
Let g(f) be the first derivative of -f**5/15 - f**4/12 + f**3/9 + f**2/6 + 4. Suppose g(m) = 0. Calculate m.
-1, 0, 1
Let s be (-3)/(-9)*12/20. Determine n, given that 0 + s*n**4 + 0*n**3 - 1/5*n**2 + 0*n = 0.
-1, 0, 1
Let o be 1075/388 + 1/(-4). Let k = o + -2/97. Factor 1 + 2*d**2 + k*d + 1/2*d**3.
(d + 1)**2*(d + 2)/2
Let k(g) be the second derivative of g**8/11200 + g**7/1050 + g**6/300 - 5*g**4/12 + 4*g. Let j(l) be the third derivative of k(l). Suppose j(r) = 0. What is r?
-2, 0
Let h be (-1 + 0)/((6/(-3))/6). Solve 4/3*q**2 - 1/3*q**h + 2/3 - 5/3*q = 0 for q.
1, 2
Let g be -17 - -22 - (-48)/(-10). Factor 3/5*a + 3/5*a**4 - 1/5*a**5 - g - 2/5*a**3 - 2/5*a**2.
-(a - 1)**4*(a + 1)/5
Let a(p) = 4*p**4 + 10*p**3 + 7*p**2 + 1. Let o(w) = -w**4 - w**3 - w**2 - 1. Let c(r) = a(r) + o(r). Factor c(m).
3*m**2*(m + 1)*(m + 2)
Solve r**2 + 6*r**3 - 3*r - r**2 - 3*r**3 = 0 for r.
-1, 0, 1
Let k(l) be the third derivative of -l**5/15 - l**4/3 + 2*l**3 + l**2 - 17. Find c such that k(c) = 0.
-3, 1
Let x = 8 - 0. Let n = -3 + x. What is o in -5*o**3 - 5*o**2 + o**3 - 4 + 8*o + n*o**3 = 0?
1, 2
Let i(h) be the second derivative of 0*h**3 + 0 + 1/105*h**6 - 3*h + 0*h**5 + 1/7*h**2 - 1/21*h**4. Determine j so that i(j) = 0.
-1, 1
Let k = -32 - -47. Factor -f**3 - 3*f**2 + 5 - k + 14.
-(f - 1)*(f + 2)**2
Let p(s) be the second derivative of s**9/13608 + s**8/7560 - s**7/3780 - s**6/1620 + s**3/3 + 2*s. Let i(r) be the second derivative of p(r). Factor i(x).
2*x**2*(x - 1)*(x + 1)**2/9
Suppose -6*o = -2*o - 20. Let t(q) be the first derivative of 1/6*q**4 - 1/3*q + 1/15*q**o + 2 + 0*q**3 - 1/3*q**2. Suppose t(p) = 0. What is p?
-1, 1
Let x(f) = 13*f - 39. Let z be x(3). Solve -1/2*r**2 + 0*r + z + 1/2*r**3 = 0 for r.
0, 1
Let b(u) = -7*u**2 + 4*u + 1. Let n(c) be the third derivative of -2*c**5/15 + c**4/8 + c**3/3 + c**2. Let q(x) = 6*b(x) - 4*n(x). Factor q(a).
-2*(a - 1)*(5*a - 1)
Let q(n) be the first derivative of 1/20*n**5 + 1/2*n**2 + 1/2*n**3 + 3*n + 1/4*n**4 - 1. Let i(c) be the first derivative of q(c). Factor i(l).
(l + 1)**3
Suppose -27/4 - 45*y - 75*y**2 = 0. Calculate y.
-3/10
Suppose 4*b - h + 8 = -5*h, -2*h - 8 = 0. Factor 6/5*n**3 - 2*n + 8/5*n**b - 4/5.
2*(n - 1)*(n + 2)*(3*n + 1)/5
Let z(y) be the first derivative of y**3/18 - y**2/3 + 2*y/3 - 32. Solve z(p) = 0.
2
Factor 8/9*p - 8/9 + 26/9*p**2 + 10/9*p**3.
2*(p + 1)*(p + 2)*(5*p - 2)/9
Let q = 17616/13 - 1354. Find f, given that -q*f + 4/13 + 12/13*f**2 = 0.
1/2, 2/3
Suppose 0 = 2*o - 4*r - 16, -4*o = -5*r + 14 - 43. Suppose 4*q - 2 = o. Suppose 4/7 + 2/7*n**q + 6/7*n = 0. What is n?
-2, -1
Suppose 3*v - 49 = -46. What is h in -1/2*h**3 + 3/2*h + 0*h**2 + v = 0?
-1, 2
Factor 102*a**5 - 29*a - 7*a - 72*a**3 + 6*a**5 + 104*a**2 - 108*a**4 + 4.
