q - 1)**2*(q + 1)/4
Let t(y) = -y**2 - 4*y - 8. Let k be t(-6). Let s be k/12 + 1*2. Let s + 1/3*i**4 + 4/3*i + 2*i**2 + 4/3*i**3 = 0. What is i?
-1
Let a = -2 - -6. Find m, given that -3*m**2 + a + 0 + 2*m**4 - m**4 - 2*m**3 + 4*m = 0.
-1, 2
Suppose 0*l = 5*l + 25. Let k = l - -5. Solve k*r + 6*r**2 + 0*r - r**3 + 6*r**3 + r = 0.
-1, -1/5, 0
Suppose -7*q + 42 = 14*q. Suppose -2/3 + 7/3*m**3 - 5*m**4 - 7/3*m + 17/3*m**q = 0. Calculate m.
-1, -1/5, 2/3, 1
Suppose 0*w - w**2 + 0 + 0*w + 1 = 0. What is w?
-1, 1
Let b(d) = 380*d - 378*d + 2 - 13. Let v be b(7). Determine o, given that -1/2*o**4 - 6*o**2 - 4*o + 0 - 3*o**v = 0.
-2, 0
Let r(a) be the first derivative of -a**3/4 - 6*a**2 - 48*a - 9. Find h such that r(h) = 0.
-8
Suppose 0*k - 6 = -3*k. Suppose 5*z = 3*o + 16, -3*z + 11 = -k*z + 2*o. What is s in s**3 - s - 3*s - 2*s**2 - z*s**3 + 6*s**3 = 0?
-1, 0, 2
Let h(k) be the first derivative of 1/2*k**3 + 0*k**4 - 1/10*k**5 - 1/2*k**2 + 0*k - 1. Solve h(b) = 0 for b.
-2, 0, 1
Let b(n) be the third derivative of n**4/12 - 7*n**3/3 - n**2. Let s be b(7). Factor 1/3 + s*v - 1/3*v**2.
-(v - 1)*(v + 1)/3
Let r be 16/15 + -3*8/36. Determine a, given that -r*a**2 + 0 + 4/5*a = 0.
0, 2
Factor -32*y**2 - 4*y**4 - 4*y**3 + 22*y**3 - 64*y + 10*y**3.
-4*y*(y - 4)**2*(y + 1)
Let z(b) = 4*b**4 - 9*b**3 - 16*b**2 + 11*b + 5. Let g(a) = 2*a**4 - 5*a**3 - 8*a**2 + 5*a + 3. Let m(h) = 5*g(h) - 3*z(h). What is n in m(n) = 0?
-2, 0, 1, 2
Let r(g) be the third derivative of -g**6/12 + 2*g**5/5 - 3*g**4/4 + 2*g**3/3 - 30*g**2. Determine y so that r(y) = 0.
2/5, 1
Suppose 4*o + 9 - 21 = 0. Let 3*f - 11*f - 68*f**o - 50*f**5 - 70*f**3 + 56*f**2 + 140*f**4 = 0. What is f?
0, 2/5, 1
Let w be 1/(-2) - (-9)/2. Determine r so that 2*r**3 + 14*r**4 + 2*r**3 + 6*r**5 - w*r**4 = 0.
-1, -2/3, 0
Let m(c) = c**3 - 10*c**2 + c - 6. Let f be m(10). Let b(z) be the first derivative of 1/2*z**4 + 0*z**3 - 3*z**2 - 4 + f*z. Suppose b(y) = 0. What is y?
-2, 1
Solve -1/9*t**4 - 20/9*t - 8/9 - 7/9*t**3 - 2*t**2 = 0 for t.
-2, -1
Let o = -26 + 33. Suppose -o*i = -6*i - 2. Factor 0 + 2/3*a + 1/3*a**i.
a*(a + 2)/3
Suppose -1/3 - 1/9*r**4 - 2/9*r + 2/9*r**3 + 4/9*r**2 = 0. What is r?
-1, 1, 3
Let g(p) be the second derivative of -p**7/1890 + p**6/2160 + p**4/3 - 4*p. Let c(i) be the third derivative of g(i). Solve c(d) = 0.
0, 1/4
Let c(l) be the third derivative of l**5/60 - l**4/8 + l**3/3 + 3*l**2. Let c(y) = 0. What is y?
1, 2
Let z = 4 + -2. Factor v**2 - 2 + v**z + v + v**2 - 2*v**2.
(v - 1)*(v + 2)
Let u(m) be the third derivative of -5*m**8/21 - 20*m**7/21 - 25*m**6/24 + 5*m**5/12 + 25*m**4/24 - 5*m**3/6 + 5*m**2. Factor u(g).
-5*(g + 1)**3*(4*g - 1)**2
Let b = -2502/7 + 358. Factor 6/7*o + b + 2/7*o**2.
