153*v**5/80 - 109*v**4/48 + 31*v**3/24 - 3*v**2/8 - 502*v. Find f, given that z(f) = 0.
1/4, 1, 3
Let j(l) = -6 - 2*l**2 - 5*l**3 + 0*l**2 + 74*l - 33*l - 40*l. Let u(t) = -t**4 + t**3 - t**2 - 1. Let y(n) = -j(n) + 6*u(n). Solve y(h) = 0 for h.
-1/6, 0, 1
Factor -49/2 - 195/8*m + 1/8*m**2.
(m - 196)*(m + 1)/8
Let o(r) be the first derivative of r**6/90 + r**5/15 - 11*r**3/3 + 32. Let n(x) be the third derivative of o(x). Factor n(l).
4*l*(l + 2)
Factor 15/8*r**2 + 7/8*r**3 + 13/8*r + 1/2 + 1/8*r**4.
(r + 1)**3*(r + 4)/8
Let g be ((-38)/(-57))/(0 + -2) - (-7)/21. Find b such that 0 - 5/2*b**2 + g*b = 0.
0
Let i be 21/(2*(-9)/48). Let p = -54 - i. Factor -1/4*u**3 + 1/4*u - 1/4*u**p + 1/4.
-(u - 1)*(u + 1)**2/4
Let i(z) be the first derivative of z**7/490 + z**6/168 - z**5/210 + 27*z**2/2 + 27. Let j(s) be the second derivative of i(s). Factor j(q).
q**2*(q + 2)*(3*q - 1)/7
Let o(r) be the third derivative of r**6/1380 + r**5/690 - 2*r**2 + 7*r. Let o(z) = 0. Calculate z.
-1, 0
Factor j**5 - 81*j**2 - j**4 - 43*j**2 - 38*j**3 + 268 - 79*j - 73*j - 332.
(j - 8)*(j + 1)*(j + 2)**3
Let z(n) = n**2 + 1. Let p(k) = -7*k**2 - 23*k + 5. Let m(g) = -p(g) - 5*z(g). Let v be m(-12). Solve -1/3*y**3 - y**v + 4/3*y + 0 = 0.
-4, 0, 1
Let w(d) be the third derivative of -d**5/15 - 8*d**4/3 - 466*d**2. Solve w(y) = 0 for y.
-16, 0
Let y(c) be the first derivative of 3 + 1/3*c**3 + 0*c**2 + 1/3*c**4 - 3*c + 1/10*c**5. Let x(t) be the first derivative of y(t). Suppose x(u) = 0. Calculate u.
-1, 0
Let g(s) = s**2 + 11*s - 99. Let v be g(6). Let o(m) be the second derivative of 8/15*m**v + 16/5*m**2 + 0 - 7*m + 1/30*m**4. Factor o(i).
2*(i + 4)**2/5
Let u(f) be the first derivative of -5*f**4/4 - 5*f**3/3 + 5*f**2/2 + 5*f + 83. What is s in u(s) = 0?
-1, 1
Let a(z) = 5*z + 3*z + 7 + 2 + z**2 - 2*z. Let m be a(-5). Determine s, given that -2*s**3 + 0*s**3 - 4*s**3 + m*s**3 - 2*s**2 = 0.
-1, 0
Solve 15/4*u**2 - 99/8*u - 3/8*u**3 + 27/2 = 0 for u.
3, 4
Let d(x) be the first derivative of -x**6/3060 + x**5/510 + 6*x**3 + 21. Let l(j) be the third derivative of d(j). Factor l(o).
-2*o*(o - 2)/17
Let b(o) be the third derivative of -o**8/336 - o**7/105 + o**6/30 + o**5/30 - o**4/8 - 106*o**2. Factor b(i).
-i*(i - 1)**2*(i + 1)*(i + 3)
Suppose -1/2*k**2 - 5/2*k + 0 = 0. Calculate k.
-5, 0
Let b(r) be the third derivative of r**7/840 - 7*r**6/160 - 3*r**5/16 - 23*r**4/96 - 30*r**2. Factor b(m).
m*(m - 23)*(m + 1)**2/4
Let g = -33 + 35. Factor -4*l**4 + l**4 + 16*l**4 + 20*l**2 + g*l**4 + 65*l**3.
5*l**2*(l + 4)*(3*l + 1)
Let k = -14323 + 71617/5. Factor 3/5 - 4/5*w**2 + k*w + 1/5*w**4 - 2/5*w**3.
(w - 3)*(w - 1)*(w + 1)**2/5
Let i = 87 + -77. Let l(v) = v**3 - 11*v**2 + 8*v + 20. Let k be l(i). Factor k*c - 2/5*c**2 + 2/5.
-2*(c - 1)*(c + 1)/5
Let j = 7388 - 66031/9. Let v = j - 51. Factor -v*q**3 + 0 + 0*q + 2/9*q**2.
-2*q**2*(q - 1)/9
Let i = 65996/17 - 3882. Determine b so that 2/17 + 0*b - i*b**2 = 0.
-1, 1
Let h(m) = -4*m**4 - 48*m**3 + 4*m**2 + 160*m + 108. Let s(d) = d**3 - 2*d**2 - d + 1. Let b(o) = -h(o) + 4*s(o). Factor b(q).
