et p = 4850 + -4846. Factor -3/2*o**3 + 2*o + o**p - 2*o**2 + 1/2*o**5 + 0.
o*(o - 1)**2*(o + 2)**2/2
Let w(y) be the first derivative of 2*y**5/35 - y**4/14 - 10*y**3/21 - 3*y**2/7 - 784. Let w(i) = 0. What is i?
-1, 0, 3
Let s = 53 + -48. Factor 0 + 23*b**2 - 2 - 16*b**3 - 1 - s*b - 3*b**3 + 4*b**4.
(b - 3)*(b - 1)**2*(4*b + 1)
Let r(k) = 7*k**3 - 45*k**2 - 276*k - 238. Let w(n) = -6*n**3 + 47*n**2 + 270*n + 239. Let x(q) = -5*r(q) - 6*w(q). Factor x(l).
(l - 61)*(l + 2)**2
Let j(q) be the first derivative of 2*q**3/21 + 4*q**2/7 - 10*q/7 - 41. Factor j(s).
2*(s - 1)*(s + 5)/7
Let g be (-2)/(-10) + -12 + 518/35. Factor 0 + 1/2*y + 6*y**g + 3*y**2 + 4*y**4.
y*(2*y + 1)**3/2
Let l(p) be the third derivative of p**7/210 - 13*p**6/120 + 19*p**5/20 - 95*p**4/24 + 25*p**3/3 + 5*p**2. Determine w so that l(w) = 0.
1, 2, 5
Let n(q) be the first derivative of -15/2*q**2 - 15 - 5*q - 5*q**3 - 5/4*q**4. Factor n(u).
-5*(u + 1)**3
Let f(w) = -5*w**2 - 26*w + 31. Let x = 23 - 10. Let d(a) = -10*a**2 - 53*a + 63. Let s(l) = x*f(l) - 6*d(l). Factor s(b).
-5*(b - 1)*(b + 5)
Let t(g) be the first derivative of 2/55*g**5 + 13 - 1/22*g**4 - 4/11*g + 5/11*g**2 - 2/11*g**3. Factor t(k).
2*(k - 1)**3*(k + 2)/11
Factor -2*w**3 - 68*w - 9 - 3*w**2 + 69*w + w**5 - 15*w**4 - 6 + 33*w**2.
(w - 15)*(w - 1)**2*(w + 1)**2
Let p(w) be the third derivative of w**7/945 + w**6/108 + w**5/45 - w**4/27 - 8*w**3/27 - 141*w**2. Solve p(a) = 0.
-2, 1
Let x(r) = r**3 + 2*r**2 + 2*r - 3. Let v be x(-3). Let a = -16 - v. Factor 4/7*h**4 - 8/7*h**3 + 8/7*h + 0*h**a - 4/7.
4*(h - 1)**3*(h + 1)/7
Let o be (-449)/(-17)*52/2366. Let t = o - 2/221. Solve -2/7*p + t - 2/7*p**2 = 0.
-2, 1
Let y(w) be the first derivative of -w**6/24 + w**5/20 + 3*w**4/16 - 5*w**3/12 + w**2/4 - 141. Factor y(p).
-p*(p - 1)**3*(p + 2)/4
Let h(s) be the first derivative of -2*s**5/15 + 9*s**4/2 - 52*s**3/9 - 163. Suppose h(u) = 0. Calculate u.
0, 1, 26
Let i(u) = 3*u - 1. Let d(n) = -2*n**2 - 466*n - 27850. Let w(f) = -2*d(f) + 4*i(f). Determine k so that w(k) = 0.
-118
Let d(p) = -2*p**2 + 7*p + 24. Let n(l) = -l**2 + l + 8. Let c(f) = -5*d(f) + 15*n(f). Factor c(z).
-5*z*(z + 4)
Let w(v) be the first derivative of v**6/810 + v**5/135 - v**4/18 - 23*v**3/3 + 10. Let j(m) be the third derivative of w(m). Determine r, given that j(r) = 0.
-3, 1
Let c(b) be the first derivative of b**4/9 + 28*b**3/27 - 8*b**2/9 - 112*b/9 - 188. Factor c(p).
4*(p - 2)*(p + 2)*(p + 7)/9
Let o(n) be the first derivative of n**7/105 - n**6/25 + 3*n**5/50 - n**4/30 + 14*n + 6. Let g(y) be the first derivative of o(y). Find c, given that g(c) = 0.
0, 1
Suppose 12*f - 8 = 10*f. Suppose 0 = -2*o - f + 8. Factor 2/7*v**o + 6/7*v + 4/7.