2*(o + 1)*(o + 2)/7
Let d(s) be the second derivative of -2*s**6/15 + 3*s**5/5 + 2*s**4/3 - 8*s**3 + 16*s**2 + 2*s - 6. Solve d(i) = 0 for i.
-2, 1, 2
Suppose 2*d = f + 7, f - 6 = -d - f. Let 0*q**d + 3*q**3 - q**3 - 2*q**5 - 2*q**4 - 2*q**2 + 4*q**2 = 0. Calculate q.
-1, 0, 1
Let o be -2 - (0 + -3 - -1). Factor 2*h**2 + 2*h**2 - h**3 + 2 - 5*h + o*h**3.
-(h - 2)*(h - 1)**2
Let d(p) = p**3 - 4*p**2 + 4*p - 3. Let t be d(3). Let n(a) = a**3 + a**2 - a + 3. Let l be n(t). Determine u, given that -u - 4*u**l + 3*u**3 + 2*u**3 = 0.
-1, 0, 1
Let j(z) be the second derivative of z**5/10 + z**4/3 - z**3/3 - 2*z**2 + 18*z. Find l such that j(l) = 0.
-2, -1, 1
Let o(x) be the third derivative of 2*x**2 + 0*x**4 + 0*x**5 + 0 + 0*x + 0*x**3 + 1/360*x**6 - 1/630*x**7. Factor o(a).
-a**3*(a - 1)/3
Factor -9/4*t**2 - 3/4 - 9/4*t - 3/4*t**3.
-3*(t + 1)**3/4
Suppose -87 - 2*b**3 - 94 - 4*b + 181 + 6*b**2 = 0. Calculate b.
0, 1, 2
Let s(t) be the third derivative of t**7/1260 - t**6/540 - t**5/90 - 2*t**3/3 + 3*t**2. Let b(l) be the first derivative of s(l). Factor b(d).
2*d*(d - 2)*(d + 1)/3
Find j such that 7*j**4 - 18*j**3 - 31*j**4 - 4*j**5 + 8*j**3 - 10*j**3 = 0.
-5, -1, 0
Solve -2*d + 9*d**2 + 2*d - 14*d**2 = 0 for d.
0
Suppose -v + 3*a + 2 = 0, 4*a = -4*v + v - 46. Let n be (1 - -2)*v/(-15). Let g**3 + 1/2*g**4 - 1/2*g - 1/2*g**5 - g**n + 1/2 = 0. What is g?
-1, 1
Let l be (-2)/(-14) + (-8)/(-42). Let b(h) be the first derivative of -l*h**3 - 1 - h + h**2. Determine a so that b(a) = 0.
1
Let s(h) be the second derivative of 0*h**3 - 1/5*h**6 - 3/20*h**5 + h + 0*h**4 + 0*h**2 + 3/14*h**7 + 0. Solve s(x) = 0 for x.
-1/3, 0, 1
Let z(l) be the second derivative of 5*l**4/12 - 5*l**2/2 + 29*l. Factor z(m).
5*(m - 1)*(m + 1)
Let y(l) be the second derivative of -l**6/540 + l**5/30 - l**4/4 + l**3 - l**2/2 + 2*l. Let g(s) be the first derivative of y(s). Find m, given that g(m) = 0.
3
Let j(w) be the second derivative of 1/11*w**2 + 0*w**3 - 1/66*w**4 + 0 - 3*w. Suppose j(r) = 0. Calculate r.
-1, 1
Let t(o) = o**2 + o. Let w(n) = -n + 1. Let j be w(-9). Let l(d) = 28*d**2 + 14*d. Let s(h) = j*t(h) - l(h). Factor s(r).
-2*r*(9*r + 2)
Let g be 2/5 + 207/45. Let -5*p**3 - 4*p**4 + p**5 + 2*p**g + 6*p**3 = 0. Calculate p.
0, 1/3, 1
Let y(i) be the third derivative of -i**5/240 - i**4/32 - 2*i**2 + 6. Determine f so that y(f) = 0.
-3, 0
Suppose 9*k - 18 = 6*k. Let x(c) be the third derivative of 0*c - 1/60*c**5 - 2*c**2 - 1/240*c**k - 1/48*c**4 + 0*c**3 + 0. Factor x(p).
-p*(p + 1)**2/2
Let h(c) = -c + 3. Let n be h(0). Suppose n*x - 3 = 3. Let 0*l - 2*l**x + 4*l - 2*l = 0. What is l?
0, 1
Let o(x) be the third derivative of -x**8/1176 - 4*x**7/735 - x**6/105 + 33*x**2. Let o(w) = 0. What is w?
-2, 0
Let v = -10 + 15. Let c(m) = m - 3. Let a be c(v). Suppose 0*p + 2/7*p**3 + 0 + 0*p**a + 4/7*p**4 + 2/7*p**5 = 0. Calculate p.
