Determine g so that v(g) = 0.
-1/2, 0, 3
Factor -116/9*o**2 + 40/9 + 2/3*o**3 - 82/9*o.
2*(o - 20)*(o + 1)*(3*o - 1)/9
Let a(l) be the third derivative of -l**6/360 - 23*l**5/60 + l**4/72 + 23*l**3/6 + 6*l**2 - 7. Let a(c) = 0. Calculate c.
-69, -1, 1
Let p be (((-378)/35)/9)/((-4)/10). Let l(f) be the second derivative of 0*f**p + 0*f**2 + 0 + 1/30*f**5 + 8*f + 1/18*f**4. Factor l(n).
2*n**2*(n + 1)/3
Let l = 225294/1225 - 69/1225. Let j = -177 + l. Factor -16/7*p**3 + 18/7 + 44/7*p**2 + 2/7*p**4 - j*p.
2*(p - 3)**2*(p - 1)**2/7
Suppose -4*t + 1 = -y - 44, -33 = -2*t - 3*y. Let n be t/14*49/14. Suppose -3*l**3 + n - 9*l**2 + 11 - 2 = 0. What is l?
-2, 1
Suppose 240 = 7*c - 13*c. Let o be (-2 - -1)*c/240. Factor -1/6*v + 0 + o*v**2.
v*(v - 1)/6
Let a(n) be the third derivative of -n**5/12 + 50*n**4/3 - 38*n**2 - 3. Factor a(m).
-5*m*(m - 80)
Let l(k) be the second derivative of -k**5/40 + k**4/4 - 3*k**3/4 + k**2 + 60*k. Solve l(s) = 0 for s.
1, 4
Let a be 6/15 - (-7)/70. Let 0*l + l**3 + 0 + a*l**2 = 0. What is l?
-1/2, 0
Suppose v + 3 - 6 = 0. Factor -15*b + 12*b + 6*b**v - 3*b**3.
3*b*(b - 1)*(b + 1)
Let b(s) be the second derivative of -s**7/77 - 8*s**6/33 - 92*s**5/55 - 57*s**4/11 - 245*s**3/33 - 50*s**2/11 - 7*s. Let b(n) = 0. Calculate n.
-5, -2, -1, -1/3
Let d(h) be the third derivative of -h**7/210 + h**6/12 - h**5/5 - 29*h**4/12 - 35*h**3/6 - 167*h**2. Let d(f) = 0. Calculate f.
-1, 5, 7
Let w(v) be the second derivative of v**6/20 + 7*v**5/20 + 17*v**4/24 + v**3/2 - 15*v + 1. Factor w(c).
c*(c + 1)*(c + 3)*(3*c + 2)/2
Solve -10/3*f - 8 - 1/3*f**3 + 13/3*f**2 = 0 for f.
-1, 2, 12
Let o(f) be the third derivative of f**6/300 - 13*f**5/150 + 11*f**4/30 - 415*f**2. Solve o(j) = 0 for j.
0, 2, 11
Let v = -19 + 31. Let x be (2/(-6))/((-2)/v). Factor 4*w**x - 32*w - 64 - 3*w**2 - 6*w**2 + w**2.
-4*(w + 4)**2
Factor 2/3*i**2 + 264*i + 26136.
2*(i + 198)**2/3
Let m(d) be the third derivative of -d**8/56 - 3*d**7/140 + d**6/80 + 2*d**2 - 202. Determine l, given that m(l) = 0.
-1, 0, 1/4
Let b(a) = a + 7. Let u be 1/(-2) + (-18)/4. Let c be b(u). Solve -4*l**3 + 5*l**4 - 46*l**c + 46*l**2 - 14*l**5 + 13*l**4 = 0.
0, 2/7, 1
Let y = 2891/10 + -289. Let u(m) be the second derivative of m - 1/100*m**5 - y*m**3 + 1/20*m**4 + 0 + 1/10*m**2. Let u(v) = 0. Calculate v.
1
Factor 0*n**5 + 3898*n**3 - 3894*n**3 - 84*n**2 + 20*n**4 - 72*n + 5*n**5 - n**5.
4*n*(n - 2)*(n + 1)*(n + 3)**2
Suppose 1260*t**3 + 8*t**4 - 629*t**3 - 627*t**3 + 4*t**5 = 0. What is t?
-1, 0
Suppose 0 = -4*s - 5*s + 387. Suppose -2*p + s = 35. Let 0 - 4/3*c**p - 16/3*c**3 - 16/3*c**2 + 0*c = 0. What is c?
-2, 0
Let v(a) be the first derivative of -6*a**5/65 - 7*a**4/13 - 34*a**3/39 - 6*a**2/13 + 166. Let v(u) = 0. What is u?
