 2*y. Let f(z) = 0. What is z?
-1/2, -1/4, 0, 1
Let m(j) be the second derivative of 0 - 2/3*j**3 - 3*j - 1/24*j**4 - 4*j**2. What is o in m(o) = 0?
-4
Suppose 128 = 2*p + 16*h, 2*p + 40 = p + 5*h. Suppose -6/13*a + 10/13*a**2 + p - 18/13*a**4 + 8/13*a**5 + 6/13*a**3 = 0. Calculate a.
-3/4, 0, 1
Suppose 0 = -13*v + 45 - 19. Let h(c) be the second derivative of 0 - v*c + 1/3*c**2 - 1/6*c**3 + 1/36*c**4. Factor h(j).
(j - 2)*(j - 1)/3
Find q, given that q**5 + 6*q**4 + 4*q + 8*q**2 - q**5 - 14*q**4 - 4*q**5 = 0.
-1, 0, 1
Let r = 2 - -2. Suppose 2*z + 33 = 3*p, r*p - 67 = 3*z - 8*z. Factor -13 + p + 3*q**2.
3*q**2
Let s = -1329/5 - -266. Let z(i) be the second derivative of 9/80*i**5 + 0*i**2 + 0*i**3 - s*i**6 - 1/48*i**4 + 0 + i + 2/21*i**7. Factor z(a).
a**2*(a - 1)*(4*a - 1)**2/4
Let b be 8/5*(-15)/(-6). Factor 2*q**3 - 2*q**4 - 5*q**3 - 9*q**b - q**4.
-3*q**3*(4*q + 1)
Let s(f) be the second derivative of f**5/90 + f**4/27 + f**3/27 - f - 20. Factor s(m).
2*m*(m + 1)**2/9
Let m(j) be the second derivative of -j**7/17640 - j**6/1680 - j**5/420 + j**4 - 17*j. Let r(g) be the third derivative of m(g). Let r(i) = 0. What is i?
-2, -1
Let j(o) be the third derivative of 0*o - 4/21*o**3 + 1/420*o**6 - 1/35*o**5 + 25*o**2 + 0 + 3/28*o**4. Suppose j(k) = 0. Calculate k.
1, 4
Let k(i) be the first derivative of 2/15*i**3 - 1/150*i**6 - 1/10*i**4 + 1 + 1/25*i**5 - 3*i - 1/10*i**2. Let a(f) be the first derivative of k(f). Factor a(n).
-(n - 1)**4/5
Let r(n) = 20*n + 66. Let j be r(-3). Let g = -4 - -5. Determine x, given that -12*x - 3 - j*x**2 - 2*x**2 - g = 0.
-1, -1/2
Let i(s) be the second derivative of -s**6/180 + s**5/90 + s**4/18 + 4*s**2 - 11*s. Let q(y) be the first derivative of i(y). Factor q(z).
-2*z*(z - 2)*(z + 1)/3
Factor 9/2*m**3 + 0 + 0*m**2 - 6*m**4 + 0*m + 3/2*m**5.
3*m**3*(m - 3)*(m - 1)/2
Let x(t) be the third derivative of 5*t**8/448 - 5*t**7/84 + t**6/8 - t**5/8 + 5*t**4/96 + 14*t**2. Suppose x(y) = 0. What is y?
0, 1/3, 1
Let n(u) = u + 11. Let z be n(-7). Suppose -s = -z*s + 33. Factor -g**2 - 3*g**2 + 17*g + s*g - 16 - 12*g.
-4*(g - 2)**2
Suppose 3*g - g - 4 = 0. Factor 180*k**3 - 6*k**4 + 2*k**4 - 16*k**g - 164*k**3.
-4*k**2*(k - 2)**2
Suppose h - 2*c = -7*c - 10, 5*h - 3*c = 6. Let m(x) be the second derivative of h + 1/2*x**2 + 1/6*x**3 - 1/20*x**5 - 1/12*x**4 - 5*x. Factor m(i).
-(i - 1)*(i + 1)**2
Let t = 48 - 77. Let n = 32 + t. Determine s so that 78*s - n*s**2 + 87*s - 162*s = 0.
0, 1
Let o be (-182)/(-6) - 2/(-6). Let t = 211/6 - o. Factor 3 + 3*y**2 + 21/2*y - t*y**3.
-3*(y - 2)*(y + 1)*(3*y + 1)/2
Suppose 3*v - 4*v = -6. Let s(k) = -5*k + 37. Let j be s(7). Determine n, given that 3*n**j + v*n**3 - 3*n**4 + 3*n**5 - 13*n**3 + 4*n**3 = 0.
