t(w) = -w + 34. Let v be t(c). Find n, given that 21*n - 12*n**3 + 6*n**2 + v - 28 + 3*n**3 = 0.
-1, -1/3, 2
Let d(f) be the third derivative of f**5/240 - f**4/16 - 414*f**2. Factor d(c).
c*(c - 6)/4
Let x(i) be the second derivative of 3*i**5/20 + i**4/4 - 8*i**3 + 30*i**2 - 6*i + 2. Let x(m) = 0. What is m?
-5, 2
Factor 9/4*v - 2*v**3 - 1 - 1/4*v**5 - 1/2*v**2 + 3/2*v**4.
-(v - 4)*(v - 1)**3*(v + 1)/4
Suppose -m - 5 = 0, -447*p + 451*p = 4*m + 32. Factor -4/5*u**2 + 4/5*u + 1/5*u**5 - 3/5*u**p + 2/5*u**4 + 0.
u*(u - 1)**2*(u + 2)**2/5
Suppose -4*g = -y - 58, 5*g + 2*y + 3*y - 85 = 0. Factor -30*u + 20*u - 5*u**4 - g*u**3 + 5*u**5 - 25*u**2 + 0*u**5 + 10*u**4.
5*u*(u - 2)*(u + 1)**3
Suppose -5*j + 5 = -2*f, 66 - 35 = 5*f + 2*j. Find c such that -2/5*c**4 - 1/5*c + 1/5*c**f + 2/5*c**2 + 0 + 0*c**3 = 0.
-1, 0, 1
Let i(j) = 9*j**3 + 164*j**2 + 35*j - 18. Let o be i(-18). Suppose 0*d - 1/3*d**2 + o = 0. What is d?
0
Suppose 0 = -2*a - 4*h + 36, -4*a + h + 27 = -0*h. Determine f, given that -30*f + a*f - 9*f**3 - 38*f**2 - 22*f - 8 = 0.
-2, -2/9
Let u(p) be the third derivative of p**5/20 + 5*p**4/4 + 9*p**3/2 - 164*p**2. Factor u(x).
3*(x + 1)*(x + 9)
Let z(t) be the second derivative of t**6/90 + t**5/6 + 7*t**4/12 - 2*t**3 - 18*t**2 + 19*t - 2. Solve z(f) = 0.
-6, -3, 2
Suppose -243 = 5*d + 2*v, d + v + 11 = -40. Let q = d + 47. Factor 2/3*n**2 + 0*n + q - 1/3*n**3.
-n**2*(n - 2)/3
Let s be -2*(-1 + 4)*1329/(-81). Let p = s + -98. Factor -2/9 - p*u - 2/9*u**2.
-2*(u + 1)**2/9
Let y(c) be the first derivative of c**6/18 - 13*c**5/15 + 21*c**4/4 - 143*c**3/9 + 76*c**2/3 - 20*c - 140. Determine n so that y(n) = 0.
1, 2, 3, 5
Let l be 144/2856*17*(-3)/(-9). Factor l*g**3 - 2*g + 8/7 + 4/7*g**2.
2*(g - 1)**2*(g + 4)/7
Let v(x) be the first derivative of 2*x**6/5 - 81*x**5/25 + 111*x**4/20 - 9*x**3/5 - 3*x**2/2 + 35. Suppose v(s) = 0. Calculate s.
-1/4, 0, 1, 5
Let q(t) be the third derivative of t**8/5040 + t**7/1890 + 3*t**4/8 - 11*t**2. Let j(b) be the second derivative of q(b). Factor j(l).
4*l**2*(l + 1)/3
Suppose 2*v - 9*d = -13*d + 6, d + 3 = v. Let h(t) be the first derivative of -8/3*t**v + 0*t - 7 - 4/5*t**5 + 5/2*t**4 + t**2. Factor h(s).
-2*s*(s - 1)**2*(2*s - 1)
Let d(i) be the third derivative of i**6/30 + 8*i**5/5 + 32*i**4 + 1024*i**3/3 + 186*i**2. Factor d(p).
4*(p + 8)**3
Suppose -167*r = -175*r + 32. Let p be 40/(-6)*1/(-4). Factor p*c**3 + 4/3*c - 8/3*c**2 - 1/3*c**r + 0.
-c*(c - 2)**2*(c - 1)/3
Find y such that 1/9*y**2 + 529 - 46/3*y = 0.
69
Suppose -15 = -3*z, -14*z = 3*v - 12*z - 28. Let a(b) be the first derivative of 1/2*b**4 + 0*b**3 - 2 + 0*b - 1/2*b**2 - 1/6*b**v + 0*b**5. Factor a(i).
-i*(i - 1)**2*(i + 1)**2
Let y(t) be the third derivative of -t**6/30 + 4*t**5/15 - t**4/2 - 27*t**2. Factor y(q).
