 -r*y + 1/2*y**2 - 1 = 0.
-1, 2
Let s(h) be the first derivative of h**6/6 + h**5/5 - 5*h**4/4 - h**3/3 + 4*h**2 - 4*h - 1. What is t in s(t) = 0?
-2, 1
Let j(l) = l + 11. Let a be j(0). Let r = a + -8. Suppose 10*u - 12*u + u**r + u**2 + 0*u**2 = 0. What is u?
-2, 0, 1
Let m(q) be the third derivative of 0*q**5 + 0*q**4 + 1/280*q**7 + 0 + 2*q**2 + 0*q**3 - 1/240*q**6 + 5/1344*q**8 + 0*q. Suppose m(k) = 0. Calculate k.
-1, 0, 2/5
Suppose 5 = -2*r - q - 2*q, 2*r = -5*q - 15. Suppose -5*j = r - 25. Suppose -k**j + k**3 - k**3 + k**2 + k**5 - k**3 = 0. What is k?
-1, 0, 1
Let j(f) be the third derivative of -f**7/2520 + f**6/1080 - 3*f**4/8 + f**2. Let t(k) be the second derivative of j(k). Factor t(m).
-m*(3*m - 2)/3
Let y(a) be the second derivative of -a**7/525 - a**6/75 - a**5/30 - a**4/30 + 9*a**2/2 + 8*a. Let x(h) be the first derivative of y(h). Factor x(z).
-2*z*(z + 1)**2*(z + 2)/5
Let n(z) be the second derivative of -z**4/90 - 2*z**3/45 + z**2/5 - 11*z. Factor n(d).
-2*(d - 1)*(d + 3)/15
Let j(d) = 10*d**2 + d - 1. Suppose -2*k + 0 = -2. Let v be j(k). What is o in 10*o**2 - v*o**2 - 2*o + 2*o**3 = 0?
-1, 0, 1
Let i(y) be the second derivative of 3/10*y**2 + 0 - 4*y + 1/20*y**4 + 1/5*y**3. Factor i(a).
3*(a + 1)**2/5
Suppose -2*l + n + 94 - 1 = 0, 3 = -n. Let t be (-1 - -4) + (-126)/l. Factor -2/5*a - t - 1/5*a**2.
-(a + 1)**2/5
Suppose 220 = 6*s - 2*s. Factor -2*y**2 + 2*y**3 + 8*y**3 + s*y - 6*y**4 - 57*y.
-2*y*(y - 1)**2*(3*y + 1)
Let i(w) be the first derivative of 2*w**3/39 - 3*w**2/13 + 4*w/13 - 6. Factor i(s).
2*(s - 2)*(s - 1)/13
Let q(d) = -7*d**2 + 2*d. Let w(j) = -j**2 + 8*j - 8. Let f be w(6). Let a = -20 - -15. Let k(x) = -6*x**2 + 2*x. Let s(c) = a*k(c) + f*q(c). Factor s(y).
2*y*(y - 1)
Suppose z - 4 = 2*z. Let y be (z/(-12)*0)/2. Solve y*d**2 + 4/3*d**3 + 0*d**4 + 0 - 2/3*d - 2/3*d**5 = 0 for d.
-1, 0, 1
Let f be 1/8*-2 - (-28)/80. Let s(c) be the second derivative of -3*c - 1/3*c**3 + f*c**5 - 1/6*c**4 + 0 + c**2. Factor s(i).
2*(i - 1)**2*(i + 1)
Let y be (464/(-15))/(12/(-70)). Let w = y - 180. Find b, given that -2/9 - w*b + 4/9*b**3 + 0*b**2 + 2/9*b**4 = 0.
-1, 1
Solve -1/3*o**2 + 1/6*o**5 - 1/6*o + 1/3*o**4 + 0*o**3 + 0 = 0 for o.
-1, 0, 1
Suppose -2*x - 30 = -2*z, 0*z = 2*z - 10. Let m be ((-12)/x)/((-6)/(-20)). Suppose -m*h**2 - 2*h**2 + 4*h**2 = 0. Calculate h.
0
Let c(n) = n**2 + 3*n. Suppose 0 = -3*z, 0*x + 2*x - 2*z + 8 = 0. Let g be c(x). Find d, given that d**2 - g*d + d**2 + 6*d = 0.
-1, 0
Let o(v) be the third derivative of -v**9/15120 + v**8/3360 - v**6/360 + v**5/120 + v**4/8 - 2*v**2. Let r(b) be the second derivative of o(b). Factor r(y).
-(y - 1)**3*(y + 1)
Let c(p) be the second derivative of -p**5/4 + 5*p**4/4 - 5*p**3/3 + 35*p. Factor c(y).