-1, 0, 1
Let f(w) be the second derivative of -15*w - 1/48*w**4 - 1/12*w**3 + 0*w**2 + 0. What is v in f(v) = 0?
-2, 0
Let a(y) = -3*y**2 + 25*y - 27. Let m(d) = d**2 - 12*d - 1. Let t be m(6). Let h = -16 - t. Let u(j) = -j**2 + 8*j - 9. Let g(k) = h*u(k) - 6*a(k). Factor g(o).
-3*(o - 3)**2
Let 27/2*y**2 + 27 - 249/2*y = 0. Calculate y.
2/9, 9
Let a(s) = s**2 + 6*s + 11. Let u be a(-3). Let l be (4 + -8)/((-4)/2). Factor 5*p**2 - 11*p**l + 8*p**u.
2*p**2
Let k = -23300 - -1514444/65. Let s = -2/455 - k. Find t such that 0*t + s*t**2 - 3*t**3 + 0 + 9/7*t**4 = 0.
0, 1/3, 2
Solve -48/7*n + 0 + 1/7*n**2 = 0.
0, 48
Let z(p) be the second derivative of -7*p**6/80 - 33*p**5/80 - 23*p**4/32 - p**3/2 - 8*p + 10. Let z(i) = 0. Calculate i.
-8/7, -1, 0
Solve 46/15*w + 4/5 + 14/15*w**2 = 0.
-3, -2/7
Let x(q) = -14*q - 36. Let l be x(-20). Find y such that -4*y**2 + 12*y**2 - 81*y**5 - 84*y**3 + l*y**4 - 87*y**5 = 0.
0, 1/6, 2/7, 1
Let v be (-2)/(-14)*(39 + -25). Let a(c) be the second derivative of -1/6*c**4 + 1/6*c**3 + 4*c + c**v - 1/20*c**5 + 0. Let a(f) = 0. What is f?
-2, -1, 1
Let o(d) be the first derivative of 3/2*d**4 - 10 + 3/5*d**5 - 3*d - 3*d**2 + 0*d**3. Find q, given that o(q) = 0.
-1, 1
Let l(w) be the third derivative of 5/2016*w**8 - 1/126*w**7 - 1/48*w**6 + 0*w**3 + 0 + 5/36*w**4 + 1/18*w**5 - 41*w**2 + 0*w. What is b in l(b) = 0?
-1, 0, 2
Let r(n) be the first derivative of n**3/5 + 174*n**2/5 + 10092*n/5 + 154. Suppose r(t) = 0. Calculate t.
-58
Let a = -16 + 19. Suppose 0 = a*k - 7 - 23. Factor -8*j**4 + 5*j**3 + 3*j**4 + k*j**3 - 20*j.
-5*j*(j - 2)**2*(j + 1)
Let y(a) be the first derivative of a**7/252 + a**6/72 + a**5/72 - 7*a**2/2 + 5*a - 8. Let p(s) be the second derivative of y(s). Factor p(d).
5*d**2*(d + 1)**2/6
Let -1756 + 11*n + 4*n**5 + 16*n - 12*n**4 - 8*n**2 + 9*n - 40*n**3 + 1776 = 0. Calculate n.
-1, 1, 5
Let d(q) be the third derivative of q**4/2 + 10*q**2. Let k(a) = -a**2 - a. Let s(t) = d(t) + 3*k(t). Solve s(b) = 0 for b.
0, 3
Let w(g) be the first derivative of 484*g**3/21 + 352*g**2 + 1792*g - 22. Suppose w(i) = 0. What is i?
-56/11
Let k(i) be the second derivative of i**7/105 - i**6/20 + i**5/10 - i**4/12 - 5*i**2/2 + 12*i. Let a(h) be the first derivative of k(h). What is u in a(u) = 0?
0, 1
Let u = 0 - -3. Find x, given that 6*x**4 - 5*x + 3*x**2 + 4*x**3 - 8*x**4 - 3*x**u + 2 + x**4 = 0.
-2, 1
Let -4350*w + 1380 - w**2 - 6280 + 4490*w = 0. What is w?
70
Let g(q) be the second derivative of q**5/40 + q**4/8 + 333*q. Factor g(x).
x**2*(x + 3)/2
Factor 2/3*w**2 - 4*w + 0.
2*w*(w - 6)/3
Let j(f) be the second derivative of 1/2*f**3 + 0 - 1/10*f**6 + 0*f**2 - 2*f + 9/20*f**5 - 3/4*f**4. Factor j(o).
-3*o*(o - 1)**3
Let f be -1*(-7 + (2142/35)/9). Let b(u) be the first derivative of 1/15*u**3 - 3/5*u + f*u**2 + 2. Solve b(o) = 0 for o.