2*(v + 1)*(v + 2)/7
Suppose b + 0*k + 4*k = 28, 4*k + 20 = b. Let s be ((-6)/(-4))/(36/b). Let i(p) = -3*p**2 + 5*p + 8. Let t(n) = n + 1. Let c(r) = s*i(r) - 5*t(r). Factor c(f).
-3*(f - 1)*(f + 1)
Let g(z) be the first derivative of z**4/18 + 8*z**3/27 + 774. Factor g(r).
2*r**2*(r + 4)/9
Let f = 396 - 396. Find l such that -2/7*l**4 + 18/7*l**3 - 54/7*l**2 + 54/7*l + f = 0.
0, 3
Factor -486*j**2 + 279*j**3 + 1/3*j**5 + 0*j - 56/3*j**4 + 0.
j**2*(j - 27)**2*(j - 2)/3
Let g(y) be the second derivative of 7*y**5/90 - 37*y**4/36 + 10*y**3/9 - 11*y**2 + 6*y. Let m(c) be the first derivative of g(c). Factor m(n).
2*(n - 5)*(7*n - 2)/3
Let g(b) be the third derivative of 0*b**3 - 5/4*b**5 + 0*b + 0 - 7/24*b**6 + 5/336*b**8 + 15/4*b**4 + 1/14*b**7 + 2*b**2. Factor g(w).
5*w*(w - 2)*(w - 1)*(w + 3)**2
Let n = 21861 + -109303/5. Factor 1/5*v**4 - 2/5*v + 0 - 1/5*v**2 + n*v**3.
v*(v - 1)*(v + 1)*(v + 2)/5
Factor -15*f**2 + 85*f - 1303 + 10*f**2 + 1223.
-5*(f - 16)*(f - 1)
Let f be -5 + 2 + 0 + 39. Let u = 130 - f. Factor -96*c**2 - 147*c**4 + u*c**3 - c + 13*c + 137*c**3.
-3*c*(c - 1)*(7*c - 2)**2
Let v = 16631/44 + -1509/4. Determine w, given that 12/11*w**3 + 2/11*w - v*w**4 + 2/11*w**5 + 0 - 8/11*w**2 = 0.
0, 1
Let t = -20652 + 20654. Factor -6/7*k**2 + t*k - 4/7.
-2*(k - 2)*(3*k - 1)/7
Suppose -r = -5*a + 30, 0*r + 12 = 2*a - r. Suppose 2*c + 3*c + 15 = 0, 4*c + 28 = 4*x. Determine l, given that 3 - 5 - a + 12*l - x*l**3 = 0.
-2, 1
Let i(b) be the first derivative of 2*b**6/15 + b**5/4 - 7*b**4/12 - b**3/3 - 7*b + 7. Let z(t) be the first derivative of i(t). What is x in z(x) = 0?
-2, -1/4, 0, 1
Let p(v) = 1115*v**3 + 750*v**2 + 155*v + 15. Let h(l) = -1116*l**3 - 748*l**2 - 155*l - 14. Let d(s) = 5*h(s) + 4*p(s). Find c such that d(c) = 0.
-2/7, -1/4, -1/8
What is w in -9*w**2 + 3*w**2 - 6*w**2 - 140*w - 24 + 42*w**2 - 6*w**2 = 0?
-1/6, 6
Determine t, given that -98280*t**2 - 1390149 + 1084*t**3 + 16*t**4 + 3013200*t - 1525851 - 20*t**4 = 0.
1, 90
Let l = -154/9 - -317/18. Let c(u) be the first derivative of -7 + u**2 - l*u**4 + 0*u + 0*u**3. Find y, given that c(y) = 0.
-1, 0, 1
Let a(m) be the third derivative of -1/180*m**5 + 5/72*m**4 + 27*m**2 + 0*m + 0 - 1/3*m**3. Determine o, given that a(o) = 0.
2, 3
Let y(z) be the third derivative of -z**7/525 - z**6/60 - z**5/50 + 3*z**4/20 + 2*z**2 - 16. Solve y(q) = 0 for q.
-3, 0, 1
Let w be 5 + (6 - 36/6). Suppose -40*q + 140 = -w*q. Let 2/3*o**q + 4/3 - 14/3*o**2 - 4/3*o**5 - 2/3*o + 14/3*o**3 = 0. Calculate o.
-2, -1/2, 1
Let s = 770 - 767. Factor -2/3*u**5 - 10/3*u**s - 4/3*u**2 - 8/3*u**4 + 0 + 0*u.
-2*u**2*(u + 1)**2*(u + 2)/3
Factor -2*g - 2017*g**3 + 10*g + 2014*g**3 + g**2 + 4.
-(g - 2)*(g + 1)*(3*g + 2)
Let h = 77 + -77. Suppose -10*i + 4*i + 18 = h. Find p such that -3*p**5 + 0*p + 0*p**2 - 3/4*p**i + 3*p**4 + 0 = 0.