-3, -1, -2/3, 0
Let r = 73/115 + 13/23. Let i(u) be the first derivative of -r*u - 1 - 4/5*u**2 - 2/15*u**3. Factor i(c).
-2*(c + 1)*(c + 3)/5
Suppose -20 = -2*w + 6*w. Let k(r) = -2*r**3 - 9*r**2 + 6*r + 5. Let d be k(w). Factor d*o**2 - 3/4*o + 1/4*o**3 + 1/2.
(o - 1)**2*(o + 2)/4
Let b(h) be the third derivative of h**6/40 - 11*h**5/20 + 5*h**4/4 - 5*h**2 + 3. Determine y, given that b(y) = 0.
0, 1, 10
Let y = -44 - -42. Let n be 2/(y*4/(-24)*3). Solve 16/7*g - 16/7 - 4/7*g**n = 0 for g.
2
Let x(d) = d**2 - 6*d - 5. Let h be x(7). Suppose -1 = -2*r - m, h*m = -r - 6 - 1. Factor -3/2*f**2 + r*f + 9/2.
-3*(f - 3)*(f + 1)/2
Let x(v) be the third derivative of v**6/30 - 2*v**5/5 + 11*v**4/6 - 4*v**3 + 252*v**2. Determine l so that x(l) = 0.
1, 2, 3
Let n(w) = -1665*w**2 + 21615*w - 67440. Let o(f) = -119*f**2 + 1544*f - 4817. Let h(m) = 6*n(m) - 85*o(m). Factor h(l).
5*(5*l - 31)**2
Let b be -3 - -3 - 5/(-1). Suppose 0*t = b*t - 10. Factor 3*m**2 - 2*m + t*m + 9*m + 6.
3*(m + 1)*(m + 2)
Let o(n) be the first derivative of 3*n**4/4 + 4*n**3 + 9*n**2/2 - 22. Factor o(j).
3*j*(j + 1)*(j + 3)
Suppose 7*a = 4*a + 87. Determine h so that 4*h + 71*h**2 - 8 - a*h**2 - 38*h**2 = 0.
-2, 1
Suppose -t + 54 = -3*u, -u = 2*u - 3*t + 48. Let l = u - -21. Determine d, given that d**2 - 4 + l*d**3 + d - 6*d**3 + 3*d**3 + 3*d = 0.
-2, 1, 2
Let k(o) = -o**2 - 20*o + 1. Let l be k(-20). Let b be (-1 + l)/((-5)/(-1 - -6)). Factor 0 + 3/5*f**4 + 3/5*f**5 - 6/5*f**3 + b*f**2 + 0*f.
3*f**3*(f - 1)*(f + 2)/5
Let c(x) = 3*x**2 - 20*x + 6. Let h(m) = m**2 - 7*m + 2. Let w(s) = -4*c(s) + 11*h(s). Factor w(q).
-(q - 2)*(q - 1)
Let y(i) be the third derivative of i**8/7560 + i**7/1890 - i**6/1620 - i**5/270 - 5*i**3/3 - 9*i**2. Let o(d) be the first derivative of y(d). Factor o(q).
2*q*(q - 1)*(q + 1)*(q + 2)/9
Let m(p) be the second derivative of -2*p**6/45 - 3*p**5/20 + 29*p**4/18 + 5*p**3/6 - p - 55. Suppose m(k) = 0. What is k?
-5, -1/4, 0, 3
Let b(l) be the first derivative of -l**6/6 - 21*l**5/5 - 147*l**4/4 - 343*l**3/3 - 115. Factor b(q).
-q**2*(q + 7)**3
Suppose -4*d = -5 - 11. Let c be (39/(-9) + d)*-6. Factor 135*y + c*y**3 - 135*y.
2*y**3
Suppose 0 = 4*p + 4*p + 96. Let h be 1 - (-4)/p*3. Determine w so that h + 2/7*w + 1/7*w**2 = 0.
-2, 0
Let j(p) be the first derivative of -2*p**3/39 + 96*p**2/13 - 4608*p/13 + 20. Factor j(a).
-2*(a - 48)**2/13
Let d = -8 + 8. Let 0*q**2 - 2*q**2 + d*q + 2*q = 0. Calculate q.
0, 1
Let t be (-17)/(714/(-12)) - 533/1890. Let c(j) be the third derivative of -t*j**5 + 0*j**3 - 1/54*j**4 + 0 + 0*j - 6*j**2. Factor c(r).
-2*r*(r + 2)/9
Suppose 217/3*r**3 + 8 - 49/3*r**4 + 188/3*r + 430/3*r**2 = 0. What is r?
-1, -2/7, 6
Let p = -2559 + 2559. Factor 0*k**2 + p + 0*k - 5/2*k**3.