-1, 0
Suppose 2*p - 5*c - 48 = 30, 176 = 5*p - 3*c. Suppose d = 4, v = -4*d + p - 15. Suppose -1/5 + 3/5*b - 3/5*b**2 + 1/5*b**v = 0. What is b?
1
Let x(d) be the third derivative of -1/630*d**7 - 1/180*d**5 + 0*d + d**2 + 0*d**4 + 1/180*d**6 + 0 + 0*d**3. Suppose x(y) = 0. Calculate y.
0, 1
Let d be 4 + -4 - 21/(-1). Suppose 0 = 3*m + 3*s - d, -m - 5*s = 2*m - 31. Find a such that -3*a**4 - 2*a**2 - m*a**3 + 6*a**3 + a**4 = 0.
0, 1
Let g(l) be the first derivative of l**6/300 - l**5/150 - l**4/60 + l**3/15 + 3*l**2/2 - 3. Let i(d) be the second derivative of g(d). Factor i(z).
2*(z - 1)**2*(z + 1)/5
Let b(t) be the third derivative of t**8/10080 - t**7/1890 + t**6/1080 + t**4/8 + t**2. Let h(c) be the second derivative of b(c). Determine g so that h(g) = 0.
0, 1
Let s = -127 - -891/7. Factor -4/7*g**3 + 2/7*g**2 + 0*g + 0 + s*g**4.
2*g**2*(g - 1)**2/7
Let w be (1 - 3 - 45)/(-9) + -3. Find q such that -10/9*q**4 - 20/9*q**2 - 10/9*q - w*q**3 - 2/9*q**5 - 2/9 = 0.
-1
Suppose 2 - 12 = -5*c. Let i(w) be the first derivative of 0*w**c + 0*w - 1/6*w**4 - 4/15*w**5 + 0*w**3 - 1/9*w**6 - 1. Factor i(s).
-2*s**3*(s + 1)**2/3
Let w be ((2 - 4) + 2)*(-1)/(-4). Let j(s) be the second derivative of 1/6*s**3 + 1/3*s**2 + w - 1/36*s**4 - 2*s - 1/90*s**6 - 1/20*s**5. Factor j(r).
-(r - 1)*(r + 1)**2*(r + 2)/3
Let c(y) = -4*y + 80. Let i be c(20). Determine w so that i + 2/11*w**2 - 2/11*w**4 - 2/11*w + 2/11*w**3 = 0.
-1, 0, 1
Suppose 0 = -0*i + 4*i. Factor 9/5*v**3 + i + 0*v - 3/5*v**2 - 9/5*v**4 + 3/5*v**5.
3*v**2*(v - 1)**3/5
Factor 4/11*d**3 - 6/11*d**2 + 8/11 + 2/11*d**4 - 8/11*d.
2*(d - 1)**2*(d + 2)**2/11
Let k = 3 - 2. Let s = k + 3. Find p, given that -s - 6*p**5 + 2*p**2 - 10*p**4 - 2*p**3 - 1 + 5 = 0.
-1, 0, 1/3
Suppose 5*t - 4*t - 2 = 0. Factor -2 + 4*a**3 + t*a**4 + 2*a**5 - 24*a + 18*a - 4*a**2 + 4*a**4.
2*(a - 1)*(a + 1)**4
Suppose -4*w + 0*w - 5*m = 29, -15 = 5*w + 2*m. Let n be (-2 + 2)*w/(-3). Factor n + 1/5*f**3 - 2/5*f**2 + 1/5*f.
f*(f - 1)**2/5
Let g(u) = 4*u**4 - 2*u**3 + 2*u**2 - 2*u - 2. Let m(l) = l**5 - 9*l**4 + 5*l**3 - 5*l**2 + 5*l + 5. Let v(h) = -5*g(h) - 2*m(h). Factor v(j).
-2*j**4*(j + 1)
Let q(u) be the second derivative of -u**4/9 + 28*u**3/9 - 98*u**2/3 - u. Factor q(w).
-4*(w - 7)**2/3
Let z be 3/(-2) + -12 + 15. Let h(b) be the first derivative of -11/4*b**4 + z*b**6 + 2*b**2 + 0*b - 2 - 4/3*b**3 + 6/5*b**5. Factor h(i).
i*(i + 1)**2*(3*i - 2)**2
Factor 12/7*j + 6/7*j**2 - 24/7 - 3/7*j**3.
-3*(j - 2)**2*(j + 2)/7
Let z(f) be the third derivative of -f**6/30 + f**5/15 + f**4/3 + 4*f**2. Factor z(y).
-4*y*(y - 2)*(y + 1)
Let t = 6 + 16. Find h such that -25