 q = 4*f - 142 - 72. Let n = f - 105/2. Factor 1/2*z + 0 + n*z**2.
z*(z + 1)/2
Let s(v) be the second derivative of -1/50*v**5 - 1/10*v**4 - 10*v + 0*v**2 + 0 - 2/15*v**3. Factor s(g).
-2*g*(g + 1)*(g + 2)/5
Let d(m) be the second derivative of -2*m**3 + 0 - 22*m + 0*m**2 + 2*m**4 + 1/10*m**6 - 3/4*m**5. What is w in d(w) = 0?
0, 1, 2
Let p = 2441 + -53613/22. Let a = 50/11 - p. Factor -1/2*s**5 - 1/2*s + 1/2*s**4 + s**3 + a - s**2.
-(s - 1)**3*(s + 1)**2/2
Let x(y) be the first derivative of y**4/12 - 5*y**3/9 + 51. What is g in x(g) = 0?
0, 5
Factor -31*a - 1132*a - 98*a**2 - a**5 + 30*a**4 - 997*a + 100*a**3 - 1728 - 262*a**2 + 3*a**5.
2*(a - 4)*(a + 1)*(a + 6)**3
Suppose 5*q - 3*z - 21 = 2*q, 2*z - 70 = -5*q. Find c, given that 35*c**2 + 13*c**3 + q*c**3 - 47*c + 57*c = 0.
-1, -2/5, 0
Let m(d) be the first derivative of 0*d**4 - 1/5*d**5 + 0*d + 0*d**3 + 0*d**2 - 9. Let m(n) = 0. What is n?
0
Let x be (-70)/(-390)*(-5)/(-10). Let h(b) be the second derivative of -1/39*b**6 + 0*b**2 - b + 9/130*b**5 + 1/273*b**7 + 2/39*b**3 - x*b**4 + 0. Factor h(a).
2*a*(a - 2)*(a - 1)**3/13
Let f(n) be the second derivative of n**6/75 + n**5/10 + 3*n**4/10 + 7*n**3/15 + 2*n**2/5 - 2*n - 27. Determine g so that f(g) = 0.
-2, -1
Let h(m) = 2*m**4 - 66*m**3 - 268*m**2 - 384*m - 184. Let d(u) = u**4 - 44*u**3 - 178*u**2 - 256*u - 123. Let o(q) = 8*d(q) - 5*h(q). Factor o(v).
-2*(v + 1)*(v + 2)*(v + 4)**2
Let k(q) be the third derivative of -q**6/420 + q**5/210 + q**2 + 14. Suppose k(t) = 0. What is t?
0, 1
Let a(x) = 52*x + 260. Let k be a(-5). Let n(j) be the third derivative of -1/2*j**4 + 0 + k*j + 0*j**3 - 81/40*j**6 + 2*j**2 - 9/5*j**5. What is o in n(o) = 0?
-2/9, 0
Factor 6*t**2 - 6*t**2 - 4*t**2 - 128*t + 126 + 6*t**2.
2*(t - 63)*(t - 1)
Let j = -93/46 + 151/69. Factor -j*p**2 - 5/3*p - 25/6.
-(p + 5)**2/6
Let p(f) be the first derivative of f**5/120 - f**4/12 + f**3/4 + 10*f**2 + 31. Let k(l) be the second derivative of p(l). Factor k(o).
(o - 3)*(o - 1)/2
Let p = 3 + -1. Let j = -82 + 102. Suppose -2*n**3 + 2*n**2 - p*n**3 + 2*n**3 - 22*n**4 + 2*n + j*n**4 = 0. What is n?
-1, 0, 1
Let x(z) be the second derivative of 0 + 14*z + 1/30*z**5 - 5/18*z**3 - 1/36*z**4 - 1/3*z**2. Find k such that x(k) = 0.
-1, -1/2, 2
Let l = 1634 - 1630. Factor -12/5*t**2 + 0*t - 3/5*t**l + 0 + 12/5*t**3.
-3*t**2*(t - 2)**2/5
Let n(o) be the second derivative of o**6/50 - 9*o**5/100 - 19*o**4/20 + 87*o**3/10 - 27*o**2 - 6*o + 16. Factor n(g).
3*(g - 3)**2*(g - 2)*(g + 5)/5
Let z(d) be the first derivative of 0*d**2 + 4 - 1/18*d**4 - d + 0*d**3. Let u(p) be the first derivative of z(p). Let u(k) = 0. Calculate k.
0
Let s be (12/(-108))/(20/(-3)). Let n(v) be the third derivative of -s*v**5 + 0 - 2*v**2 + 1/3*v**3 + 0*v + 1/24*v**4. Factor n(u).
-(u - 2)*(u + 1)
Let r = -52 - -52. Find o such that 3/5*o**5 + 0*o**4 + 0*o**2 + r*o - 3/5*o**3 + 0 = 0.
