 2, 3
Let y be 11/(-88)*2/(-5) - 0. Let r(n) be the second derivative of 0*n**3 + 0*n**2 - 1/36*n**4 + 2/45*n**6 + 0 + y*n**5 + 2*n. Suppose r(k) = 0. What is k?
-1, 0, 1/4
Let v be 12/(-6)*4/((-24)/9). Let q(z) be the first derivative of -6 - 4/3*z**v + 1/5*z**4 - 12/5*z + 14/5*z**2. Factor q(p).
4*(p - 3)*(p - 1)**2/5
Let o(g) = -g**3 + g**2 + g - 1. Let b be (-1)/6 - (-657)/54. Let s(f) = -4*f**3 + 2*f**2 - 6. Let n(l) = b*o(l) - 2*s(l). Determine q so that n(q) = 0.
-1, 0, 3
Let g be (-2)/(-27) + (-656)/(-1107). Factor -g - 2*z**2 + 8/3*z.
-2*(z - 1)*(3*z - 1)/3
Let r(j) = 15*j**2 - 268*j - 72. Let c(s) = -7*s**2 + 134*s + 37. Let d(p) = -9*c(p) - 4*r(p). Let d(q) = 0. Calculate q.
-1/3, 45
Let f(m) be the first derivative of -2*m**6/45 - 11*m**5/30 - m**4 + 20*m**3/3 + 6. Let u(x) be the third derivative of f(x). Factor u(p).
-4*(p + 2)*(4*p + 3)
Factor -54*b + 89*b**4 + 33*b**2 - 17 + 41 - 92*b**4.
-3*(b - 2)*(b - 1)**2*(b + 4)
Let t(q) be the third derivative of q**2 + 0*q + 0*q**3 + 1/280*q**6 + 1/140*q**5 - 13 + 1/1470*q**7 + 1/168*q**4. Determine a, given that t(a) = 0.
-1, 0
Let c(d) be the second derivative of d**4/36 + d**3/9 - 40*d**2/3 - 2*d - 72. What is a in c(a) = 0?
-10, 8
Let l(x) = -2*x**4 - 69*x**3 - 40*x**2. Let g(q) = q**4 + 17*q**3 + 10*q**2. Let w(z) = 9*g(z) + 2*l(z). Factor w(m).
5*m**2*(m + 1)*(m + 2)
Let o(n) be the third derivative of 2*n**3 + 1 + 0*n**4 + 0*n - 1/20*n**5 + 7*n**2. Factor o(w).
-3*(w - 2)*(w + 2)
Suppose 0 = 3*x + 8*x + 902. Let r = -80 - x. Factor 9/4*a + 1/2 + 7/4*a**r.
(a + 1)*(7*a + 2)/4
Solve 169/2*t**2 + 225/2 + 195*t = 0 for t.
-15/13
Suppose 6*v - v - 2*v = 0. Suppose v = -t - 2 + 7. Factor g**2 - 1/2 + 1/2*g**t + 1/2*g - g**3 - 1/2*g**4.
(g - 1)**3*(g + 1)**2/2
Suppose 24 + 40 = 2*r. Let b = r - 28. Factor -9/5*p**3 - 3/5*p**b + 0 - 9/5*p**2 - 3/5*p.
-3*p*(p + 1)**3/5
Suppose 0 = 17*d - 19*d + 2*g + 4, -d - 5*g + 20 = 0. Let p(u) be the third derivative of 0 + 0*u**3 - 5*u**2 + 0*u + 0*u**4 - 1/135*u**d. Solve p(b) = 0.
0
Let c = 3790 - 18948/5. Find n such that 0 - 4/15*n**2 - 2/15*n**4 + 0*n + c*n**3 = 0.
0, 1, 2
Let s(m) be the third derivative of 0 + 0*m - 13/70*m**7 - 7/20*m**5 + 1/8*m**4 + 0*m**3 + 4*m**2 + 1/28*m**8 + 3/8*m**6. Factor s(d).
3*d*(d - 1)**3*(4*d - 1)
Let y = 182 - 180. Suppose -5*l + 7 = -3. Suppose d**l - 3*d**y - d**2 - d**2 - 8 - 12*d = 0. What is d?
-2, -1
Suppose -3*d = 5*d - 16. Suppose 0 = 5*p - 5*h - 15, -7*p + 5*p - d*h = -10. Suppose 3/2*k**p + 0*k + 0*k**3 + 0 + 3/2*k**5 + 0*k**2 = 0. Calculate k.
-1, 0
Let j(v) = -v**2 + 8*v + 2. Let i be j(8). Let o be 1/(57/27 - i). Determine h, given that 6*h - 3 - 6*h**3 + h**5 - 4*h**5 + o*h**4 - 6*h**2 + 3*h = 0.