-5*y*(y - 2)*(y - 1)
Let g(i) be the first derivative of -7*i**4/6 - i**3/18 + i**2/6 + 11. Factor g(u).
-u*(4*u - 1)*(7*u + 2)/6
Let s(j) be the third derivative of 0*j**3 - 7*j**2 + 1/36*j**4 + 0*j + 1/36*j**5 + 1/630*j**7 + 0 + 1/90*j**6. Let s(i) = 0. Calculate i.
-2, -1, 0
Let v(d) be the second derivative of 9*d**7/70 + 2*d**6/5 + d**5/4 - d**4/4 - d**2/2 + 2*d. Let g(f) be the first derivative of v(f). Factor g(m).
3*m*(m + 1)**2*(9*m - 2)
Let n = 4 + -1. Suppose 0 = -n*d + p + 5, 0 = p - 1 - 0. Find j, given that 2/9*j**4 + 0*j + 0 + 0*j**d - 2/9*j**3 = 0.
0, 1
Let y(g) be the third derivative of -1/8*g**4 - 3/40*g**5 - 1/8*g**3 - 3*g**2 - 1/40*g**6 + 0*g + 0 - 1/280*g**7. Factor y(b).
-3*(b + 1)**4/4
Let i be (-1)/(-4) - 3/(-12). Let h = 417 - 415. Determine x so that -3/4*x - 1/4*x**h - i = 0.
-2, -1
What is b in 0 - 1/3*b**2 + b = 0?
0, 3
Suppose -5*b + 7 = -28. Find d such that -2*d + 2*d**2 - 2*d**3 + d**2 - b*d**2 = 0.
-1, 0
Let z(s) = 2*s**2 - 4*s - s**2 + 0*s**2 - 5 - 2. Let i be z(6). Let 0 - 1/4*r**4 + 1/4*r**2 + 0*r + 1/4*r**i - 1/4*r**3 = 0. What is r?
-1, 0, 1
Determine k so that -44 + 2*k**5 + 2*k**4 + 44 - 4*k - 6*k**3 - 10*k**2 = 0.
-1, 0, 2
Suppose -j**5 - 8*j**2 + 54*j**2 - 3*j**5 - 32 + 6*j**5 + 14*j**3 - 16*j - 14*j**4 = 0. Calculate j.
-1, 1, 4
Let y(s) be the first derivative of -2*s**6/3 + 8*s**5/5 - 8*s**3/3 + 2*s**2 + 15. Factor y(o).
-4*o*(o - 1)**3*(o + 1)
Let y = 49 - 881/18. Let x(h) be the second derivative of 0 + y*h**4 - 2/9*h**3 + 1/3*h**2 - h. Factor x(s).
2*(s - 1)**2/3
Let t be ((-1)/35)/((-8)/56). Factor -4/5*l - t*l**2 - 4/5.
-(l + 2)**2/5
Let w(r) be the second derivative of 6*r**6/5 + 33*r**5/5 + 19*r**4/3 + 2*r**3 + 36*r. Factor w(y).
4*y*(y + 3)*(3*y + 1)**2
Suppose 9 = -3*a + 6*a. Determine j so that j - a*j + j - j**2 = 0.
-1, 0
Let d be ((-692)/(-8))/((-2)/(-8)). Let g = d + -1022/3. Find w such that 38/3*w**3 + 50/3*w**5 + 8/3 + 110/3*w**4 - g*w - 46/3*w**2 = 0.
-1, 2/5
Let c(v) be the third derivative of -v**5/540 + v**3/54 - 26*v**2. Determine l so that c(l) = 0.
-1, 1
Let p(l) be the second derivative of l**4/6 - 4*l**3/3 + 4*l**2 - 2*l. Factor p(t).
2*(t - 2)**2
Let p = 1831 - 9187/5. Let j = -6 - p. Factor j*s**4 - 4/5*s**2 + 0*s**3 + 2/5 + 0*s.
2*(s - 1)**2*(s + 1)**2/5
Suppose -1 = 3*k - 7. Let v(f) be the first derivative of -1/9*f**3 - 1/3*f + 1/3*f**2 + k. Factor v(x).
-(x - 1)**2/3
Let d(c) be the second derivative of -c**6/30 + c**4/12 + 27*c. Factor d(u).
-u**2*(u - 1)*(u + 1)
Let p(v) be the second derivative of -35/12*v**4 + 6*v - 4*v**3 - 3/5*v**5 - 2*v**2 + 0. Suppose p(u) = 0. What is u?
-2, -2/3, -1/4
Suppose -3*y + 27 = -0*y. Suppose -4*t + 15 = 3*n + 2*n, 2*t - y = -3*n. Let -4*u + 2*u**3 + 4*u - n*u**2 + 5*u**2 = 0. Calculate u.