-1, 0, 1
Suppose -21*b + 280 = -20*b. Let h be (b/(-77) + 4)/(1*2). Factor h - 2/11*s**2 + 2/11*s - 2/11*s**3.
-2*(s - 1)*(s + 1)**2/11
Let q(u) = u**3 - 16*u**2 + 21*u. Let o(k) = -15*k**2 + 20*k. Suppose -2*x = 2 + 8. Let f(j) = x*q(j) + 6*o(j). Factor f(t).
-5*t*(t - 1)*(t + 3)
Factor 1875/2 + 3/2*o**2 - 75*o.
3*(o - 25)**2/2
Suppose 0 = -2*m + 4*p + 1 + 17, 2*m - 15 = 3*p. Let r**3 + 0*r**m - 3*r + 3*r - r = 0. Calculate r.
-1, 0, 1
Suppose 1032*d**2 + 16*d**3 + 4190551 - 14*d**3 + 177504*d + 5986345 = 0. What is d?
-172
Factor -2/5*n + 0*n**2 + 1/5*n**4 + 2/5*n**3 - 1/5.
(n - 1)*(n + 1)**3/5
Let i be (-18)/21 + 30/35. Let d(u) be the second derivative of -4/3*u**3 + 1/3*u**4 + i*u**2 + 0 - 4*u. What is l in d(l) = 0?
0, 2
Let y = 27/2 + -66/5. Let p(g) be the first derivative of 0*g**2 + y*g**5 + 7 + 0*g**3 + 0*g**4 + 1/4*g**6 + 0*g. Factor p(k).
3*k**4*(k + 1)/2
Let j(t) be the second derivative of t**7/84 + t**6/15 + 3*t**5/40 + t - 6. Factor j(w).
w**3*(w + 1)*(w + 3)/2
Let h(p) be the third derivative of p**5/135 - 5*p**4/54 + 4*p**3/9 + 120*p**2. Let h(z) = 0. Calculate z.
2, 3
Let j(x) be the second derivative of 1/18*x**4 + 4*x + 0*x**3 + 0 - 4/3*x**2. Find l, given that j(l) = 0.
-2, 2
Let f(d) = 8*d**3 - 7*d**2 + 9*d + 5. Let v(u) = 2*u**3 - u**2 + u + 1. Let z(i) = -f(i) + 5*v(i). Factor z(j).
2*j*(j - 1)*(j + 2)
Let w(y) be the first derivative of -y**5/5 - y**3 + 3*y**2 + 6*y - 9. Let v(g) = -g**4 + g**3 + g + 1. Let i(b) = 6*v(b) - 3*w(b). Factor i(j).
-3*(j - 2)**2*(j + 1)**2
Suppose -7*c + 10*c - 6 = 0. Let j(u) be the first derivative of -2/3*u**3 - 2/5*u**5 + 0*u + 0*u**c - 2 + u**4. Determine y, given that j(y) = 0.
0, 1
Let z = 30 + -22. Suppose 40 = z*o + 16. Solve 0 + 0*u - 2/13*u**o + 0*u**2 = 0.
0
Let y(u) be the second derivative of -22/21*u**4 - 2/105*u**6 - 8 - 8*u**3 - 14*u**2 + 12/35*u**5 - u. Find j such that y(j) = 0.
-1, 7
Factor 1/3*y**3 - 5/3*y**2 - 8*y + 0.
y*(y - 8)*(y + 3)/3
Let d = 1780 - 1777. Solve 2*t**5 + 0 + 0*t + 32/5*t**d + 8/5*t**2 + 34/5*t**4 = 0 for t.
-2, -1, -2/5, 0
Let h = 1827 + -1823. Find j such that 6*j**2 + 3/2*j**5 - 3*j**3 + 3/2*j - 3*j**h - 3 = 0.
-1, 1, 2
Let j(w) = 5*w**3 - 21*w**2 + 6*w + 6. Let m(a) = 70*a**3 - 295*a**2 + 85*a + 85. Let d be 9/(27/24) - 2. Let g(h) = d*m(h) - 85*j(h). Factor g(p).
-5*p**2*(p - 3)
Factor 0*s**2 + 0 - 2/3*s**3 + 8/3*s.
-2*s*(s - 2)*(s + 2)/3
Suppose -7*j + 12*j = 105. Let 24*a - 3*a**4 + 60*a**2 + 13*a**4 + 11*a**4 + j*a**3 + 33*a**3 + 3*a**5 = 0. Calculate a.
-2, -1, 0
Let b = 407/7340 + -2/367. Let m(n) be the third derivative of -b*n**5 - 1/210*n**7 + 1/40*n**6 + 0*n + 0*n**3 - 5*n**2 + 0 + 1/24*n**4. Solve m(o) = 0 for o.
