 third derivative of -r**7/2940 - r**6/1260 + r**5/420 + r**4/84 + r**3/6 + 2*r**2. Let i(s) be the first derivative of t(s). Solve i(u) = 0.
-1, 1
Let v(l) = l**2 - 2*l + 1. Let b be v(3). Suppose -3*k**3 - 2*k**3 + k**4 + 4*k**3 - 3*k**b = 0. What is k?
-1/2, 0
Suppose -2*y + 7*t - 6*t = -8, 2*y + 3*t = 16. Let 4*o - 3*o + 1 - y*o + o**2 + 2*o = 0. What is o?
1
Suppose g - b = -2*g + 3, -3*b = -4*g - 1. Let z(n) be the second derivative of 0*n**5 + 2*n + 1/5*n**g + 0 - 1/15*n**4 + 0*n**3 + 1/75*n**6. Factor z(i).
2*(i - 1)**2*(i + 1)**2/5
Let t(l) = -8*l + 4. Let n be t(-3). Let v = n - 18. Factor -10*j + v*j + 2*j**3 - 2*j**2.
2*j**2*(j - 1)
Let x(k) be the third derivative of 1/3*k**3 + 1/120*k**6 + 1/8*k**4 + 1/20*k**5 + 0*k + 0 + 3*k**2. Let m(o) be the first derivative of x(o). Factor m(d).
3*(d + 1)**2
Let o = 24 - 4. Let j be 3/4*o/5. Find m, given that 3*m + 0*m**2 - 3*m**2 - 5*m - 1 - m**j - m = 0.
-1
Suppose 3*z - g = -0*z + 11, 3*z - 3*g = 21. Factor 2/3*h**z + 0 + h**4 + 0*h + 7/3*h**3.
h**2*(h + 2)*(3*h + 1)/3
Let x = 2245/7882 - -1/1126. Solve 4/7 + 8/7*j**2 - x*j**3 - 10/7*j = 0.
1, 2
Factor 10 - 2*q**3 - 3*q**3 - 10.
-5*q**3
Let r = 108617/666 - -89/666. Let z = r + -163. Factor 0 + 0*w - z*w**2.
-2*w**2/9
Let a(c) be the third derivative of c**8/336 + c**7/105 - c**6/120 - c**5/30 - 6*c**2. Factor a(f).
f**2*(f - 1)*(f + 1)*(f + 2)
Let j(v) be the second derivative of 27*v**5/100 - 3*v**4/4 - 16*v**3/5 - 18*v**2/5 - v. Determine y so that j(y) = 0.
-2/3, 3
Let d = 99 + -92. Let s(i) be the third derivative of 0 - 1/30*i**5 + 0*i**4 + 0*i**3 - 1/35*i**d - 1/168*i**8 - 1/20*i**6 - 4*i**2 + 0*i. Factor s(j).
-2*j**2*(j + 1)**3
Solve -4*r**2 + 9*r**2 + 6*r + 5 - 4*r**2 + 3 = 0 for r.
-4, -2
Let c(l) = -5*l**4 + 14*l**3 - 15*l**2 + 6*l + 2. Let p(x) = -11*x**4 + 29*x**3 - 30*x**2 + 12*x + 5. Let k(a) = -5*c(a) + 2*p(a). Factor k(w).
3*w*(w - 2)*(w - 1)**2
Let 4 + 16/3*l + 4/3*l**2 = 0. What is l?
-3, -1
Suppose -2/21*b**3 + 0 - 2/21*b - 4/21*b**2 = 0. Calculate b.
-1, 0
Let h(a) be the first derivative of 8*a**5/25 + a**4 - 4*a**3/5 - 12. Let h(c) = 0. What is c?
-3, 0, 1/2
Let n be 66/(-12) + 6 + 1/(-2). Factor 4/7*x**3 - 2/7*x**4 + 0*x - 2/7*x**2 + n.
-2*x**2*(x - 1)**2/7
Suppose -5*y - 68 = -5*b - 13, -2*b + 2 = 3*y. Factor 3*o + 6*o - o - b*o + 2*o**4 - o**5 - 2*o**2.
-o*(o - 1)**3*(o + 1)
Suppose -1215*u - 1498 - 135*u**2 - 7*u**3 + 2*u**3 - 2147 = 0. Calculate u.
-9
Let f(b) be the first derivative of 2*b**5/35 + 3*b**4/14 + 2*b**3/21 - 3*b**2/7 - 4*b/7 + 5. Factor f(l).
2*(l - 1)*(l + 1)**2*(l + 2)/7
Let d = -6 + 6. Suppose 27 = -0*b + b + 5*z, -5*z = 3*b - 31. Solve 1/3*u**4 + 0 + 0*u + d*u**3 + 0*u**b = 0 for u.
