(n + 1)
Let b(p) be the second derivative of 1/21*p**7 + 1/6*p**4 + 0 + 2/3*p**3 + 3*p - 1/15*p**6 - 3/10*p**5 + 0*p**2. Let b(w) = 0. What is w?
-1, 0, 1, 2
Let x(p) = p**3 - 14*p**2 + 17*p - 9. Let m be x(13). Suppose -m*l**5 - l**3 - l**3 + l + 44*l**5 = 0. Calculate l.
-1, 0, 1
Let s(u) be the first derivative of -1/3*u**3 + 0*u**2 - 1/120*u**6 + 0*u + 0*u**5 + 3 + 1/8*u**4. Let g(m) be the third derivative of s(m). Factor g(l).
-3*(l - 1)*(l + 1)
Factor -2232/11*b**3 - 2028*b**2 - 54/11*b**4 + 15624/11*b - 2646/11.
-6*(b + 21)**2*(3*b - 1)**2/11
Solve -24*d**2 + 39/2*d + 3/2*d**3 + 45 = 0.
-1, 2, 15
Let m(i) be the second derivative of 3*i**5/20 + i**4/6 - 7*i**3/6 + i**2 + 103*i. Factor m(k).
(k - 1)*(k + 2)*(3*k - 1)
Let i = 456/7 + -65. Let u(b) be the first derivative of 8/21*b**3 - 4 + 2/7*b - 2/21*b**6 + 4/7*b**2 - 2/7*b**5 - i*b**4. What is n in u(n) = 0?
-1, -1/2, 1
Let o(y) = y**3 - 19*y**2 + 90*y - 22. Let r be o(11). Suppose r + 3/2*i**3 - 10*i**2 + 1/4*i**5 + 2*i**4 + 25/4*i = 0. What is i?
-5, 0, 1
Let v(h) = 4*h**3 - 16*h**2 - 4*h - 4. Suppose -5*c + 2*g - 11 = 0, g + g = -3*c + 3. Let w(m) = m**4 - m**3 + m + 1. Let x(o) = c*v(o) - 4*w(o). Factor x(l).
-4*l**2*(l - 2)*(l + 2)
Let a(y) be the first derivative of 2*y**6/3 - 24*y**5/5 + 12*y**4 - 32*y**3/3 + 25. Factor a(n).
4*n**2*(n - 2)**3
Solve -345*g + 2*g**5 - 50 - 1034*g**2 - 438*g**3 - 110*g**4 - 11*g**5 + 402*g**2 = 0.
-5, -1, -2/9
Let b(x) be the second derivative of 0 + 5/4*x**2 + 5/12*x**3 - 1/8*x**5 - 5/24*x**4 + 8*x. Let b(p) = 0. What is p?
-1, 1
Factor 3/8*h**3 - 21/8*h**2 + 33/8*h - 15/8.
3*(h - 5)*(h - 1)**2/8
Let k(d) be the first derivative of 6 - d - 22/9*d**3 + 1/9*d**6 - 7/3*d**2 - d**4 + 1/15*d**5. Factor k(w).
(w - 3)*(w + 1)**3*(2*w + 1)/3
Let y(i) be the second derivative of i**4/3 - 14*i**3 - 3*i. Determine c, given that y(c) = 0.
0, 21
Let h(k) = -k**4 + k**2 - k + 1. Let s = 151 - 149. Let f(g) = -6*g**4 - 2*g**3 + 8*g**2. Let w = 0 + -1. Let c(l) = s*h(l) + w*f(l). Factor c(y).
2*(y - 1)*(y + 1)**2*(2*y - 1)
Let s be (-87)/1450*15/(-18). Let l(g) be the second derivative of -7*g + s*g**5 + 0*g**4 + 0*g**2 - 1/15*g**6 + 1/42*g**7 + 0 + 0*g**3. What is y in l(y) = 0?
0, 1
Let s(j) be the first derivative of -j**5/180 - j**4/36 + 9*j**2/2 + 45. Let r(v) be the second derivative of s(v). Solve r(d) = 0.
-2, 0
Solve 170*i - 1402 + 434 + 0*i**3 + 402*i + i**3 - 46*i**2 = 0.
2, 22
Let l(f) be the second derivative of f**4/24 - 2*f**3/9 - f**2/4 + 97*f. Factor l(j).
(j - 3)*(3*j + 1)/6
Determine w so that -8/7*w + 0 + 5/7*w**4 + 2/7*w**3 - 20/7*w**2 = 0.
-2, -2/5, 0, 2
Suppose 5*s - u = s + 66, -5*u = -4*s + 74. Let b be (-5)/135*s*(-3)/2. Suppose -b*h**2 - 2/3*h**4 - 20/9*h**3 + 0 + 16/9*h = 0. What is h?