-1, 1
Let l(o) be the third derivative of o**8/336 + o**7/210 - o**6/120 - o**5/60 + 13*o**2. Factor l(h).
h**2*(h - 1)*(h + 1)**2
Solve -g**3 + 135 + 48*g**2 + 1528 + 2433 - 768*g = 0 for g.
16
Factor 3*r**4 + 12 + 57*r + 6 + 59*r**2 + 23*r**3 + 6 - 6.
(r + 1)*(r + 3)**2*(3*r + 2)
Let g(r) be the third derivative of r**5/60 + r**4/24 - 7*r**2. Factor g(d).
d*(d + 1)
Let w(i) be the second derivative of 1/10*i**5 + 0 + 1/20*i**6 + 10*i - 3/8*i**3 + 1/168*i**7 - 1/24*i**4 - 1/2*i**2. Factor w(k).
(k - 1)*(k + 1)**3*(k + 4)/4
Let o(w) = 2*w**3 + 23*w**2 - 2*w - 20. Let j(d) = 3*d**3 + 25*d**2 - 3*d - 21. Let a(f) = 3*j(f) - 4*o(f). Factor a(v).
(v - 17)*(v - 1)*(v + 1)
Let a be (0 + 1 - 5)/(3 + -5). Let t(c) be the second derivative of -1/15*c**4 - 2/3*c**3 + 1/25*c**5 + 9*c + 0 - 6/5*c**a. Solve t(f) = 0 for f.
-1, 3
Let o(r) = -r**2 - 29*r - 134. Let w(z) = -z**3 - 25*z**2 + 3*z + 52. Let y be w(-25). Let a be o(y). Solve -8/3*i**3 - i**a - 1/3*i**2 + 4/3 + 8/3*i = 0.
-2, -1, -2/3, 1
Find s, given that 16*s**2 + 36 - 4*s**3 + 30 + 16*s**2 - 42 - 52*s = 0.
1, 6
Let v(n) be the first derivative of -3/8*n**2 + 0*n + 3/8*n**3 + 3/32*n**4 - 9/40*n**5 + 1/16*n**6 - 31. Suppose v(a) = 0. What is a?
-1, 0, 1, 2
Let m = -710 - -2132/3. Let a(c) be the first derivative of -2/3*c**3 - c**2 - m*c - 1/6*c**4 + 8. Factor a(n).
-2*(n + 1)**3/3
Suppose 5 = 13*x - 60. Let r(y) be the third derivative of x*y**2 - 3/40*y**5 + 0 + 0*y**4 + 0*y - 1/80*y**6 + 0*y**3. Solve r(b) = 0.
-3, 0
Let h(n) be the first derivative of -2*n**3/27 + 9*n**2 + 74. Factor h(f).
-2*f*(f - 81)/9
Let p(h) = 2*h**3 - 22*h**2 + 14*h - 6. Let w(k) = -2*k**3 + 24*k**2 - 14*k + 6. Let l(s) = -7*p(s) - 6*w(s). Factor l(c).
-2*(c - 3)*(c - 1)**2
Let p be ((-58)/(-203))/((-6)/(-14)). Let y(t) be the first derivative of -1/2*t**4 + 6 - 1/3*t**2 + 0*t - p*t**3 - 2/15*t**5. Solve y(v) = 0 for v.
-1, 0
Factor -2/7*k + 0 - 2/7*k**3 - 4/7*k**2.
-2*k*(k + 1)**2/7
Let o(v) be the third derivative of -v**6/450 + 4*v**5/75 + 19*v**3/6 + 4*v**2. Let i(c) be the first derivative of o(c). Factor i(f).
-4*f*(f - 8)/5
Let k(q) be the first derivative of -3*q**4/4 + 14*q**3 - 48*q**2 - 384*q - 98. Factor k(s).
-3*(s - 8)**2*(s + 2)
Let u(c) be the third derivative of 0 - 2/15*c**5 + 0*c**4 - 1/10*c**6 + 1/84*c**8 + 10*c**2 + 0*c**7 + 0*c**3 + 0*c. Factor u(k).
4*k**2*(k - 2)*(k + 1)**2
Let b be (-14)/90 + 34/153. Let g(r) be the first derivative of -4 + b*r**3 + 1/20*r**4 - 1/10*r**2 - 1/5*r. Find u, given that g(u) = 0.
-1, 1
Let w(c) be the first derivative of c**6/35 + 9*c**5/140 - 2*c**4/7 + 3*c**3/14 - 3*c + 9. Let v(h) be the first derivative of w(h). Solve v(s) = 0.
-3, 0, 1/2, 1
Suppose 0 = -2*c + 24 - 12. Let y be c/9*1/3. Let -y*m**2 + 0 + 2/9*m = 0. Calculate m.