0
Suppose -5*g + 84 = -1. Factor -y**5 - g*y**4 - 2*y + y**2 + 8*y**5 + 36*y**4 + 15*y**3.
y*(y + 1)**3*(7*y - 2)
Let a be -8*(-2)/((-4)/(-2)). Let p = a - 5. Factor 5 + 2*f**4 - 5 + 2*f**p.
2*f**3*(f + 1)
Let b = 5/91 + 491/1001. Find l, given that 16/11 - 8/11*l - b*l**3 - 20/11*l**2 = 0.
-2, 2/3
Let l(x) be the second derivative of -1/30*x**5 - x**6 + 0 - 8/3*x**3 + 4/3*x**2 + 3*x + 25/63*x**7 + 41/18*x**4. Find m, given that l(m) = 0.
-1, 2/5, 1
Let b(d) = -d - 3. Let j be b(0). Let y be 0/(0 - -2) - j. Factor 0*h + 6*h**3 - 3*h**5 - 3*h + 2*h**4 - 6*h**2 + 0*h**4 + h**4 + y.
-3*(h - 1)**3*(h + 1)**2
Let p = 18 - 10. Let v be p/10*10/4. Factor g**2 + 2*g - g + 17*g - 4*g**v - 27.
-3*(g - 3)**2
Suppose 0 = 4*h + 12, 2*s + h - 3 = -0. Let q(t) be the third derivative of 2*t**2 + 1/12*t**4 + 0*t + 0 + 1/60*t**5 + 1/6*t**s. Let q(g) = 0. What is g?
-1
Factor 2/7*b**4 + 6/7 - 8/7*b**2 - 4/7*b**3 + 4/7*b.
2*(b - 3)*(b - 1)*(b + 1)**2/7
Let f be (-12)/(-20)*(4 + 1). Factor 0 + 1/3*t + 0*t**2 - 1/3*t**f.
-t*(t - 1)*(t + 1)/3
Factor 1 - 5*b**2 - 4 - 7*b**2 - 3 + 27*b.
-3*(b - 2)*(4*b - 1)
Let m(s) be the third derivative of 0*s**3 - 1/300*s**5 + 0*s + 1/60*s**4 + 0 - s**2. Factor m(r).
-r*(r - 2)/5
Let b be (18/132)/((-3)/(-4)). Determine v so that 4/11*v + b*v**2 + 0 = 0.
-2, 0
Let f(d) be the second derivative of -d**6/60 + d**2/2 - 2*d. Let l(k) be the first derivative of f(k). Factor l(n).
-2*n**3
Factor 3/4 + 3/2*k + 3/4*k**2.
3*(k + 1)**2/4
Let v be 2/(-9) - 40/(-18). Let q(x) = x**3 + 8*x**2 + 6*x - 2. Let t be q(-7). Let -2 + 3*c**3 - 8*c**2 - c**4 + t*c**2 + v + c = 0. What is c?
0, 1
Let n(f) = 2*f**2 + 20*f + 48. Let x(s) = -8*s**2 - 80*s - 191. Let v(j) = 18*n(j) + 4*x(j). Solve v(y) = 0 for y.
-5
Let z(w) be the second derivative of -2*w**7/21 + 6*w**6/5 - 32*w**5/5 + 56*w**4/3 - 32*w**3 + 32*w**2 - 7*w. Let z(r) = 0. What is r?
1, 2
Let a = -5 - -7. Solve 2*b + 2 + b**2 - a*b + 3*b = 0.
-2, -1
Let k(c) = 18*c - 178. Let g be k(10). Find t, given that 0*t + 1/2*t**4 + 0 - 1/2*t**g + 2*t**3 - 2*t**5 = 0.
-1, 0, 1/4, 1
Factor 5/3*t + 1/6*t**2 + 25/6.
(t + 5)**2/6
Factor 4/3*o - 16/9 - 2/9*o**2.
-2*(o - 4)*(o - 2)/9
Suppose -h + 2*c = -13, -3*c - c - 1 = 3*h. Let l(x) be the first derivative of -1/20*x**4 + 0*x + h + 1/15*x**3 + 1/5*x**2. Factor l(y).
-y*(y - 2)*(y + 1)/5
Let a(n) = -4*n. Let v be a(-2). Determine o so that -4*o - o - 2*o**3 + v*o - o = 0.
-1, 0, 1
Let b(x) = -x**2 - 3*x - 4. Let r be b(-3). Let o = 8 + r. Factor -5*w**2 - 4*w**3 - 3*w + 2*w**4 + w - 3*w**o.
-w*(w + 1)**2*(w + 2)
Solve 5/3*s**2 + 0 - 4/3*s**3 - 2/3*s + 1/3*s**4 = 0 for s.
0, 1, 2
Let i(v) = 5*v**3 - 5*v**2 - 3*v - 3. Let a(y) = -4*y**3 + 4*y**2 + 2*y + 2. Let f(k) = -3*a(k) - 2*i(k). Factor f(d).