0, 1/2
Let n(q) be the second derivative of q**7/28 + 3*q**6/20 - 21*q**5/40 - 7*q**4/8 + 9*q**3/2 - 6*q**2 + 56*q - 2. Factor n(d).
3*(d - 1)**3*(d + 2)*(d + 4)/2
Let y(o) be the second derivative of -1/240*o**5 + 1/504*o**7 - 1/120*o**6 + 0*o**2 + 0*o**3 + 1/48*o**4 + 0 - 27*o. Solve y(t) = 0.
-1, 0, 1, 3
Let s(r) = r**2 + 3*r - 14. Let k be s(4). Find t, given that 25*t**2 - 23*t**2 - k*t + 6*t = 0.
0, 4
Let n(g) be the first derivative of 9/2*g**2 + g**3 + 1 + 6*g. Determine x, given that n(x) = 0.
-2, -1
Find z, given that 36 + 38*z**2 + 2/3*z**4 - 26/3*z**3 - 66*z = 0.
1, 3, 6
Let g(t) be the second derivative of -t**7/210 - t**6/60 - t**2/2 + 9*t. Let x(c) be the first derivative of g(c). Determine b, given that x(b) = 0.
-2, 0
Let s(x) be the first derivative of -x**3 + 45 - 27/2*x**2 + 30*x. Solve s(d) = 0 for d.
-10, 1
Suppose 30 = 16*r - 6*r. Factor 4*c**r + 2 - 4*c**4 + 4*c**3 - 18 - 16*c + 0*c + 12*c**2.
-4*(c - 2)**2*(c + 1)**2
Let k = 1613 - 1613. Let o(y) be the second derivative of -1/100*y**5 + k - 12*y + 1/20*y**4 - 1/10*y**3 + 1/10*y**2. Suppose o(s) = 0. Calculate s.
1
Suppose -4*c + 9 = -c. Factor 0 + 6*l**2 + 8*l**4 + 3*l + c*l**5 - 6*l**3 + 9*l**4 - 20*l**4 - 3.
3*(l - 1)**3*(l + 1)**2
Let x(g) be the third derivative of g**6/60 + g**5/30 - g**4/8 + g**3/6 - 30*g**2. Let i be x(1). Factor 2/11*p**i - 4/11 + 2/11*p.
2*(p - 1)*(p + 2)/11
Let n be 1 + (-8)/6 - (-11640)/36. Suppose -163 - 4*a**3 + 0*a - 24*a**2 + 4*a + n - 136 = 0. What is a?
-6, -1, 1
Factor 11*j**2 + 4*j**2 + 17*j**3 - 5*j**4 - 15 + 18*j**3 - 5*j**3 - 45 - 80*j.
-5*(j - 6)*(j - 2)*(j + 1)**2
Let c(i) be the second derivative of i**6/10 + 3*i**5/5 - 3*i**4/2 - 18*i**3 - 81*i**2/2 - 315*i. Determine z, given that c(z) = 0.
-3, -1, 3
Let w be 0*((-45)/(-12))/15. What is o in 0 + 0*o**2 + w*o + 4/5*o**4 + 12/5*o**3 = 0?
-3, 0
Let j(d) be the first derivative of -d**4/16 + d**3/2 - 11*d**2/8 + 3*d/2 - 74. Factor j(g).
-(g - 3)*(g - 2)*(g - 1)/4
Factor -2/5*p**3 - 4/5*p**2 + 0*p + 2/5*p**4 + 0.
2*p**2*(p - 2)*(p + 1)/5
Let w(o) be the first derivative of o**6/210 + 2*o**5/105 - o**4/6 + 8*o**3/21 + 13*o**2/2 + 19. Let p(h) be the second derivative of w(h). Factor p(y).
4*(y - 1)**2*(y + 4)/7
Let m = -130 + 201. Let j = m - 68. Factor -5/3*g + 1/3*g**5 + 4/3*g**4 - 2/3*g**2 + 4/3*g**j - 2/3.
(g - 1)*(g + 1)**3*(g + 2)/3
Let r(p) = -p**2 + 12*p + 4. Let o be r(12). Suppose -3*b = -2*u - 2*u - 18, -5*b + o*u = -22. Factor 3/2*v**3 + 12*v + 6 + 15/2*v**b.
3*(v + 1)*(v + 2)**2/2
Factor 805*v**2 - 3337 + 1054*v - 15016 - 14452 - 5*v**3 - 33049*v.
-5*(v - 81)**2*(v + 1)
Let k be (6 - 4)*(-4)/(-4). Find a such that 176*a**3 + 2*a - 96*a**4 - k*a - 36*a**5 - 5