-3, 1
Suppose -3*p + 1 = -11. Let y(k) = 15*k + 737. Let s be y(-49). Factor -1/3*i**p - 2/3*i + 0*i**s + 1/3 + 2/3*i**3.
-(i - 1)**3*(i + 1)/3
Let u(c) be the second derivative of -5/9*c**3 + 0 + 23*c - 1/18*c**4 - c**2 + 1/30*c**5. Factor u(f).
2*(f - 3)*(f + 1)**2/3
Let p = 6 - -4. Suppose -2*f - 2 + p = 0. Factor -9*r - 5*r**3 + 12*r**2 + f + 0 - 2.
-(r - 1)**2*(5*r - 2)
Let l(o) be the second derivative of 1/30*o**3 + 6/5*o**2 + 9 + o - 1/60*o**4. Factor l(y).
-(y - 4)*(y + 3)/5
Let v(r) be the second derivative of -3*r**5/50 + 11*r**4/20 - 13*r**3/10 + 6*r**2/5 - 2*r + 11. Factor v(u).
-3*(u - 4)*(u - 1)*(2*u - 1)/5
Let t(w) be the third derivative of -w**5/180 + 3*w**4/8 - 13*w**3/9 - 129*w**2. Determine l so that t(l) = 0.
1, 26
Let y(g) be the second derivative of 5*g**4/12 + 215*g**3/2 + 320*g**2 + 3*g - 1. Suppose y(u) = 0. Calculate u.
-128, -1
Solve 24*c**2 + 310*c**3 - 370*c**3 + 4*c**4 + 21*c**2 - 29*c**4 = 0.
-3, 0, 3/5
Factor -784/3 + 112/3*c - 4/3*c**2.
-4*(c - 14)**2/3
Let t(z) = -14*z**2 + 17*z - 12. Suppose 0 = -2*x - 3*u - 49, 4*x + 9 = 2*u - 49. Let d(m) = 5*m**2 - 6*m + 4. Let s(l) = x*d(l) - 6*t(l). Factor s(f).
-(f - 2)*(f + 2)
Solve 96 + 928/5*g + 14/5*g**4 + 656/5*g**2 - 2/5*g**5 + 192/5*g**3 = 0.
-2, 15
Let m be (-5 - -3) + (1116/8)/9. Let f = 16 - 12. Factor -m*k**2 + 27*k + 3*k**3 - 1/4*k**f - 81/4.
-(k - 3)**4/4
Let o = -82 + 84. Factor 0 + 4/7*y**o - 4/7*y.
4*y*(y - 1)/7
Find d such that -16/11*d - 6/11*d**5 + 0 - 24/11*d**2 + 14/11*d**4 + 12/11*d**3 = 0.
-1, -2/3, 0, 2
Let d(n) be the third derivative of n**9/7560 - n**7/630 + n**5/60 + n**4/3 + 10*n**2. Let o(z) be the second derivative of d(z). Factor o(k).
2*(k - 1)**2*(k + 1)**2
Let y(i) be the second derivative of -i**6/45 + 11*i**5/30 - 35*i**4/18 + 25*i**3/9 + 3*i - 38. Factor y(c).
-2*c*(c - 5)**2*(c - 1)/3
Determine p, given that -2*p + 2*p**3 - 23/5*p**2 - 1/5*p**4 + 24/5 = 0.
-1, 1, 4, 6
Let 4*p**4 - 25804*p + 3*p**2 + 25800*p + 4*p**3 - 7*p**2 = 0. What is p?
-1, 0, 1
Let p(s) = 1 - 14*s + 2 + 13*s - 4. Let v(m) = m**2 - 11*m - 21. Let i(a) = 20*p(a) - 4*v(a). Factor i(g).
-4*(g - 8)*(g + 2)
Let k(c) be the second derivative of c**4/54 - 11*c**3/3 + 4*c - 54. Suppose k(s) = 0. What is s?
0, 99
Let l = 563/1100 - 72/275. Determine f, given that -l*f**4 + 1/4*f**2 + 1/4*f**3 + 0 - 1/4*f**5 + 0*f = 0.
-1, 0, 1
Let c(j) be the second derivative of 0 - 1/8*j**4 - 11*j + 0*j**3 + 0*j**2 + 3/40*j**5. Suppose c(g) = 0. What is g?
0, 1
Let v = -28423/2 - -14214. Let y be (4/1)/(0 - -2). What is t in y*t - v*t**2 - t**3 + 3/2 = 0?
-3, -1/2, 1
Suppose -9/4*h + 9/4 - 1/4*h**2 + 1/4*h**3 = 0. Calculate h.
-3, 1, 3
Factor -7 - 4 + w*