2*d**2*(d - 1)
Factor 0 - 4/9*m**4 + 14/9*m**5 + 0*m**3 + 0*m**2 + 0*m.
2*m**4*(7*m - 2)/9
Let s(z) = -10*z**3 + 11*z**2 - 20*z + 5. Let y(r) = 3*r**3 - 4*r**2 + 7*r - 2. Let u(w) = 6*s(w) + 21*y(w). Factor u(l).
3*(l - 4)*(l - 1)**2
Let d(v) = v**3 + v. Let t(n) = 15*n**3 - 35*n**2 - 55*n - 45. Let r(a) = -20*d(a) + t(a). Solve r(o) = 0.
-3, -1
Suppose 8 = 2*m + 2*m. Let j be 5/7*(-90)/(-25). Suppose 32/7*l**m + j*l**3 + 0 - 8/7*l = 0. Calculate l.
-2, 0, 2/9
Let t be (-1)/(-4) + (-39)/300. Let h = 13/100 + t. Determine r, given that 3/4*r**2 + 3/4*r + 1/4*r**3 + h = 0.
-1
Let t be (1/3)/((-6)/(-9)). Let a be (((-4)/(-6))/((-2)/3))/(-2). Determine n, given that 0 - 1/2*n**4 + 0*n - a*n**3 + 1/2*n**2 + t*n**5 = 0.
-1, 0, 1
Suppose y + y = 4. Let t be 14/10 - (-3)/5. Solve 1 + 3*c**3 - 2*c**t - 4*c - c**2 + c + y = 0 for c.
-1, 1
Let g be (-5 - -5)/(2/1). Let v(q) be the third derivative of 1/60*q**5 - 1/240*q**6 + 0 - 1/48*q**4 - q**2 + g*q + 0*q**3. Factor v(x).
-x*(x - 1)**2/2
Let k(z) = 205*z**3 + 365*z**2 + 197*z + 37. Let j(i) = 512*i**3 + 912*i**2 + 492*i + 92. Let o(n) = -5*j(n) + 12*k(n). Factor o(q).
-4*(q + 1)*(5*q + 2)**2
Let z(d) be the first derivative of -d**6/120 + d**5/60 + d**4/24 - d**3/6 - 3*d**2/2 + 3. Let j(h) be the second derivative of z(h). Solve j(a) = 0 for a.
-1, 1
Suppose -5*g + 238 = -377. Let o = g - 853/7. Let -o*t**3 + 2/7*t - 6/7*t**2 + 0 = 0. What is t?
-1, 0, 1/4
Suppose -4*b + 10 = 5*m, 4*m = 3*b + 8*m - 8. Let t(j) be the second derivative of b*j**2 + 0 - 1/110*j**5 + 0*j**3 - 1/66*j**4 - 3*j. Factor t(d).
-2*d**2*(d + 1)/11
Let h = -191/4 - -48. Let a(p) be the first derivative of -h*p + 1/4*p**2 - 1/8*p**4 + 2 + 0*p**3 + 1/20*p**5. Suppose a(t) = 0. Calculate t.
-1, 1
Let q(g) = -g**3 + g**2 + g + 1. Let d(i) = 3*i**3 + 3*i**2 - 3*i - 13. Let n(v) = d(v) + 5*q(v). Factor n(r).
-2*(r - 4)*(r - 1)*(r + 1)
Let f = 6 + -2. Let o = 1 + f. Factor 1/2*l**4 + 1/4*l**o + 0*l**2 + 0*l + 1/4*l**3 + 0.
l**3*(l + 1)**2/4
Let u(c) be the first derivative of c**5/20 - c**4/2 + 2*c**3 - 4*c**2 - 8. Let p(t) be the second derivative of u(t). Factor p(g).
3*(g - 2)**2
Solve -5*v - 1/4*v**2 - 25 = 0 for v.
-10
Let n be ((-8)/12)/(1/3). Let w be n/(-3) - 24/(-18). Factor j**4 + 2*j**5 + 2*j**5 - 3*j**3 - j**3 - j**w.
j**2*(j - 1)*(j + 1)*(4*j + 1)
Let p(j) = j**4 - j**3. Let f(r) = -12*r**4 + 8*r**3. Let z(k) = f(k) + 8*p(k). Solve z(a) = 0.
0
Let r = 14 + -9. Let f(s) be the second derivative of -2*s + 0*s**2 - 1/40*s**r - 1/48*s**4 + 0*s**3 + 0 - 1/120*s**6. Find z such that f(z) = 0.
-1, 0
Let o(b) be the third derivative of -b**7/180 + b**6/360 + 7*b**5/360 - b**4/72 + 5*b**2. Find u, given that o(u) = 0.
-1, 0, 2/7, 1
Let d be ((-1)/(-54)*-1)/(21/(-63)). Let z(i) be the first derivative of 2/27*i**3 - 2/