1, 0
Let s(o) be the third derivative of o**7/105 - o**6/60 - 7*o**5/30 + o**4/12 + 2*o**3 + 111*o**2. Find l such that s(l) = 0.
-2, -1, 1, 3
Let s(b) be the third derivative of -1/240*b**6 + 0 - 5/48*b**4 - 26*b**2 + 0*b + 1/30*b**5 + 1/6*b**3. Suppose s(m) = 0. What is m?
1, 2
Let k(u) = -5*u**2 + 335*u. Let v(r) = -9*r. Let i(c) = k(c) + 5*v(c). Solve i(s) = 0 for s.
0, 58
Let a(n) be the third derivative of n**7/280 + 13*n**6/160 + 3*n**5/20 - 64*n**2. Solve a(o) = 0.
-12, -1, 0
Let r(o) = -16*o**2. Let p(l) = -l**2. Let i(g) = 36*p(g) - 2*r(g). Factor i(s).
-4*s**2
Let j = -49 - -42. Let r be (30/105)/((-6)/j). What is k in -r*k**5 + 1/3*k**4 + 2/3*k**3 - 2/3*k**2 - 1/3*k + 1/3 = 0?
-1, 1
Let s(d) be the first derivative of d**3/3 - d + 6. Let n(q) = 2*q**3 + 5*q**2 - 2*q - 5. Let w(b) = -n(b) + 3*s(b). Factor w(g).
-2*(g - 1)*(g + 1)**2
Let c(f) be the third derivative of -f**9/7560 - f**8/1680 - f**7/1260 - f**4/24 + 8*f**2. Let q(b) be the second derivative of c(b). Factor q(s).
-2*s**2*(s + 1)**2
Let s(x) = x**5 - 37*x**3 + 41*x**2 + 5*x - 5. Let z(v) = v**4 + v**3 - v**2 - v + 1. Let u(n) = s(n) + 5*z(n). Solve u(m) = 0 for m.
-9, 0, 2
Suppose -2*x + 16 = 3*o - 7*x, -4*o + 5*x + 18 = 0. Factor -4*w**2 - 4*w**o + 4*w + 4*w**2.
-4*w*(w - 1)
Let s(k) be the first derivative of -24/5*k**2 + 192/5*k + 1/5*k**3 - 8. Determine m, given that s(m) = 0.
8
Let x(d) be the third derivative of -d**6/80 + 3*d**5/40 + 9*d**4/8 + d**2 + 87*d. Factor x(o).
-3*o*(o - 6)*(o + 3)/2
Factor 8/3*z**3 + 1/3*z**4 - 26/3*z**2 - 56*z + 147.
(z - 3)**2*(z + 7)**2/3
Let p be 4/(-14)*(-35)/400. Let z(k) be the second derivative of -1/168*k**7 + 0*k**6 + p*k**5 + 0 + 0*k**2 + 0*k**4 - 1/24*k**3 + 4*k. Factor z(n).
-n*(n - 1)**2*(n + 1)**2/4
Let h(u) = 2*u**2 - 4*u + 2. Let f be h(2). Suppose -5*z + 29 - 4 = 5*x, -4*z + f*x + 14 = 0. Solve -1 + 16*c - 6 - 6 - z*c**2 + 1 = 0 for c.
1, 3
Suppose 2 - 28 = -2*p. Let a = p - 8. Determine w, given that -2*w**2 + 8*w**3 + 9*w**4 - 5*w**4 - 5*w - 4*w**3 + w**a - 2 = 0.
-2, -1, 1
Let l(y) be the second derivative of -3*y**4/16 - y**3/3 + y**2/8 + 224*y. Factor l(v).
-(v + 1)*(9*v - 1)/4
Let b(x) be the third derivative of 0*x**4 + 0*x + 1/30*x**5 - 4/3*x**3 + 0 - 2*x**2. Let b(v) = 0. Calculate v.
-2, 2
Let t(n) be the second derivative of 1/6*n**3 - 2 + 1/36*n**4 - 2/3*n**2 + 33*n. Factor t(w).
(w - 1)*(w + 4)/3
Suppose -2*m - m + 18 = 0. Let 2*j**4 + 4*j**3 + 0*j**4 - m*j**2 + 4*j**2 - 4*j**4 = 0. Calculate j.
0, 1
Suppose 11*i = 52*i - 23 - 59. Suppose 248/5*n - 150*n**3 - 98/5*n**5 - 48/5 - 4*n**i - 532/5*n**4 = 0. What is n?
-3, -2, -1, 2/7
Let d(w) be the first derivative of 0*w**2 + 2/35*w**5 + 0*w + 8/21*w**3 + 2/7*w**4 - 45. Factor d(a).
2*a**2*(a + 2)**2/7
Factor 0*v**5 + v**3 - 6*v**2 - 3*v**3 + 3*v**5 - 2*v**3 + v**3 + 6*v**4.