-2, 0, 2/3
Suppose 3*y = 4*j + 1 - 69, -j + 3*y = -26. Factor -j*c**2 + 7*c**2 + 9*c**2.
2*c**2
Let s = -2081/148 - -548/37. Suppose s*d**2 + 0 - 3/4*d + 3/4*d**3 - 3/4*d**4 = 0. What is d?
-1, 0, 1
Let g(j) be the second derivative of 15/2*j**4 + 9*j + 540*j**2 + 1/4*j**5 + 90*j**3 + 0. What is a in g(a) = 0?
-6
Let t(o) = 7*o**3 - 2*o**2 + o. Let w be t(1). Let f(h) = -h**2 + 4. Let q(k) = -9 + 6*k**2 - 5*k**2 + 3*k - 2*k. Let s(z) = w*q(z) + 14*f(z). Factor s(c).
-2*(c - 1)*(4*c + 1)
Let x(t) = 8*t**5 + 33*t**4 + 25*t**3 + 17*t**2 + 17*t. Let v(o) = o**5 + 4*o**4 + 3*o**3 + 2*o**2 + 2*o. Let f(p) = -51*v(p) + 6*x(p). Factor f(a).
-3*a**3*(a + 1)**2
Suppose -2*u + 21*u = 0. Let v(x) be the second derivative of 8/5*x**5 + 2/21*x**7 + 0*x**3 + 4/3*x**4 + 0*x**2 + u + 8*x + 2/3*x**6. Factor v(o).
4*o**2*(o + 1)*(o + 2)**2
Let p be (-3)/(60/(-215))*24. Let n be (-1 - -2)/2 - p/1204. Solve n*s + 0 + 2/7*s**2 = 0.
-1, 0
Let t(g) be the third derivative of -5*g**5/12 - 35*g**4/24 + 5*g**3 + 47*g**2. Factor t(f).
-5*(f + 2)*(5*f - 3)
Let u be -32 - (-6 - -7)*-6. Let j = u + 28. Factor -2/5*p**3 + 0*p**j + 0 + 8/5*p.
-2*p*(p - 2)*(p + 2)/5
Find d such that -4/3*d + 4/3*d**3 + 2/3*d**4 + 0*d**2 - 2/3 = 0.
-1, 1
Let o(q) be the second derivative of 2*q**7/63 - 8*q**6/45 - 2*q**5/5 + 4*q**4/9 + 10*q**3/9 - 5*q + 4. Determine l so that o(l) = 0.
-1, 0, 1, 5
Let i = 86 + -83. Factor -12 - 25*t + 13*t + 0 - 16*t - 20*t**2 - 4*t**i.
-4*(t + 1)**2*(t + 3)
Let m(r) be the first derivative of -2*r**5/25 - r**4/5 + 8*r**3/5 - 14*r**2/5 + 2*r + 87. Determine i so that m(i) = 0.
-5, 1
Suppose -11*q = -q - 370. Factor 0*z**5 + q*z - 80*z**2 + z**4 + 13*z + 12*z**3 + 15*z**4 + 2*z**5.
2*z*(z - 1)**2*(z + 5)**2
Let f = 47 + -31. Let o be 9/(-6)*f/(-12). Find c, given that -3*c**5 + 14*c**5 - 4*c**o - 12*c**4 - 7*c**5 + 12*c**3 = 0.
0, 1
Let m(c) = 3*c**3 - 8*c**2 + 45*c - 141. Let u be m(3). Factor 2 - 1/2*d**u + 1/2*d - 2*d**2.
-(d - 1)*(d + 1)*(d + 4)/2
Let o = 872/5 - 1739/10. Let d be -2 - 0 - (-5)/2. What is f in o - d*f**2 + 1/2*f - 1/2*f**3 = 0?
-1, 1
Let j(s) be the third derivative of -s**6/24 + 2*s**5/3 + 55*s**4/8 - 347*s**2 - 2. Suppose j(w) = 0. What is w?
-3, 0, 11
Let b(s) = -40*s**2 - 156*s - 1048. Let j(q) = -7*q**2 - 26*q - 175. Let u(y) = 6*b(y) - 34*j(y). Factor u(g).
-2*(g + 13)**2
Suppose -5*v - r + 18 = 14, 2*r - 8 = -3*v. Factor v - d**2 + d**4 + 0*d**3 + 1/2*d - 1/2*d**5.
-d*(d - 1)**3*(d + 1)/2
Let g(x) be the third derivative of -x**5/12 + 105*x**4/4 - 6615*x**3/2 - 594*x**2. Factor g(z).
-5*(z - 63)**2
Suppose 0 = -g + 12 - 52. Let m = g + 42. What is f in 5/2*f - m - 1/2*f**2 = 0?
1, 4
Suppose 7 + 13 = 4*o. Factor -o*v**2 + 0*v**2 + 3*v**2 - 2*v**2.
