- 6 - 9*n + 5*n**3.
3*(n - 2)*(n + 1)**2
Factor 100*b**2 + 28*b**3 + 0*b**2 - 8*b**3 + b**4.
b**2*(b + 10)**2
Suppose 9*h = 3*h + 24. Let z(s) be the second derivative of 0 - 1/15*s**6 + 0*s**2 + 2*s - 1/6*s**h + 3/20*s**5 + 1/12*s**3 + 1/84*s**7. Factor z(j).
j*(j - 1)**4/2
Suppose -6 = 5*z - 56. Let r = -10 + z. Suppose r + 2/3*l**2 + 1/3*l**3 - l = 0. What is l?
-3, 0, 1
Let u(v) be the third derivative of -1/390*v**5 + 0 + 0*v**3 + 33*v**2 + 1/39*v**4 + 0*v. Factor u(t).
-2*t*(t - 4)/13
Let n(w) = -6*w**4 + 76*w**3 - 206*w**2 - 16*w. Let v(p) = -4*p**4 + 51*p**3 - 137*p**2 - 10*p. Let f(m) = 5*n(m) - 8*v(m). Determine q, given that f(q) = 0.
0, 3, 11
Let d be -2 + 1 + 3 + 10. Suppose w + d = 5*w. Solve 12*x**4 - 15*x**2 + 6*x - 3*x**4 + 2 - 3*x**w - 3*x + 4 = 0.
-1, -2/3, 1
Suppose 4*a - 6 = 14. Suppose 8*l + a*g = 4*l + 15, -2*l - 2*g = -8. Solve 2/5*u**3 + 7/5*u - 8/5*u**2 - 1/5*u**l + 2/5*u**4 - 2/5 = 0.
-2, 1
Let x(f) be the third derivative of 0*f**4 + 0*f + 0*f**3 + 6*f**2 + 1/140*f**5 + 0. What is v in x(v) = 0?
0
Let n(a) = a**2 - 5*a + 2. Let m be n(5). Let l(g) = 9*g**4 - 29*g**3 + 29*g**2 + g. Let o(c) = c**2 + c. Let w(z) = m*l(z) - 10*o(z). Factor w(v).
2*v*(v - 2)*(v - 1)*(9*v - 2)
Let a(x) be the third derivative of -2*x**7/35 + 2*x**6/9 + x**5/9 - 10*x**4/9 + 8*x**3/9 + 2*x**2. What is r in a(r) = 0?
-1, 2/9, 1, 2
Let k(c) be the first derivative of -16*c**3/15 - 104*c**2/5 - 676*c/5 + 81. Factor k(l).
-4*(2*l + 13)**2/5
Suppose 0 = -m - 10*m + 33. Let p(n) be the third derivative of 0*n**m + 0 + 1/2*n**4 + 3*n**2 + 1/15*n**5 + 0*n. Factor p(x).
4*x*(x + 3)
Let q(k) be the second derivative of -5/21*k**3 + 10*k + 4/7*k**2 + 0 + 1/42*k**4. Factor q(z).
2*(z - 4)*(z - 1)/7
Let d(b) be the third derivative of b**5/60 - 47*b**4/24 + 23*b**3/3 - 295*b**2. Let d(k) = 0. Calculate k.
1, 46
Let d(z) be the third derivative of -3/100*z**6 + 0*z + 0 + 11*z**2 - 1/90*z**4 + 0*z**3 - 23/1575*z**7 - 1/360*z**8 - 13/450*z**5. Factor d(p).
-2*p*(p + 1)**3*(7*p + 2)/15
Let b = 5434/174285 + -2/1291. Let m(q) be the second derivative of 0*q**2 - 4/45*q**5 - b*q**6 - 1/27*q**3 - 5/54*q**4 + 0 - 4*q. Factor m(k).
-2*k*(k + 1)*(2*k + 1)**2/9
Let d(a) be the third derivative of 1/5*a**3 + 0 - 13*a**2 - 1/120*a**4 - 1/300*a**5 + 0*a. Find u such that d(u) = 0.
-3, 2
Factor -12/11*z**4 + 0*z**2 - 2/11*z**5 - 16/11*z**3 + 0*z + 0.
-2*z**3*(z + 2)*(z + 4)/11
Let z(k) be the first derivative of k**6/27 - 4*k**5/45 - 2*k**4/9 + 4*k**3/27 + k**2/3 + 125. Let z(f) = 0. What is f?
-1, 0, 1, 3
Let k be (-333)/27 - (-1)/3. Let z(i) = -22*i**4 - 26*i**3 + 28*i**2 - 4*i. Let v(b) = -b**4 - b**3 + b**2 - b. Let t(w) = k*v(w) + z(w). Factor t(g).