3*v**2*(v - 1)*(v + 1)*(v + 2)
Let u(h) = 10*h**3 + 2*h**2 - h. Let o be u(-2). Let w = 70 + o. Factor 2/3*x**2 - 4/3*x + w.
2*x*(x - 2)/3
Let l(g) = g**2. Let q(f) be the second derivative of f**5/20 + 7*f**4/12 + 6*f. Let u(b) = 14*l(b) - 2*q(b). Factor u(h).
-2*h**3
Let b be 1*3 + 1 + 0 + 6. Factor -7*m + 5*m - 8*m**3 + b*m**2 + 49 - 49.
-2*m*(m - 1)*(4*m - 1)
Let o(z) = 2*z**2 + 9*z - 3. Let f be o(-5). Suppose 3*u = -2*u - 3*k + 5, -2*k - 26 = -4*u. What is v in 0 - 2/5*v**u + 2/5*v**f + 0*v**3 + 0*v = 0?
-1, 0, 1
Suppose 2*g = 2*h - 16, 35*h = 37*h + g - 1. Let z(a) be the first derivative of 1/3*a - 6 - 1/9*a**h + 0*a**2. Factor z(q).
-(q - 1)*(q + 1)/3
Let s be (3/45*-3)/(27/(-60)). Factor 0 - 2/9*c - 4/9*c**4 + s*c**2 + 0*c**3 + 2/9*c**5.
2*c*(c - 1)**3*(c + 1)/9
Let t(h) = h**3 - 6*h**2 - 17*h + 8. Let f be t(8). Factor -2/11*w**3 + f + 4/11*w**2 + 0*w.
-2*w**2*(w - 2)/11
Let f(b) be the second derivative of -b**4/4 - 19*b**3/2 - 72*b**2 + 2*b + 15. Find k such that f(k) = 0.
-16, -3
Let u = -31 + 26. Let k(g) = -9*g**2 + 40*g - 100. Let w(d) = -4*d**2 + 20*d - 50. Let j(p) = u*w(p) + 2*k(p). Determine x so that j(x) = 0.
5
Let b(s) = -s**2 - 3*s + 2. Let m be b(-3). Suppose -10*r**2 - r + 2*r + 9*r**m - 2*r = 0. What is r?
-1, 0
Let q(p) be the third derivative of -p**8/2016 + p**7/315 + 7*p**6/240 - 116*p**2. Factor q(d).
-d**3*(d - 7)*(d + 3)/6
Let z be 310/65 - 492/(-2132). Factor -5*k - z + 5*k**3 + 5/4*k**4 + 15/4*k**2.
5*(k - 1)*(k + 1)*(k + 2)**2/4
Let c be -22 - 1490/(-70) - -1. Factor c*k**2 - 6/7*k - 8/7.
2*(k - 4)*(k + 1)/7
Let y(m) = 2*m - 3. Let l be y(4). Factor 8*w**3 - 6*w**3 - 3*w**2 + 3*w**4 - l*w**3 + 3*w.
3*w*(w - 1)**2*(w + 1)
Let r(i) be the first derivative of -i**6/21 + 6*i**5/35 + i**4/7 - 4*i**3/7 - i**2/7 + 6*i/7 + 42. Solve r(d) = 0.
-1, 1, 3
Let h(s) = -s**3 - 73*s**2 - 4*s - 292. Let z be h(-73). Factor -5/2*f**3 + 0 + z*f + 25/4*f**2 + 1/4*f**4.
f**2*(f - 5)**2/4
Factor -1/3*y**2 + 8/3*y - 16/3.
-(y - 4)**2/3
Suppose 5*l + 180 - 220 = 0. Let j(q) be the second derivative of 4/21*q**3 + 0*q**2 - l*q - 3/70*q**5 + 0 - 2/21*q**4. Factor j(f).
-2*f*(f + 2)*(3*f - 2)/7
Solve -3/8*w**2 + 0 + 9/4*w = 0.
0, 6
Let x(p) be the third derivative of -1/140*p**7 + 1/16*p**6 + 0 + 0*p + 38*p**2 + 3/2*p**3 - 5/16*p**4 - 1/8*p**5. Solve x(z) = 0 for z.
-1, 1, 2, 3
Let v(n) = 4*n - 1. Let y be v(-4). Let l = y - -22. Factor -3*w**2 + 3*w - 5 + l.
-3*w*(w - 1)
Let y(u) = u**2 + 7*u + 9. Let f be y(-6). Suppose 9*s + s + 6*s = 4*s. Factor 0 - 1/4*v**f + 1/4*v + s*v**2.
-v*(v - 1)*(v + 1)/4
Find c such that -226/11*c**2 - 74/11 + 27*c + 3/11*c**3 = 0.