-4*q*(q - 3)*(q - 1)
Suppose -51*h = -52*h + 2. Find w such that -8 + 4*w + 8 + 2*w**h - 4*w**3 - 7*w**4 + 5*w**4 = 0.
-2, -1, 0, 1
Let c = -39524 + 830416/21. Let b = -58/3 + c. Solve 2/7*l**4 + 2/7*l - b*l**2 - 2/7*l**3 + 0 = 0.
-1, 0, 1
Let k be 4/6 - (-66)/9. Suppose -2*y - 6 = 5*q, -4*q - 2*y = -2 + k. Factor -54 - 4*g**4 - 72*g**2 + 24*g + q*g**4 + 2*g**4 + 84*g + 20*g**3.
-2*(g - 3)**3*(g - 1)
Find j, given that 34/13*j**3 - 2/13*j**4 - 34/13*j + 0 + 2/13*j**2 = 0.
-1, 0, 1, 17
Let v(f) = f**3 + f**2. Let p(x) = 15*x**3 + 78*x**2 + 420*x + 600. Let k(g) = p(g) - 12*v(g). Factor k(b).
3*(b + 2)*(b + 10)**2
Let b(t) be the second derivative of 5*t - 5/42*t**3 - 1/84*t**4 + 0 - 2/7*t**2. Solve b(v) = 0 for v.
-4, -1
Suppose -8*o = -2 - 46. Let j(n) be the second derivative of -2*n - 1/15*n**o + 8/3*n**3 + n**4 + 0 + 0*n**5 + 3*n**2. Solve j(r) = 0.
-1, 3
Let a(h) be the first derivative of -h**5 - 35*h**4 - 130*h**3/3 + 70*h**2 + 135*h + 196. Find w such that a(w) = 0.
-27, -1, 1
Suppose 0 = 20*y - 43 - 17. Determine q so that 6/7*q**4 - 39/7*q + 6/7 + 78/7*q**y - 39/7*q**5 - 12/7*q**2 = 0.
-1, 2/13, 1
Suppose 2*t = 7*t + 100. Let n be t - -27 - (0 - 4). Factor 3*k**3 + 3*k + 6 - 6*k**2 - n + 5.
3*k*(k - 1)**2
Let 2/11*l**3 + 12/11*l**2 - 28/11 - 18/11*l = 0. Calculate l.
-7, -1, 2
Let r = 74 - 72. Suppose -17*j - 11*j + 2*j**r + 14*j = 0. Calculate j.
0, 7
Let n(t) be the first derivative of -4*t**3/3 - 54*t**2 + 99. What is x in n(x) = 0?
-27, 0
Let y be 18 - (11 - 4) - 8. Factor 0 - 2/3*r**y - 1/3*r**4 - 1/3*r**2 + 0*r.
-r**2*(r + 1)**2/3
Let o(x) be the second derivative of -x**6/540 + x**5/72 + x**4/24 + 3*x**3/2 + 18*x. Let k(f) be the second derivative of o(f). Factor k(r).
-(r - 3)*(2*r + 1)/3
Suppose s = -5*k + 12, -2*s + 5*k = -0*s + 6. Let f be 0 + 0/2 + 0. Find m, given that -2/3*m + f + 2/3*m**s = 0.
0, 1
Let i(q) be the third derivative of q**8/2016 - 31*q**7/252 + 1247*q**6/144 - 3557*q**5/72 + 2185*q**4/18 - 1444*q**3/9 - 11*q**2. Find r such that i(r) = 0.
1, 76
Let f(g) = -11*g**2 + 90*g - 679. Let b(j) = 9*j**2 - 90*j + 678. Let m(r) = 4*b(r) + 3*f(r). Factor m(k).
3*(k - 15)**2
Let h(c) = -c**4 - 16*c**3 + 24*c**2 + 7*c + 7. Let d(j) = -9*j**3 + 12*j**2 + 3*j + 3. Let o(k) = -7*d(k) + 3*h(k). Let o(f) = 0. Calculate f.
0, 1, 4
Factor -52/11 + 2/11*x**2 + 50/11*x.
2*(x - 1)*(x + 26)/11
Let t(z) be the third derivative of -5/336*z**8 + 5/42*z**7 + 0 - 1/3*z**5 - 1/4*z**6 + 0*z + 5/3*z**4 + 18*z**2 + 0*z**3. Factor t(k).
-5*k*(k - 2)**3*(k + 1)
Let y(z) be the third derivative of 0 + 1/2*z**3 + 0*z + 1/8*z**4 - 11*z**2 + 1/80*z**5. Factor y(c).
