0 for f.
0, 2
Let y(w) be the first derivative of -w**4/6 + w**2 - 4*w/3 + 33. Suppose y(z) = 0. What is z?
-2, 1
Suppose 5*b + 3 = 4*v, -3*v - 2*b = -3*b - 5. Let -4*j**4 + v*j**4 + 6*j - 2*j**2 - 6*j + 4*j**3 = 0. What is j?
0, 1
Factor -6/17*t + 2/17*t**3 + 0*t**2 + 4/17.
2*(t - 1)**2*(t + 2)/17
Let p = -5 - -10. Suppose p + 27 = 4*q. Suppose 3*u**2 - 9*u**3 - 2*u**3 + 2*u**3 + u**4 - 3*u**5 + q*u**4 = 0. What is u?
0, 1
Let y = -538 + 3774/7. Find u such that -2/7*u + y*u**3 - 6/7*u**2 + 0 = 0.
-1/4, 0, 1
Let t(p) = -2*p**2 + 2. Let g(a) = a**2 - 1. Let r(l) = -3*g(l) - 2*t(l). Factor r(i).
(i - 1)*(i + 1)
Let v be (4 - 2) + -1 + 39/(-45). Let a(c) be the first derivative of 0*c - 1/5*c**2 + v*c**3 - 2. Factor a(m).
2*m*(m - 1)/5
Let o = 2 + 0. Let u(y) be the second derivative of 0 + 0*y**2 - 1/30*y**4 + o*y - 1/15*y**3. Factor u(m).
-2*m*(m + 1)/5
Let y = 49 - 44. Let h(u) be the first derivative of -5/2*u**4 + 10/3*u**3 - 5/2*u**2 + u**y - 1/6*u**6 + 3 + u. Let h(v) = 0. What is v?
1
Let n be 2/(-3)*54/(-6). Suppose n*u - 4*u = 0. Factor u*q**3 + 0 + 0*q - 1/5*q**4 + 1/5*q**2.
-q**2*(q - 1)*(q + 1)/5
Find n such that 37*n**2 + 15*n**2 + 20*n - 60 + 5*n**4 - 30*n**3 - 7*n**2 = 0.
-1, 2, 3
Let p(j) = j**3 + 8*j**2 - 8*j + 11. Let m be p(-9). Find g such that -4 - 4*g**4 + 2*g**2 - 8*g**3 - 15*g**4 + 7*g**4 + 14*g**m + 8*g = 0.
-1, 1/3, 1
Let n = 2 - -3. Suppose 1 = -n*f + 11. Factor 4*k**2 - 4*k - 10*k**3 - 5*k**2 + 15*k**f.
-2*k*(k - 1)*(5*k - 2)
Let p(v) be the first derivative of 0*v**2 - 4/5*v**5 + 3/4*v**4 + 0*v - 3 + 1/3*v**3. Factor p(j).
-j**2*(j - 1)*(4*j + 1)
Let c(k) be the first derivative of k**3/3 - 9*k**2/2 + 8*k - 46. Suppose c(q) = 0. What is q?
1, 8
Let r(g) = 8*g**4 - 2*g**3 + 4*g**2 + 2*g. Let f(p) = -p**4 - p**2. Let h = -9 + 15. Let u(b) = h*f(b) + r(b). Solve u(j) = 0 for j.
-1, 0, 1
Let b be 12/30 - 13/(-5). Let t(s) be the first derivative of -1/6*s**2 + 1/9*s**b + 0*s - 2 - 1/15*s**5 + 1/12*s**4. Factor t(h).
-h*(h - 1)**2*(h + 1)/3
Let s(x) = -x + 7. Let i be s(0). Let c(q) = -q**3 + 14*q**2 - 10*q - 2. Let v(u) = -2*u**3 + 43*u**2 - 29*u - 7. Let a(y) = i*c(y) - 2*v(y). Factor a(f).
-3*f*(f - 2)**2
Let x = -24 + 24. Factor -3/5*l**2 + x - 6/5*l.
-3*l*(l + 2)/5
Find y, given that 8/9 - 10/9*y**2 - 16/9*y = 0.
-2, 2/5
Let p(u) be the first derivative of 0*u**2 + 1/8*u**4 + 1/6*u**3 + 0*u + 2. Suppose p(t) = 0. What is t?
-1, 0
Let r = 6 - 4. Let t(k) be the third derivative of 0*k**3 - 1/168*k**8 - 4/105*k**7 - 1/15*k**5 + 0*k**4 + 0 - 1/12*k**6 + k**r + 0*k. Factor t(n).
-2*n**2*(n + 1)**2*(n + 2)
Let y(m) = -m**2 + m. Let b(r) = -2*r**2 + 2*r. Suppose -5*c - 3*q = -23 + 9, 4*q = -5*c + 17. Let k(i) = c*b(i) + 2*y(i). Factor k(h).