-2*g*(g - 1)*(g + 2)*(5*g + 2)
Let s = -2/319 + 652/2233. Factor -2/7*b**2 + s + 0*b.
-2*(b - 1)*(b + 1)/7
Let u(c) = -239*c + 242. Let y be u(1). Find w such that 1/4*w + 3/8*w**2 + 1/8*w**y + 0 = 0.
-2, -1, 0
Let c be (10/(-25))/((-93)/165). Let j = c - 79/155. Factor 3/5*k - 3/5*k**3 - j*k**4 - 1/5*k**2 + 2/5.
-(k - 1)*(k + 1)**2*(k + 2)/5
Let p(r) = -23*r + 12*r**2 + 11*r - 44 - 18*r + 14*r**3. Let w(t) = -9*t**3 - 8*t**2 + 20*t + 29. Let u(z) = 5*p(z) + 8*w(z). Factor u(l).
-2*(l - 2)*(l + 1)*(l + 3)
Let i(l) = 2 + 11*l**2 + 5 + 21*l + 1 + 2*l**2. Let q(g) = -6*g**2 - 10*g - 4. Let t(b) = 2*i(b) + 5*q(b). Factor t(c).
-4*(c + 1)**2
Let p(f) be the third derivative of -f**5/15 - 7*f**4/6 + 16*f**3/3 - 3*f**2 + 9. Factor p(n).
-4*(n - 1)*(n + 8)
Let v(o) be the third derivative of o**8/1512 - 2*o**7/315 - o**6/54 + 8*o**5/135 + 11*o**4/36 + 14*o**3/27 - o**2 - 26*o. Factor v(h).
2*(h - 7)*(h - 2)*(h + 1)**3/9
Let m(n) = n**2 + 9. Let c be m(4). What is v in -28*v + 2*v**2 + c*v + v**2 = 0?
0, 1
What is w in -558*w - 405*w**2 - 3*w**5 - 549*w + 1107*w - 297*w**3 - 63*w**4 = 0?
-15, -3, 0
Suppose 4*r - 54 = -14*r. Let i(d) be the first derivative of 0*d**2 - 4 + 0*d + 2/27*d**r + 0*d**4 - 2/45*d**5. Solve i(p) = 0 for p.
-1, 0, 1
Let q(m) be the first derivative of -25*m**4/2 + 60*m**3 + 39*m**2 + 8*m + 15. Suppose q(o) = 0. What is o?
-1/5, 4
Suppose 6*t - 12*t + 9 = -15. What is m in 16/3*m**2 - 8/3*m - 4/3*m**t + 8/3*m**3 - 4 = 0?
-1, 1, 3
Let g(i) be the third derivative of 0*i**3 - 1/270*i**6 + 1/1512*i**8 + 16*i**2 + 0*i**7 + 0*i**5 + 1/108*i**4 + 0*i + 0. Find f, given that g(f) = 0.
-1, 0, 1
Suppose 2*u - 2*y - 2*y = 18, -4*u + y + 8 = 0. Let t be (1/(-2)*-13 - 4)/u. Factor -1/2*p**4 - 2*p**3 + 0 - p - t*p**2.
-p*(p + 1)**2*(p + 2)/2
Let -12/7*p + 0*p**2 - 3/7*p**4 + 9/7*p**3 + 0 = 0. Calculate p.
-1, 0, 2
Let k = 12 + -10. Factor 2/3*j**k + 2/3*j + 0.
2*j*(j + 1)/3
Let h(l) = -l**3 - 3*l**2 + 18*l + 22. Let x(w) = -5*w**2 + 35*w + 45. Let u(b) = 5*h(b) - 2*x(b). Suppose u(p) = 0. What is p?
-2, -1, 2
Let j(z) = 5*z**2 + 14*z - 15. Let n(x) = x - 16*x - 37 - 5*x**2 + 52. Let d(r) = 5*j(r) + 4*n(r). Factor d(p).
5*(p - 1)*(p + 3)
Let c = 38 - 35. Factor -4*m**4 - 4*m**4 - 28*m**3 - 6*m**2 + 5*m**4 + 37*m**c.
-3*m**2*(m - 2)*(m - 1)
Let y(s) be the third derivative of -s**6/30 + 3*s**5/5 - s**4 - 32*s**3/3 + s**2 + 58*s. Suppose y(p) = 0. Calculate p.
-1, 2, 8
Suppose -20*m = -12*m - 16. Solve -82*o**m - 196 - 47 + 79*o**2 - 54*o = 0.
-9
Let n(j) be the second derivative of j**7/720 + j**6/120 - j**5/60 + j**4/2 + 8*j. Let s(o) be the third derivative of n(o). Find i such that s(i) = 0.
