
-6, -3
Let n(u) be the second derivative of 1/30*u**6 + 2*u + 0 + 0*u**3 - 1/40*u**5 - 1/84*u**7 + 0*u**2 + 0*u**4. Determine o, given that n(o) = 0.
0, 1
Let y = -64 - -28. Let p be ((-5)/6)/(6/y). Find a such that -a**5 + 5*a**5 - 6*a**p + 4*a**3 - 2*a**5 = 0.
-1, 0, 1
Factor 1/5*u**2 - 12/5 - 4/5*u.
(u - 6)*(u + 2)/5
Let m(g) be the third derivative of 1/60*g**6 + 3/4*g**4 + 0*g + 1/5*g**5 + 22*g**2 + 0*g**3 + 0. Find p such that m(p) = 0.
-3, 0
Let o(u) = -u**3 + 14*u**2 + 19*u - 18. Let i be o(15). Let y = i - 40. Factor 10*r - y*r**3 - 6*r**2 + 10*r - 24*r.
-2*r*(r + 1)*(r + 2)
Let j be (3 - (-87)/(-30))*(27 + -8 + -3). Determine h so that j - h**2 + 1/5*h**3 + 2/5*h = 0.
-1, 2, 4
Let i = 669 - 666. Let y(a) be the first derivative of 0*a - 2/9*a**3 + 1/15*a**4 + 2/15*a**5 + i - 2/15*a**2. Solve y(g) = 0.
-1, -2/5, 0, 1
Let h(s) be the third derivative of -s**9/3024 - s**8/1680 + s**7/105 + s**6/30 - 9*s**3/2 - 13*s**2. Let c(f) be the first derivative of h(f). Factor c(v).
-v**2*(v - 3)*(v + 2)**2
Find z such that -127 - 74 - 5*z + 389 - 4*z**2 - 88 - z**2 = 0.
-5, 4
Let l(m) be the first derivative of -9*m**4/16 + 65*m**3/12 - 7*m**2/4 - 139. Factor l(j).
-j*(j - 7)*(9*j - 2)/4
Let h = 102/259 + -4/37. Suppose 3*m - 94*n - 9 = -91*n, -6 = -5*m - 4*n. Factor 2/7*l**m - 4/7 - h*l.
2*(l - 2)*(l + 1)/7
Factor -1/5*x**3 + 6/5*x**2 - 20 + 3*x.
-(x - 5)**2*(x + 4)/5
Let f(i) be the third derivative of -1/42*i**7 + 0 + 1/12*i**6 - 5/2*i**3 + 6*i**2 + 1/3*i**5 + 0*i - 5/12*i**4. Let f(u) = 0. What is u?
-1, 1, 3
Let n(j) = j**5 + j**4 - j**2 + j - 1. Let t(d) = 20*d**5 + 6*d**4 + 16*d**3 - 14*d**2 - 10. Let i(y) = 36*n(y) - 2*t(y). Factor i(k).
-4*(k - 4)*(k - 1)**3*(k + 1)
Let a(k) be the first derivative of k**5 - 67*k**4/2 + 1724*k**3/15 - 532*k**2/5 + 192*k/5 + 30. Let a(n) = 0. Calculate n.
2/5, 2, 24
Let t(q) be the first derivative of q**5/5 + q**4/4 + q**2/2 - q - 7. Let j(i) = -18*i**4 - 12*i**2 - 15*i + 15. Let n(a) = j(a) + 15*t(a). Factor n(l).
-3*l**2*(l - 4)*(l - 1)
Let d be (0 + 4)/(2/5). Suppose -9*m - 6 = -d*m. What is c in -27*c**3 - 19*c**2 + 10*c**4 + 29*c**4 + m*c + 16*c**2 - 15*c**5 = 0?
-2/5, 0, 1
Solve -264/7*b - 144/7 - 30/7*b**3 - 2/7*b**4 - 14