4*(a - 1)*(a + 1)*(3*a - 1)**3
Let o = 101 + -101. Factor o - 1/3*x**2 - 1/3*x**3 + 2/3*x.
-x*(x - 1)*(x + 2)/3
Suppose -k + 22 = 5*q + 7, 2*q = 6. Let l(g) be the first derivative of 0*g**2 - 3/5*g**5 - 1/3*g**3 + k*g + 1/6*g**6 + 3/4*g**4 - 2. Find t such that l(t) = 0.
0, 1
Suppose 4*y - 26 - 22 = 0. Suppose 4*v - 7*v = -3, -y = -4*n - 4*v. Determine a so that a**2 - 4*a**2 + a**n - 4*a = 0.
-2, 0
Let q(o) be the third derivative of 1/96*o**4 + 0 + 0*o**7 - 1/240*o**6 + 0*o + 0*o**5 + 0*o**3 + 1/1344*o**8 - 3*o**2. Factor q(a).
a*(a - 1)**2*(a + 1)**2/4
Factor 4/5 + 1/5*j**3 + j**2 + 8/5*j.
(j + 1)*(j + 2)**2/5
Suppose -4*o = 2 - 14. Let n(m) be the second derivative of m**o + 1/6*m**4 + 2*m**2 + 3*m + 0. Suppose n(q) = 0. What is q?
-2, -1
Factor -160 + 35*q**3 + 374*q + 136*q**2 + 106*q + 134*q**2.
5*(q + 4)**2*(7*q - 2)
Let p(v) be the third derivative of -1/270*v**5 - 1/54*v**4 + 0*v - 2*v**2 + 0*v**3 + 0 + 1/540*v**6. Factor p(d).
2*d*(d - 2)*(d + 1)/9
Find r, given that -2*r**2 + 7*r**2 + r**3 - 2*r**2 = 0.
-3, 0
Let y(j) = -j**3 - j + 1. Let p(l) = 119*l**3 - 75*l**2 + 9*l + 5. Let u(b) = 5*p(b) - 30*y(b). Factor u(o).
5*(5*o - 1)**3
Let w(s) be the first derivative of 1/150*s**6 + 0*s**2 - 2*s - 2 + 0*s**3 + 0*s**5 - 1/60*s**4. Let h(b) be the first derivative of w(b). Factor h(y).
y**2*(y - 1)*(y + 1)/5
Factor 4*f - 3*f - f**2 + 3*f - 7*f**2 + 4*f**3.
4*f*(f - 1)**2
Let k(g) be the second derivative of -g**5/50 + g**4/10 - 4*g**2/5 + 4*g. Find n, given that k(n) = 0.
-1, 2
Let p(y) be the first derivative of -338*y**5/5 - 559*y**4/2 - 332*y**3 - 116*y**2 - 16*y - 27. Determine w so that p(w) = 0.
-2, -1, -2/13
Let t(k) = -2*k**2 - k + 1. Let a be t(-3). Let w be 4/a + 72/105. Find q such that 2/5*q**2 + 0*q - w = 0.
-1, 1
Solve 0*w + 8/5*w**2 - 12/5*w**3 + 0 = 0.
0, 2/3
Suppose 1 - 17 = -4*j. Factor 0*f - 2*f**3 - 26*f**4 - 4*f**3 + 8*f + 28*f**j.
2*f*(f - 2)**2*(f + 1)
Let u be -1 + (-16)/14 - (-5 - -2). Determine o, given that -4/7*o**2 + 0*o - u*o**5 - 2*o**3 - 16/7*o**4 + 0 = 0.
-1, -2/3, 0
Suppose -4*i - 10 = -6*i. Solve -i - 20*w - 2 + 0*w**2 - 9 - 4*w**2 = 0 for w.
-4, -1
Let v be -3*(-1 + 1 - 1). Factor -30*n**v - 4 - 19*n**3 + 53*n**3 + 12*n - 12*n**2.
4*(n - 1)**3
Let -6/7*n**3 - 9/7*n**5 + 15/7*n + 3/7 - 3*n**4 + 18/7*n**2 = 0. What is n?
-1, -1/3, 1
Let b(q) be the first derivative of -1/2*q**2 - 1/6*q**6 - 4/5*q**5 + 3 + 0*q - 3/2*q**4 - 4/3*q**3. Factor b(z).
-z*(z + 1)**4
Let w(t) = -2*t**5 + 7*t**4 - 17*t**3 + 4*t**2 + 29*t - 16. Let v(s) = s**5 - 4*s**4 + 9*s**3 - 2*s**2 - 14*s + 8. Let n(a) = -5*v(a) - 2*w(a). Factor n(y).
-(y - 2)**3*(y - 1)*(y + 1)
Let u = 22 + -31. Let o = 12 + u. Solve 1/5*g + 0 + 1/5*g**o + 2/5*g**2 = 0 for g.