-1, 0
Suppose 5 = t - 5. Factor 4 - t*i - 5*i**3 + 14*i + i**3 - 4*i**2.
-4*(i - 1)*(i + 1)**2
Let a(x) be the second derivative of x**7/56 + x**6/120 - x**5/16 - x**4/48 + x**3/12 - 17*x. What is r in a(r) = 0?
-1, 0, 2/3, 1
Let c(u) be the third derivative of 7*u**5/40 + 23*u**4/16 + 3*u**3/2 + 3*u**2 + 9*u. Find i, given that c(i) = 0.
-3, -2/7
What is s in -1/2*s**2 + 0*s - 1/2*s**4 + 0 + s**3 = 0?
0, 1
Let p(r) be the second derivative of -2*r + 0*r**2 + 0 + 0*r**3 - 1/10*r**5 - 1/21*r**4 - 1/21*r**6. Factor p(z).
-2*z**2*(z + 1)*(5*z + 2)/7
Suppose 5*n = 14 + 11. Factor 7*r**5 + 19*r**2 - 7*r**4 + 5*r**5 - 3*r**n + 2*r - 11*r**3 - 12*r**2.
r*(r - 1)**2*(r + 1)*(9*r + 2)
Let q(d) be the second derivative of d**5/60 - d**3/6 + d**2/2 - 3*d. Let h(j) be the first derivative of q(j). Suppose h(l) = 0. Calculate l.
-1, 1
Suppose -4*g = -5 - 7. Suppose -3 = -3*v - 3*t + 3, -g*t - 6 = -3*v. Determine b so that 3*b - 3/4 + 3/4*b**v - 3*b**3 = 0.
-1, 1/4, 1
Let p be 0 + 0 + 1 - -3. Factor -3*i**3 + i**2 + 2 + p*i**4 - i**4 - 2 - i**5.
-i**2*(i - 1)**3
Let w = 575/4 + -143. Find v such that 3/4*v**2 - 3/4*v**4 + 3/4*v**5 - w*v**3 + 0 + 0*v = 0.
-1, 0, 1
Factor 2/13*r**2 + 0 + 0*r.
2*r**2/13
Let p = 5/22 + 3/11. Let k be 2/(12 + -6 - 5). Let -1/2*v**k + 7/4*v - 7/4*v**3 + p = 0. What is v?
-1, -2/7, 1
Let x(p) = -p. Let k(n) = -n**3 + 11*n**2 - 29*n - 36. Let s(q) = -2*k(q) + 10*x(q). Determine o so that s(o) = 0.
-1, 6
Let l(j) = -4*j + 4. Let p be l(1). Let a(f) be the first derivative of -1/3*f**6 - 1 - 2/3*f**3 + 2/5*f**5 + 1/2*f**4 + p*f**2 + 0*f. Factor a(k).
-2*k**2*(k - 1)**2*(k + 1)
Suppose -8 = -2*f - 2. Suppose t - 2*g + f = -5, -3*t - 3*g = -21. Factor -6 + r**t + 6 + r.
r*(r + 1)
Let i(r) = -r**3 + 9*r**2 + r - 5. Let y be i(9). Let n be (y - 5)*1/(-2). Find c, given that -1/2 - n*c**2 - c = 0.
-1
Find i such that 3 - 3*i**2 + 3*i**3 - 5*i + 2*i + i - i = 0.
-1, 1
Let a = 2/147 - -29/1470. Let c(g) be the second derivative of 1/135*g**6 + g - 1/27*g**3 - a*g**5 + 0*g**2 + 1/18*g**4 + 0. Factor c(t).
2*t*(t - 1)**3/9
Find w such that -2/3*w + 0 + 2/3*w**2 = 0.
0, 1
Let v(o) = -o**3 - 10*o**2 - o - 5. Let p be v(-10). Find d such that d**4 + d - p*d**3 + 4*d**4 + d**2 + 0*d**2 - 2*d**4 = 0.
-1/3, 0, 1
Determine r so that -2/21*r**4 + 8/21*r**2 - 4/21*r**3 + 0 + 16/21*r = 0.
-2, 0, 2
Factor -12*g - 21/5*g**3 - 3/5*g**4 - 54/5*g**2 - 24/5.
-3*(g + 1)*(g + 2)**3/5
Let i(u) be the second derivative of u**6/15 - u**5/20 - u**4/6 + u**3/6 - 19*u. Determine a so that i(a) = 0.
-1, 0, 1/2, 1
Let z be (-3 - -1) + 11/4. Let 3/2 + 3*s**2 + z*s**3 + 15/4*s = 0. What is s?
-2, -1
Let q(g) = -g. Let d(v) = 4*v**2 + 2*v. Let n(r) = d(r) + 6*q(r). Suppose n(h) = 0. 