-2, 2/7
Let s(h) be the first derivative of h**4/4 - 10*h**3/3 - 64*h**2 - 288*h - 189. Let s(u) = 0. Calculate u.
-4, 18
Let k(r) = -5*r**4 + 2*r**3 + 3*r**2 + 7*r. Let a(v) = -5*v**4 + v**3 + 4*v**2 + 6*v. Let t(n) = 7*a(n) - 6*k(n). Factor t(g).
-5*g**2*(g - 1)*(g + 2)
Let g be (-13 + (2 - -1))/(-2). Suppose -103 + 98 + g*w**2 - 2*w + 2*w = 0. What is w?
-1, 1
Let i = -34 - -38. Determine b, given that -4*b + b**4 - 11*b**i + 3*b**3 + 30*b**2 + 40 + 104*b - 28*b**3 = 0.
-2, -1/2, 2
Let v(j) = j**3 + 10*j**2 + 85*j + 1311. Let k be v(-12). Let 8*o**4 - 20/3*o**2 - 40/3*o**k + 6*o**5 - 4/3 + 22/3*o = 0. What is o?
-2, -1, 1/3, 1
Let b(v) be the first derivative of 1/6*v**4 + 4*v**2 - 5 - 4/3*v**3 + v. Let h(f) be the first derivative of b(f). Let h(t) = 0. Calculate t.
2
Let z = -65197/5 - -13041. What is h in -2/5*h**2 - 2*h - z = 0?
-4, -1
Let w(m) = m**3 - m**2 + 2*m + 2. Let u(l) = -20*l**3 + 44*l**2 + 26*l + 6. Let h(g) = 2*u(g) + 44*w(g). Factor h(j).
4*(j + 1)*(j + 5)**2
Let u(t) be the third derivative of -t**8/10080 - t**7/3780 + t**6/1080 + t**5/180 - 3*t**4/8 - 13*t**2. Let k(g) be the second derivative of u(g). Factor k(z).
-2*(z - 1)*(z + 1)**2/3
Let m = -33 - -61. Factor 20*b**2 + 12*b**2 + 3 + m*b**3 + 11*b**4 + 18*b + 2*b**5 + 1 + b**4.
2*(b + 1)**4*(b + 2)
Let j(k) be the second derivative of k**4/4 - 22*k**3 + 726*k**2 - 50*k - 4. Determine g so that j(g) = 0.
22
Let k(a) be the third derivative of 6*a**7/245 + 7*a**6/60 + a**5/21 + 2*a**2 + 375. Determine h, given that k(h) = 0.
-5/2, -2/9, 0
Let y(m) be the first derivative of m**6/720 - m**5/96 + m**4/48 + 2*m**3 + 8. Let a(w) be the third derivative of y(w). Determine o so that a(o) = 0.
1/2, 2
Suppose -4*v + o = -124, -v - o + 31 = o. Let l = v - -1. Factor 136*t**2 - 17*t**3 - 19*t**3 - 45*t - l - 67*t.
-4*(t - 2)**2*(9*t + 2)
Let t(s) = 4*s**2 - 8*s - 32. Let a = 75 - 68. Let i(j) = 6*j**2 - 12*j - 48. Let b(u) = a*t(u) - 5*i(u). Factor b(o).
-2*(o - 4)*(o + 2)
Let w(q) be the third derivative of q**8/1680 + 2*q**7/315 + q**6/180 - q**5/5 - 29*q**4/24 + 13*q**2. Let j(r) be the second derivative of w(r). Factor j(k).
4*(k - 1)*(k + 2)*(k + 3)
Let t(m) = -m**3 + 2*m**2 - m. Let y(n) = 9*n**3 - 10*n**2 - 23*n - 24. Let s(l) = 5*t(l) + y(l). Suppose s(f) = 0. Calculate f.
-2, -1, 3
Suppose -35*f = -51*f + 96. Let i(z) be the second derivative of -1/78*z**4 - 1/13*z**3 - 2/13*z**2 + 0 + f*z. Factor i(u).
-2*(u + 1)*(u + 2)/13
Let b(x) be the third derivative of 5*x**8/504 - 8*x**7/315 - x**6/45 - 21*x**2 + 7. Let b(z) = 0. What is z?
-2/5, 0, 2
Let p(g) be the third derivative of 2*g**7/105 + g**6/30 - g**5/5 - g**4/6 + 4*g**3/3 - 11*g**2 + 24*g. Factor p(u).
4*(u - 1)**2*(u + 1)*(u + 2)
Let f(q) be the third derivative of q**5/15 - 2*q**4/3 + 8*q**3/3 + 6*q**2. Factor f(t).
4*(t - 2)**2
Let a = -38 - -130. Suppose 3*f + a - 98 = 0. Let 1/4*k + 0 + 1/