3*(c + 2)**2/4
Let h(d) = d**3 + d**2 + d. Let c(u) = -2*u**3 - 13*u**2 + 6*u. Let i(j) = -c(j) - 3*h(j). Suppose i(a) = 0. Calculate a.
0, 1, 9
Factor -4000 - 2/5*w**2 + 80*w.
-2*(w - 100)**2/5
Let q(w) be the first derivative of 3*w**4/4 + w**3 - 27*w**2/2 - 27*w - 4. Factor q(y).
3*(y - 3)*(y + 1)*(y + 3)
Find b such that 109*b**3 + 423*b**5 - 64*b - 875*b**5 + 432*b**5 - 32*b**4 - 13*b**3 + 128*b**2 = 0.
-2, 0, 2/5, 2
Let s(x) = 3*x**2 - 85*x. Let l(y) be the first derivative of -16*y**3/3 + 234*y**2 + 53. Let t(r) = -5*l(r) - 28*s(r). Suppose t(p) = 0. What is p?
0, 10
Let f(z) be the second derivative of z**6/20 - 9*z**5/20 + 3*z**4/8 + 5*z**3/2 - 394*z. Determine b, given that f(b) = 0.
-1, 0, 2, 5
Let z(b) be the first derivative of -b**4/12 - 25*b**3/3 - 625*b**2/2 - 15625*b/3 - 18. Factor z(y).
-(y + 25)**3/3
Let m(l) = -3*l**3 + 1166*l**2 + 43307*l + 548707. Let a(o) = -o**3 + 582*o**2 + 21654*o + 274354. Let u(w) = 13*a(w) - 6*m(w). Factor u(p).
5*(p + 38)**3
Let q = 333 - 329. Let t(u) be the third derivative of 0 + 0*u**6 + 0*u + 0*u**4 + 1/315*u**7 - q*u**2 - 1/90*u**5 + 0*u**3. Factor t(p).
2*p**2*(p - 1)*(p + 1)/3
Suppose -2*k = 2*k - 12. Let r be (-1)/5 - (3 + 41/(-5)). Find m such that 0*m + 1/4*m**k - 1/2*m**2 + 1/2*m**4 + 0 - 1/4*m**r = 0.
-1, 0, 1, 2
Suppose 2*q + 7*k - 5*k + 4 = 0, -2*q + 24 = -5*k. Let y(h) be the second derivative of 0*h**q + 1/33*h**3 + 1/110*h**5 - 7*h + 0 + 1/33*h**4. Factor y(d).
2*d*(d + 1)**2/11
Let u be (-14)/8*90/(-315). Let w(o) be the first derivative of 0*o + 4/3*o**3 - 5 + o**2 + u*o**4. Factor w(y).
2*y*(y + 1)**2
Suppose -p = 18*p - p. Factor -14/5*k**2 + p + 4/5*k.
-2*k*(7*k - 2)/5
Find c, given that 660*c - 140*c**2 - 245*c**4 - 180 - 843*c**3 - 159*c**2 + 73*c**3 + 114*c**2 = 0.
-2, 3/7
Let j(w) = -6*w**2 + 2*w + 12. Let c(a) = a**3 + 12*a**2 - 5*a - 26. Let h(s) = -2*c(s) - 5*j(s). Factor h(q).
-2*(q - 2)**2*(q + 1)
Let d(w) be the first derivative of w**5/60 - w**4/24 + 23*w**2/2 + 6. Let b(p) be the second derivative of d(p). Suppose b(z) = 0. Calculate z.
0, 1
Let i be 44/6 - (-16)/(-48). Suppose -1 = -4*y + i. Determine l, given that 5*l - 5*l**2 + 4*l**4 + 4 - 1 - 3*l**3 - y*l - 2 = 0.
-1, -1/4, 1
Factor 21/5*z + 3/5*z**2 + 36/5.
3*(z + 3)*(z + 4)/5
Determine c, given that 50*c**2 + 2*c**4 - 5*c**3 + 0*c**4 + 20*c - 70*c**2 + 3*c**4 = 0.
-2, 0, 1, 2
Let h = -50 - -48. Let w(j) = 12*j**2 + 15*j + 3. Let u(q) = -3*q**2 - 4*q - 1. Let l(y) = h*w(y) - 9*u(y). Factor l(m).
3*(m + 1)**2
Suppose -197 = -5*s + 38. Suppose 45*r = s*r - 8. Factor 0*k**2 - 1/5 + 2/5*k - 2/5*k**3 + 1/5*k**r.
(k - 1)**3*(k + 1)/5
Let p be (20/16*2)/((-10)/(-24)). Let s(a) be the second derivative of -1/6*a**5 + 0 - a + 1/9*a**4 + 2/45*a**p + 0*a**2 + 0*a**3. Factor s(n).
2*n**2*(n - 2)*(2*n - 1)/3
Let d(w) be the second deriva