-1, 0
Suppose 2*g - 12 = -2*c, -c - 5*g - 5 = -3*c. Suppose c*s**4 - 6*s**2 + 0*s - 4*s - 2*s**4 - s**4 = 0. What is s?
-1, 0, 2
Let o = 8 + -4. Factor -2*c**3 + 4*c - c**4 + 2*c**4 + c**2 - 4*c**2 + o.
(c - 2)**2*(c + 1)**2
Suppose 5*c = -2*p + 8, 4*c - 20 = -5*p - 0*c. Factor -81/2 + 0*d - 12*d**3 + 27*d**2 + 3/2*d**p.
3*(d - 3)**3*(d + 1)/2
Let d = 711341/1140986 - 1/14818. Let o = 10/11 - d. Let 0 - 2/7*m**2 + o*m = 0. Calculate m.
0, 1
Let i be (-120)/(-675) + 2/9. Let z = 4 + -2. Factor 0 + 1/5*p + 1/5*p**3 - i*p**z.
p*(p - 1)**2/5
Let a(s) be the first derivative of 7*s**3/6 - 3*s**2/4 - 2*s + 19. Determine g so that a(g) = 0.
-4/7, 1
Let a(s) = -s + 12. Let j be a(8). Let l be 0 + 1 + (-2)/j. Factor 1/2 + l*d**4 - d**2 + 0*d**3 + 0*d.
(d - 1)**2*(d + 1)**2/2
Factor 16/3 - 14/3*y**3 - 40/3*y + 12*y**2 + 2/3*y**4.
2*(y - 2)**3*(y - 1)/3
Let n = -399 - -402. Let 1/5*u - 1/5*u**2 + 1/5 - 1/5*u**n = 0. What is u?
-1, 1
What is p in 11 - 7 - 4*p - 4 - 2*p**3 + 6*p**2 = 0?
0, 1, 2
Suppose -5*q + 10 = -0. Solve -2/7*h**5 + 0 + 4/7*h**4 - 2/7*h**3 + 0*h**q + 0*h = 0 for h.
0, 1
Factor 25/3*b**5 + 4*b**2 - 11/3*b**3 + 4/3*b + 0 - 10*b**4.
b*(b - 1)**2*(5*b + 2)**2/3
Determine d, given that -2/7*d**3 + 0 + 4/7*d + 2/7*d**2 = 0.
-1, 0, 2
Let j(m) = m**2 - 4. Let k be j(2). Let h(c) be the first derivative of c**2 + k*c - 1 + 2/3*c**3. Find r, given that h(r) = 0.
-1, 0
Let o be ((-12)/(-63))/(3/(-21)*-6). Factor 4/9*x**2 - o*x**3 + 0*x + 2/3*x**5 - 8/9*x**4 + 0.
2*x**2*(x - 1)**2*(3*x + 2)/9
Let z(g) be the first derivative of 0*g**2 - 1/18*g**4 - 2/9*g**3 + 2 + 3*g. Let s(u) be the first derivative of z(u). Factor s(f).
-2*f*(f + 2)/3
Let w be (-8)/((-1)/1) + -2. Suppose w*j = 3*j + 9. Suppose 0*a**2 + 0 - 2/3*a**5 + 0*a**4 + 4/3*a**j - 2/3*a = 0. What is a?
-1, 0, 1
Let j(b) be the first derivative of b**7/210 - 4*b**3/3 - 2. Let l(h) be the third derivative of j(h). Factor l(f).
4*f**3
Let m be ((-15)/3)/(-1)*1. Suppose -o = -m*o + 12. Find f such that -21*f**o - 10*f**2 - 14*f**4 - 11*f**3 - 12*f**2 - 4*f = 0.
-1, -2/7, 0
Let k(o) be the third derivative of -o**6/15 + o**5/5 + o**4/3 - 8*o**2. Find s such that k(s) = 0.
-1/2, 0, 2
Let j(h) be the second derivative of h**6/45 - 2*h**5/15 + 5*h**4/18 - 2*h**3/9 + 4*h. Factor j(b).
2*b*(b - 2)*(b - 1)**2/3
Factor 4*s + 1/2*s**3 + 2 + 5/2*s**2.
(s + 1)*(s + 2)**2/2
Let j be 2/14 - (-148)/140. Factor -2/5*r**3 + j*r + 0*r**2 - 4/5.
-2*(r - 1)**2*(r + 2)/5
Let t = -8 - 12. Let c = t + 142/7. Find z, given that -c*z**2 + 0*z + 0 = 0.
0
Factor 0*b**3 - b**2 - b - 2*b**4 + 3*b**4 + b**3.
b*(b - 1)*(b + 1)**2
Let b(j) be the third derivative of 5*j**8/336 - j**7/42 - j**6/24 + j**5/12 + 18*j**2. Suppose b(g) = 0. Calculate g.
-1, 0, 1
Let n(h) = 