1/3, 1, 74
Suppose 5 + 4 = -3*a, 45 = 4*m - 3*a. Let c(b) be the second derivative of 1/10*b**5 + 0*b**2 + 1/30*b**6 + 1/12*b**4 - m*b + 0*b**3 + 0. Factor c(p).
p**2*(p + 1)**2
Let 25/2*t**2 - 1/2*t**3 - 25/2 + 1/2*t = 0. What is t?
-1, 1, 25
Let n(a) be the first derivative of -65*a**4/4 - 380*a**3/3 - 525*a**2/2 + 90*a - 62. Factor n(h).
-5*(h + 3)**2*(13*h - 2)
Let f be 9/(27/(-6)) - -11. Let 3*q**2 + 0*q**4 + 3*q**2 + 21*q**3 + 12*q**4 + 12*q**4 + f*q**5 = 0. What is q?
-1, -2/3, 0
Let n(o) = o**5 - 9*o**4 + 59*o**3 - 51*o**2 - 11*o. Let a(b) = b**5 - 4*b**4 + 29*b**3 - 26*b**2 - 6*b. Let j(t) = -11*a(t) + 6*n(t). Let j(w) = 0. What is w?
-4, 0, 1
Suppose -3 = x + 3. Let b(s) = -2*s**2 - 12*s + 3. Let y be b(x). Suppose -48*a**y - 3*a + 9*a**2 + 9*a**2 + 6*a**2 = 0. Calculate a.
0, 1/4
Factor 96/13 + 70/13*m - 28/13*m**2 - 2/13*m**3.
-2*(m - 3)*(m + 1)*(m + 16)/13
Let d(z) be the third derivative of 1/160*z**6 + 0*z - 1/2*z**3 + 1/4*z**4 - 1/16*z**5 - 15*z**2 + 0. Factor d(b).
3*(b - 2)**2*(b - 1)/4
Let z(x) be the first derivative of 4*x**5/5 + 9*x**4/4 - 10*x**3/3 - 3*x**2/2 + 272. Factor z(a).
a*(a - 1)*(a + 3)*(4*a + 1)
Suppose n = -3*n - f - 689, 523 = -3*n - 2*f. Let b = n - -173. Find l, given that -4/17*l - 14/17*l**4 - 4/17*l**b + 16/17*l**3 + 2/17 + 4/17*l**5 = 0.
-1/2, 1
Let t(y) be the first derivative of 3 + 0*y + 4/3*y**3 - 2*y**2. Factor t(b).
4*b*(b - 1)
Suppose -3*l - 9 = -5*x, 7*x - 2*l - 8 = 3*x. Determine u, given that -10*u**3 + 10*u + 7 - 5*u**4 - 5 + 6 - x = 0.
-1, 1
Factor 4/5*t**2 - 1/5*t**4 - 2/5*t**3 + 0 + 8/5*t.
-t*(t - 2)*(t + 2)**2/5
Let o(v) be the third derivative of -v**10/105840 + v**8/7840 - v**7/4410 + 13*v**4/12 + 33*v**2. Let u(k) be the second derivative of o(k). Factor u(y).
-2*y**2*(y - 1)**2*(y + 2)/7
Let p be (-14 - -2)/(8/(-12)). Suppose -p*n + 9 = -15*n. Factor -2/7*y**4 + 0 - 6/7*y**n + 0*y - 4/7*y**2.
-2*y**2*(y + 1)*(y + 2)/7
Let s be 1/(-54)*-12*36. Let d(i) be the first derivative of -s + 13/3*i**3 - 3*i**5 + 2*i - 11/2*i**2 + 11/4*i**4. Find r, given that d(r) = 0.
-1, 1/3, 2/5, 1
Let t(y) = y**3 - 1. Let f(r) = -4*r**3 - 10*r**2 - r + 18. Let l(o) = f(o) + 5*t(o). Let s be l(10). Factor 2*p**4 - s*p**3 + 3*p**4 - 2*p**4.
3*p**3*(p - 1)
Let q(l) be the second derivative of 0*l**4 + 30*l + 0*l**2 + 0 - 1/189*l**7 - 1/45*l**6 - 1/45*l**5 + 0*l**3. Factor q(h).
-2*h**3*(h + 1)*(h + 2)/9
What is s in 15*s**2 - 20*s**3 + 96*s - 2*s**4 - 3*s**4 - 6*s = 0?
-3, 0, 2
Let n be (-10)/6*(-63)/35. Suppose -10/3*o - 2/3*o**2 + 2/3*o**n - 2 = 0. What is o?
-1, 3
Factor -1/2*d**2 - 4*d + 9/2.
-(d - 1)*(d + 9)/2
Let c(s) = 14*s**4 + 114*s**3 - 122*s**2 - 294*s - 112. Let t(u) = -2*u**4 + u**2 + u. Let j(r) = c(r) - 2*t(r). Factor j(b).
2*(b - 2)*(b + 7)*(3*b + 2)**2
Let m = -19