-4*h*(h - 1)
Let z(n) be the first derivative of 5*n**5 + 35*n**4/4 + 10*n**3/3 - 30. Suppose z(k) = 0. Calculate k.
-1, -2/5, 0
Suppose a**3 + 0*a**3 + 2*a**3 - 2*a**3 = 0. Calculate a.
0
Let s = -125 + 125. Find g, given that -3/5*g**2 + 3/5*g**4 + s*g + 0*g**3 + 0 = 0.
-1, 0, 1
Let u(g) be the first derivative of 2*g**3/15 - 18*g**2/5 + 162*g/5 - 34. Solve u(b) = 0.
9
Suppose 0 - 9/2*t**4 - 3/2*t**2 + 9/2*t**3 + 3/2*t**5 + 0*t = 0. What is t?
0, 1
Let y(i) be the second derivative of -i**7/315 + i**5/45 - i**3/9 - i**2/2 - 4*i. Let o(f) be the first derivative of y(f). Factor o(m).
-2*(m - 1)**2*(m + 1)**2/3
Suppose l = 3*l. Factor -2/3*y**2 + l + 2/3*y.
-2*y*(y - 1)/3
Find w, given that -18/5*w**2 - 48/5*w**3 + 224/5*w**4 + 4/5*w + 0 = 0.
-2/7, 0, 1/4
Let v be (1/3)/(4/36). Let g = -1/4 + 3/4. Determine t so that -1/4*t**4 + 0*t**2 - 1/2*t + 1/4 + g*t**v = 0.
-1, 1
Let x(k) be the second derivative of 4/15*k**6 + 2/3*k**4 + 4*k - 1/3*k**3 + 0*k**2 - 1/21*k**7 + 0 - 3/5*k**5. Factor x(s).
-2*s*(s - 1)**4
Let z(p) = 2 + 34*p**3 - 5*p**2 - 38*p**3 - p**4 - 2 + 3*p. Let d(t) = -3*t**3 - 6*t**2 + 3*t. Let y(j) = -5*d(j) + 6*z(j). Factor y(o).
-3*o*(o + 1)**2*(2*o - 1)
Let j(y) be the third derivative of y**5/60 + y**4/12 - 5*y**2. Factor j(i).
i*(i + 2)
Suppose -8*k = -5*k - 12. Factor -69/2*q**3 + 81/2*q**2 + 21/2*q**k - 39/2*q + 3.
3*(q - 1)**3*(7*q - 2)/2
Let w(q) be the second derivative of 0*q**4 + 1/90*q**6 + 0 + 0*q**2 + 0*q**3 - q + 1/30*q**5. Solve w(z) = 0.
-2, 0
Let w(g) be the first derivative of g**4/36 + g**3/27 - g**2/18 - g/9 + 13. Let w(c) = 0. Calculate c.
-1, 1
Let o be 7 - 3 - 1*2. Suppose 0 = d - 1 - o, 5*h + d = 28. Suppose -a**3 - 6*a**4 - 5*a**3 + 0*a**2 - 2*a**2 - 2*a**h = 0. What is a?
-1, 0
Let i(s) be the third derivative of 1/120*s**5 - 1/240*s**6 + 0 - 1/420*s**7 + 1/48*s**4 + 0*s**3 + 2*s**2 + 0*s. Factor i(r).
-r*(r - 1)*(r + 1)**2/2
Find c such that -19*c**3 - c**5 + 2 + 2*c**2 + 23*c**2 + 2 + 7*c**4 - 16*c = 0.
1, 2
Let d(n) be the first derivative of 0*n + 2/11*n**5 + 4/33*n**3 + 2 - 7/22*n**4 + 0*n**2. Let d(l) = 0. Calculate l.
0, 2/5, 1
Let l = 4 - 3. Suppose 0 = 4*m + q - 10, 3*q + 9 + 0 = m. Find j such that l - j**2 + j - 4*j - m = 0.
-2, -1
Let s(c) = c**2 + c - 1. Let n(i) = 3*i**5 - 6*i**3 + 3*i**2 + 6*i - 3. Let q(m) = n(m) - 3*s(m). Factor q(u).
3*u*(u - 1)**2*(u + 1)**2
Let g(x) be the second derivative of -x**5/20 - x**4/6 - x**3/6 - 10*x. Factor g(n).
-n*(n + 1)**2
Suppose -15 = -3*b - 2*b. Let h(i) be the first derivative of -1/4*i + 1/12*i**b - 3/16*i**4 + 3/8*i**2 - 1. Factor h(n).
-(n - 1)*(n + 1)*(3*n - 1)/4
Suppose -4 = 2*c - 12. Factor -3*g**4 + 4*g**4 + g**4 - 3*g**c.
-g**4
Let k(a) = -3*a - 4. Let m be k(-3). Suppose 5*n - 25 = 0, 3*z + 5*n - 25 = m*z. Factor 2/3*d + 2/3*d**2 + z.