0, 1
Let r(i) be the second derivative of -i**6/120 + i**5/10 - 11*i**4/24 + i**3 - 9*i**2/8 + 2*i + 13. Factor r(p).
-(p - 3)**2*(p - 1)**2/4
What is a in -3*a**4 + 0*a - 3/2*a**2 - 25/4*a**3 + 7/4*a**5 + 0 = 0?
-1, -2/7, 0, 3
Let f(i) be the second derivative of -i**6/540 - i**5/90 - 7*i**3/2 + 16*i. Let m(d) be the second derivative of f(d). What is v in m(v) = 0?
-2, 0
Let a be (16/(-32))/(1/2) - -5. Let m(p) be the third derivative of 0*p**3 + 0*p + 1/42*p**a + 0 - 3/140*p**6 - p**2 + 1/30*p**5. What is j in m(j) = 0?
-2/9, 0, 1
Find v, given that -15/8*v**2 + 9 + 3/8*v**3 - 3/4*v = 0.
-2, 3, 4
Suppose 2 = -55*q + 56*q. Let p = 32/73 - -9/146. Factor 0*c - p + 1/2*c**q.
(c - 1)*(c + 1)/2
Let g(f) be the third derivative of -f**6/1320 + f**5/330 + 7*f**4/264 + 2*f**3/33 - 40*f**2 - 2. Factor g(j).
-(j - 4)*(j + 1)**2/11
Let z be 1995/(-18) + (-2)/(-4). Let t = 111 + z. Factor 2/3*u**2 + t*u**3 + 0*u + 0.
2*u**2*(u + 1)/3
Let h = -609 - -611. Let k(c) be the first derivative of 1/10*c**h - 3 + 0*c + 1/15*c**3. Factor k(u).
u*(u + 1)/5
Let z(q) = 16*q**3 + 16*q**2 - 16*q - 20. Let o(c) = c**4 + 33*c**3 + 31*c**2 - 33*c - 42. Let w(d) = 4*o(d) - 10*z(d). Factor w(j).
4*(j - 8)*(j - 1)*(j + 1)**2
Let h = -48072 + 624938/13. Factor h*b**2 - 8/13*b - 10/13.
2*(b - 5)*(b + 1)/13
Suppose 76*j - 349 + 121 = 0. Let a(c) be the second derivative of 5/12*c**4 + 0 + 5*c**2 + 11*c + 5/2*c**j. Find u such that a(u) = 0.
-2, -1
Suppose -7*g + 3*z = -5*g - 12, 0 = 2*g + z + 4. Let t(f) be the second derivative of g - 9/2*f**2 + 5/2*f**3 - 1/2*f**4 + f. Factor t(p).
-3*(p - 1)*(2*p - 3)
Let r be (19 - 6897/330) + -3*(-5)/6. Let j be (-2)/(-10)*(-1 - -4). Solve -3/5*c + j + r*c**3 - 3/5*c**2 = 0.
-1, 1
Let f(h) be the third derivative of h**7/210 - h**6/30 + 2*h**4/3 + 7*h**3/6 + 19*h**2. Let m(j) be the first derivative of f(j). What is y in m(y) = 0?
-1, 2
Let o(m) = -4*m**3 - 79*m**2 - 32*m + 39. Let z(u) = -u**3 - u**2 - 2*u. Let g(r) = o(r) + 2*z(r). Factor g(k).
-3*(k + 1)*(k + 13)*(2*k - 1)
Let u be 132/27*3 + (-4)/6. Let i be ((-24)/21)/(8/u - 1). Determine p so that -i*p - 20/3*p**2 + 4/3*p**4 + 0 + 4/3*p**5 - 4*p**3 = 0.
-1, 0, 2
Let x be 40/48*(-420)/(-175). Solve 6/5*t + 3/5*t**x + 3/5 = 0 for t.
-1
Suppose 38*s = -3*b + 43*s - 14, 4*b - 3*s + 4 = 0. Solve 2*k**b + 2/3 + 2*k + 2/3*k**3 = 0.
-1
Let g(h) be the first derivative of -h**3 - 15*h**2 - 27*h - 31. Determine a, given that g(a) = 0.
-9, -1
Let z(l) be the first derivative of -1/8*l**2 - 16 + 1/6*l**3 - 1/16*l**4 + 0*l. Factor z(i).
-i*(i - 1)**2/4
Solve 3/7*m**2 - 678/7*m + 38307/7 = 0 for m.
113
Let d = 1971 - 1966. Let f(s) be the first derivative of -6 + 0*s + s**4 - 8/9*s**3 - 8/15*s**d + 1/3*s**2 + 1/9*s**6. Factor f(x).
2*x*(x - 1)**4/