-4*v**2
Let n(k) = 2*k**2 - 19*k - 9. Let l be n(11). Suppose 5*r = -l + 24. Determine j so that -1/6*j**3 + 1/6*j**2 + r*j + 0 = 0.
0, 1
Let f = -290 + 21461/74. Let n = f - -589/222. Factor -2/3*o**2 - 8/3 + n*o.
-2*(o - 2)**2/3
Let q(v) be the first derivative of -3/8*v**2 + 0*v + 1/4*v**3 - 21. Factor q(s).
3*s*(s - 1)/4
Suppose 2*u = -5*c + 17 + 95, -2*u = -4*c - 76. Find g such that 428*g**2 - 256*g**5 + 100*g + u*g**4 + 8 - 39*g**4 + 656*g**3 + 57*g**4 = 0.
-1, -1/4, 2
Let s(x) = 5*x**5 + 10*x**4 + 60*x**3 + 20*x**2 + 25*x + 15. Let d(u) = u**4 - u**3 + u**2 - u - 1. Let t(w) = 15*d(w) + s(w). Solve t(k) = 0 for k.
-2, -1, 0
Let t = 1/4816 - -24077/14448. Suppose 0 = -2*u + 6*u. Factor -t*n**3 + 2/3*n**2 + 4/3*n**4 - 1/3*n**5 + u + 0*n.
-n**2*(n - 2)*(n - 1)**2/3
Factor -527 + 18*m + 30*m - 3*m**2 + 335 + 0*m**2.
-3*(m - 8)**2
Suppose -3*p = -4*k - 24, 2*p + 4*k + 28 = 6*p. Suppose 2*t + 10 = p*t. Find q such that 0*q**4 - 4*q**t + 4*q**4 + 5*q**3 + 0*q**3 + 3*q**3 = 0.
-1, 0, 2
Find r such that 32 + r**4 + 6*r**3 + r**4 - 16*r**2 + 580*r - 604*r = 0.
-4, -2, 1, 2
Let d(l) be the second derivative of 2*l**6/55 + l**5/110 - l**4/11 - l**3/33 - 3*l - 19. Solve d(x) = 0.
-1, -1/6, 0, 1
Suppose 22 = 2*m - 8*n - 18, m + n = -5. Factor m + 2/3*f**2 + 2/3*f.
2*f*(f + 1)/3
Let a(z) be the first derivative of -2*z**6/3 + z**5 + 19*z**4/4 + 7*z**3/3 - 3*z**2/2 + 76. Let a(h) = 0. Calculate h.
-1, 0, 1/4, 3
Let b(n) be the third derivative of -n**8/43680 + n**7/5460 - n**6/2340 + 2*n**4/3 - 6*n**2. Let v(x) be the second derivative of b(x). Factor v(c).
-2*c*(c - 2)*(c - 1)/13
Factor 3/5*k**4 + 12/5*k**3 + 0 + 6/5*k + 3*k**2.
3*k*(k + 1)**2*(k + 2)/5
Let q = 92 - 83. Solve 11*w**4 - 20*w**2 - 27*w**3 + 42*w**3 + 5*w**5 + q*w**4 - 20*w = 0.
-2, -1, 0, 1
Let u(c) be the second derivative of 5*c**7/42 - 2*c**5 + 5*c**4/2 + 35*c**3/6 - 15*c**2 - 459*c. Find w such that u(w) = 0.
-3, -1, 1, 2
Let o be (1 - 2)*((-147)/14)/7. Let a(h) be the second derivative of -7/3*h**3 - 7*h + 0 - o*h**4 - 2*h**2 - 1/2*h**5 - 1/15*h**6. Solve a(l) = 0.
-2, -1
Let z(t) be the third derivative of 0*t + 0*t**3 + 23*t**2 - 1/280*t**6 + 3/70*t**5 + 0 + 0*t**4. Solve z(m) = 0 for m.
0, 6
Let z = 1445/849 - 10/283. Factor 0 - z*p**2 + 1/3*p**4 + p**3 - 1/3*p**5 + 2/3*p.
-p*(p - 1)**3*(p + 2)/3
Let j be (-3721)/(-1830) + -1 + -1. Let b(u) be the second derivative of -j*u**4 + u - 2/5*u**3 - 9/5*u**2 + 0. Factor b(l).
-2*(l + 3)**2/5
Let r(s) be the third derivative of -s**7/1260 - s**6/72 - 2*s**5/45 + 3*s**2 + 28. Factor r(q).
-q**2*(q + 2)*(q + 8)/6
Suppose -2/11*b**4 + 6/11*b**2 + 0 + 4/11*b + 0*b**3 = 0. What is b?
-1, 0, 2
Suppose 26/9*v - 2/9*v**2 + 28/9 = 0. What is v?
-1, 14
Let s(v) be the third derivative of 25*v**8/39