2*d*(d + 1)/3
Let g = -16 + 18. Factor -1 + 10*o**2 - 6*o**g + 4*o - o**3 - 3*o**3 - 3.
-4*(o - 1)**2*(o + 1)
Suppose -2*j + 4*j - 4*k + 4 = 0, -6 = -2*j - k. Let m be -2 + j + 2/6. Factor y + m + y**2 + 1/3*y**3.
(y + 1)**3/3
Let w = 86 - 86. Let g(p) be the second derivative of 0*p**4 + 0*p**2 + 1/42*p**7 - 3*p + 1/5*p**5 + w*p**3 + 0 + 2/15*p**6. Suppose g(h) = 0. Calculate h.
-2, 0
Suppose -5*w - 2*f = 2*f + 15, -6 = 2*w - 2*f. Let l(d) = -2*d**2 - 6*d - 7. Let g(j) = j**2 + j + 1. Let h(s) = w*l(s) - 15*g(s). Factor h(n).
-3*(n - 1)*(3*n + 2)
Suppose 3 = 2*n - p - 6, -10 = 2*p. Suppose -4 = -0*m - n*m. Factor 2*v**3 + 3*v**4 - m*v**4 - 3*v**3.
v**3*(v - 1)
Suppose 0 = 4*n, 0*n - n = 5*b + 285. Let d = -169/3 - b. Solve -d*m**2 + 0*m**3 - 1/3*m**5 + 2/3*m**4 + 0 + 1/3*m = 0.
-1, 0, 1
Suppose -4*c + 2*c - 2*v = -8, 0 = 5*c + v - 28. Let k(m) = m**2 - 6*m + 2. Let n be k(c). Factor -2*h**2 + 4*h**2 - 6*h**2 + 2*h**4 + n.
2*(h - 1)**2*(h + 1)**2
Let u(t) = -3*t**4 - 12*t**3 - 9*t**2 + 2*t + 2. Let y(k) = 6*k**4 + 25*k**3 + 19*k**2 - 3*k - 3. Let o(l) = 5*u(l) + 2*y(l). Determine h, given that o(h) = 0.
-2, -1, 2/3
Let y(x) = 10*x**3 + 2*x**2 - 1. Let d be y(1). Factor -3*z**4 + 2 - 2 + d*z**3 - 8*z**3.
-3*z**3*(z - 1)
Suppose 4 = t - 3. Let a(i) be the third derivative of -1/315*i**t - 2*i**2 + 1/36*i**4 + 0 + 1/90*i**5 + 0*i**3 + 0*i - 1/180*i**6. Factor a(c).
-2*c*(c - 1)*(c + 1)**2/3
Let p = -9 + 9. Let y be p/(3*3/(-9)). Determine u so that -2/3*u**3 + y + 2/3*u + 0*u**2 = 0.
-1, 0, 1
Suppose -8*n - 11*n = -5*n. Let y(a) be the first derivative of n*a + 1/4*a**4 + 2*a**2 - 4/3*a**3 - 1. Determine b, given that y(b) = 0.
0, 2
Let z(h) be the first derivative of -1/7*h**2 + 2/35*h**5 + 1 + 1/7*h**4 + 2/7*h - 4/21*h**3 - 1/21*h**6. Determine y so that z(y) = 0.
-1, 1
Let t = 11 - 9. Determine s, given that -2/3*s**t + 4/9 - 2/9*s = 0.
-1, 2/3
Let w(r) = -r**2 + 12*r. Let h be w(12). Let y(x) be the third derivative of h*x + 1/21*x**3 - 2*x**2 + 0 + 1/210*x**5 + 1/42*x**4. Factor y(q).
2*(q + 1)**2/7
Let c(j) be the second derivative of j**9/52920 - j**8/11760 + j**7/8820 - j**4/6 - j. Let o(p) be the third derivative of c(p). Find n, given that o(n) = 0.
0, 1
Suppose 0 = 5*g + 5*y - 30, 2*g + 0*g - 2*y = 24. Suppose 0 = g*o - 7*o - 8. Determine j so that j**2 + 3*j**3 - j - 7*j**3 + 3*j**3 + 2*j**3 - j**o = 0.
-1, 0, 1
Let u(f) be the first derivative of -3*f**4/4 - f**3 + 3*f**2/2 + 3*f - 14. Let u(d) = 0. Calculate d.
-1, 1
Let i be 1 + -8*(-3)/6. Factor 0*y**2 + 4/11*y**3 + 0*y**4 - 2/11*y**i - 2/11*y + 0.
-2*y*(y - 1)**2*(y + 1)**2/11
Let w(g) be the second derivative of -5*g**4/12 + g**3 - g**2/2 - 17*g. What is a in w(a) = 0?
1/5, 1
Let u(l