-5*k**3/2
Factor -15/2*z**3 + 25/4*z - 5/2*z**2 - 5/4*z**4 + 5/4*z**5 + 15/4.
5*(z - 3)*(z - 1)*(z + 1)**3/4
Let t(h) be the first derivative of 2*h**5/75 + h**4/15 - 14*h**3/45 - 4*h**2/3 - 8*h/5 + 141. Solve t(f) = 0.
-2, -1, 3
Suppose -18*l = -12*l - 18. What is w in 9*w**2 + 19*w**2 - 2 - 29*w**2 + l*w = 0?
1, 2
Let m = -3/229 + -2971/458. Let v = m - -29/4. Factor -3/4*x**2 + v*x - 3/4*x**3 + 3/4.
-3*(x - 1)*(x + 1)**2/4
Let d = -234 - -381. Solve 42*m - 22*m**2 + 14*m**2 + 5*m**2 - d = 0.
7
Let o be -3 + 1 + (-519)/(-69). Let h = -1/46 + o. Factor -2 + 4*u + h*u**2 + 3/2*u**3.
(u + 2)**2*(3*u - 1)/2
Factor 38*b - 22/3*b**2 - 54 + 2/9*b**3.
2*(b - 27)*(b - 3)**2/9
Let u(d) be the third derivative of -d**5/20 + d**4/4 + 3*d**3/2 + 2*d**2 + 6. What is b in u(b) = 0?
-1, 3
Let r(k) = 4*k + 12. Let a be r(-2). Let l(s) be the third derivative of -3*s**2 + 0 - 1/12*s**a + 0*s + 0*s**3 + 1/15*s**5 - 1/60*s**6. Factor l(b).
-2*b*(b - 1)**2
Suppose 0*y + 4 = y. Factor 19*i**3 - 4*i**2 - 7*i**3 - 8*i**4 + 0*i**y.
-4*i**2*(i - 1)*(2*i - 1)
Let j(s) be the third derivative of s**7/315 + s**6/36 - 7*s**5/30 + 23*s**4/36 - 8*s**3/9 + 68*s**2. Determine x so that j(x) = 0.
-8, 1
Let l(j) be the first derivative of 11 + 0*j + 0*j**2 - 1/32*j**4 - 1/24*j**3. Let l(v) = 0. Calculate v.
-1, 0
Let o(a) be the third derivative of -a**6/180 - 7*a**5/90 + 48*a**2. Factor o(v).
-2*v**2*(v + 7)/3
Let b(v) = 7*v**3 + 2*v**2 + 4*v. Suppose -k - 36 = -9. Let n(c) = 48*c**3 + 15*c**2 + 27*c. Let r(s) = k*b(s) + 4*n(s). Solve r(u) = 0.
-2, 0
Let b(w) be the first derivative of w**5/80 - w**4/48 - w**3/4 - 2*w - 25. Let i(q) be the first derivative of b(q). Let i(p) = 0. What is p?
-2, 0, 3
Factor 0 - 56/3*d**2 - 4*d - 7/3*d**3 + 3*d**4.
d*(d - 3)*(d + 2)*(9*d + 2)/3
Let a = 411 - 407. Let f(w) be the first derivative of -4/3*w**3 + 4/3*w**2 - 2/3*w + 2/3*w**4 + a - 2/15*w**5. Factor f(g).
-2*(g - 1)**4/3
Let w(k) be the third derivative of k**6/150 - k**5/75 - 2*k**2 - 64. Factor w(u).
4*u**2*(u - 1)/5
Let l(x) be the first derivative of 2/9*x + 2/9*x**2 + 2/27*x**3 + 4. Suppose l(m) = 0. Calculate m.
-1
Suppose 25*i = 12*i. Suppose 128*a - 131*a = i. Factor 1/4*r**2 + a + 0*r - 1/4*r**3.
-r**2*(r - 1)/4
Let g(y) be the second derivative of y**6/20 + 3*y**5/40 - 41*y. Factor g(b).
3*b**3*(b + 1)/2
Let j(x) be the first derivative of -2*x**3/11 + 156*x**2/11 - 4056*x/11 - 90. Factor j(l).
-6*(l - 26)**2/11
Let g(l) be the first derivative of 8/3*l**2 - 2*l**6 - 7/3*l**4 - 16/3*l**3 + 32/5*l**5 - 7 + 0*l. Find v, given that g(v) = 0.
-2/3, 0, 1/3, 1, 2
Let q = 74 + -71. Factor -117*v**q + 231*v**3 + 2*v + 12*v**2 - 96*v**3.
2*v*(3*v + 1)**2
Let j be (238/(-51) - -5)*(-2 + 8). Find t such that -1/2*t