0, 1
Suppose j - 4*j = 3*f + 150, -2*j + 35 = -f. Let r = -41 - f. Find c, given that -2/9*c**5 + 0 + 0*c**r + 0*c + 2/9*c**3 + 0*c**2 = 0.
-1, 0, 1
Let h be -5 - (145/(-4))/(621/92). Let x(d) be the first derivative of 8/9*d**2 + 8/9*d + 1/18*d**4 - 3 + h*d**3. Solve x(c) = 0.
-2, -1
Suppose 2*k = 9*k + 9*k. Let 3/2*p + k + 15/4*p**2 = 0. Calculate p.
-2/5, 0
Let w = 364 - 363. Let c(m) be the first derivative of 1/9*m**3 + 0*m - w + 1/12*m**4 + 0*m**2. Find p, given that c(p) = 0.
-1, 0
Let o(p) be the second derivative of p**7/273 + 4*p**6/195 + p**5/130 - p**4/13 - 72*p. Let o(y) = 0. What is y?
-3, -2, 0, 1
Find d such that -128/7*d + 0 - 2/7*d**2 = 0.
-64, 0
Suppose -45 - 75 = -40*y. Factor 0*c + 8/13*c**2 + 16/13*c**y + 2/13*c**5 + 0 + 10/13*c**4.
2*c**2*(c + 1)*(c + 2)**2/13
Factor 26/9 - 2/9*q**2 - 8/3*q.
-2*(q - 1)*(q + 13)/9
Let -12/11 - 82/11*u - 8*u**4 - 188/11*u**2 - 192/11*u**3 - 14/11*u**5 = 0. What is u?
-3, -1, -2/7
Let d(j) = j**3 - 9*j**2 - 9*j - 13. Let b be d(10). Let m(z) = z**2 + 5*z. Let y(n) = 3*n. Let w(o) = b*m(o) + 4*y(o). Suppose w(l) = 0. Calculate l.
-1, 0
Let c(r) be the second derivative of -r**7/840 + 23*r**4/12 + 3*r. Let s(z) be the third derivative of c(z). Determine x, given that s(x) = 0.
0
Suppose 3*y = -y + 12. Suppose -y*x = -x - 98. Factor -s**3 + 49*s + 3*s**3 - 4*s**2 - x*s.
2*s**2*(s - 2)
Suppose -5*l = -9 - 6. What is g in 2*g**3 + 5*g**4 + l*g**4 - 2*g**5 - 6*g**4 - 2*g**2 = 0?
-1, 0, 1
Factor 28/5 + 4/5*o**3 - 34/5*o**2 + 38/5*o.
2*(o - 7)*(o - 2)*(2*o + 1)/5
Let a(t) be the second derivative of -t**7/336 - t**6/48 - 3*t**5/160 + 3*t**4/32 - 44*t - 1. Factor a(s).
-s**2*(s - 1)*(s + 3)**2/8
Factor 361/2 + 35/4*s**3 + 249/4*s**2 + 1/4*s**4 - 1007/4*s.
(s - 2)*(s - 1)*(s + 19)**2/4
Suppose -57*s - 46*s - 30*s = 0. Factor s*n**2 - 1/7*n**3 + 0 + 0*n - 1/7*n**5 - 2/7*n**4.
-n**3*(n + 1)**2/7
Factor -16*k**2 - 2*k**2 + 4*k**4 + 14*k**2.
4*k**2*(k - 1)*(k + 1)
Let i be 0 - (0 + (-4)/(-8))*0. Let p be i + (-2 - 1) - (-94)/26. Find o such that 8/13*o**4 + 6/13*o**5 - 2/13*o + 0 - p*o**2 - 4/13*o**3 = 0.
-1, -1/3, 0, 1
Factor -40 + 6*t**2 + 7*t + 5*t**2 - 21*t**2 - t + 11*t**2.
(t - 4)*(t + 10)
Let p(k) be the second derivative of -k**4/48 - 2*k**3/3 + 17*k**2/8 - k + 48. Determine y so that p(y) = 0.
-17, 1
Let f(g) = 8*g - 3. Let q be f(1). Suppose -2*b = 5 - q. Factor 6/5*o**2 + 2/5*o**3 + b + 4/5*o.
2*o*(o + 1)*(o + 2)/5
Let l(r) be the first derivative of 0*r**5 - 1/2*r**6 + 9/4*r**4 + 0*r - 2*r**3 + 33 + 0*r**2. Solve l(m) = 0.
-2, 0, 1
Let r(t) = t**3 + 3*t**2 - t. Let p(n) = -3*n**3 - 7*n**2 + 7*n - 9. Let w(g) = -p(g) - 4*r(g). Factor w(x).
-(x - 1)*(x + 3