4*(q - 2)*(q + 1)**2*(q + 13)
Let l(t) = t**2 + t - 21. Let x be l(-7). Suppose 3*d - 3*v + 19 = -8*v, 5*v = -2*d - x. Factor 1/3*g + 1/3*g**3 + 0 + 2/3*g**d.
g*(g + 1)**2/3
Let d(p) = -p. Let s be d(-3). Let v = 9/2 - s. Suppose -v*a + 0*a**2 + 3/2*a**3 + 0 = 0. Calculate a.
-1, 0, 1
Factor -1608908 - 1095*q**2 - 80883*q + 16*q**3 - 336177 + 948*q + 13*q**3 - 34*q**3.
-5*(q + 73)**3
Let p = 46 + -42. Let j be 4/10 + (6 - 2 - p). Factor -j - 10*x**2 - 4*x.
-2*(5*x + 1)**2/5
Let k(z) be the third derivative of -2*z**7/105 + 19*z**6/30 - 29*z**5/5 + 121*z**4/6 - 104*z**3/3 - 5*z**2 - 26. Determine c, given that k(c) = 0.
1, 4, 13
Let d = 6 + -4. Let a = -241/4 - -61. Find r such that a*r**3 + 1/2 + 2*r**d + 7/4*r = 0.
-1, -2/3
Let d(k) be the first derivative of k**5/6 - 25*k**4/24 + 5*k**3/6 + 15*k**2/4 - 124. Determine b, given that d(b) = 0.
-1, 0, 3
Let z(x) be the second derivative of 5*x + 0 - 1/4*x**4 + 0*x**2 - x**3. Factor z(p).
-3*p*(p + 2)
Let f(x) be the third derivative of -x**5/180 - 29*x**4/36 - 841*x**3/18 - 72*x**2. Factor f(g).
-(g + 29)**2/3
Find l, given that 4*l**3 + 2 - 263*l**2 - 264*l**2 + 0 + 785*l**2 - 4*l - 260*l**2 = 0.
-1, 1/2, 1
Let j(r) be the first derivative of 8 - 12/5*r**5 - 2*r**4 - 1/2*r**3 + 8*r + 0*r**2. Let v(z) be the first derivative of j(z). Find h such that v(h) = 0.
-1/4, 0
Let j = 661 - 661. Let d(q) be the third derivative of -1/48*q**4 - 1/120*q**5 - 7*q**2 + 0 + 0*q + j*q**3. Factor d(c).
-c*(c + 1)/2
Let k(t) be the third derivative of -t**6/320 + 13*t**5/160 + t**4/16 - 13*t**3/4 + 4*t**2 - 16. Determine f so that k(f) = 0.
-2, 2, 13
Let t(q) = 3*q**2 + 3*q - 10. Let k(b) = 2*b**2 + 4*b - 9. Let h(f) = -4*k(f) + 3*t(f). Let o be h(6). Factor o - 4/5*l + 4/5*l**3 + 0*l**2.
4*l*(l - 1)*(l + 1)/5
Let i(p) = -40*p**2 - 25*p + 14. Let u(v) = -10*v**2 - 6*v + 4. Let f(h) = -6*i(h) + 22*u(h). Factor f(m).
2*(2*m + 1)*(5*m + 2)
Let z(y) be the first derivative of y**8/1260 + y**7/210 - 2*y**6/135 - y**3 + 6. Let s(x) be the third derivative of z(x). Factor s(a).
4*a**2*(a - 1)*(a + 4)/3
Let s(y) be the first derivative of 2/9*y - 2/27*y**3 + 28 + 1/9*y**2 - 1/18*y**4. Factor s(k).
-2*(k - 1)*(k + 1)**2/9
Let 1 - 2120*j - 1 - 22*j**4 + 3*j**5 - 52*j**2 + 55*j**3 + 2132*j = 0. What is j?
0, 1/3, 2, 3
Let n be (-3)/(3/(-11)) + (-18)/6. Let s be (-2 - (-6 + 1))/(42/n). Factor 2/7*k**3 + 0 - 6/7*k**2 + s*k.
2*k*(k - 2)*(k - 1)/7
Suppose -14 = 13*o - 27*o. Let j(w) be the first derivative of 4*w - 2/3*w**3 + o + w**2. Factor j(p).
-2*(p - 2)*(p + 1)
What is x in -44*x**2 - 5*x**4 + 20*x + 14*x**4 - 4*x**4 - 140*x - 110*x**3 - 191*x**2 = 0?
-1, 0, 24
Factor 4/9 - 10/9*s - 32/9*s**2 - 2*s**3.
-2*(s + 1)**2*(9*s - 2)/9
Let q(z) be the first derivative of 2*z**3/9 + 20*z**2/3 + 24*z - 236. Find g such that q(g) = 0.
-18, -2
Let r(w) be the first derivative of -w**7/3780 - w**6/1620 + w**5/540 + w**4/108 + 11*w**3/3 - 12. Let b(g) be the third derivative of r(g). Factor b(z).
-2*(z - 1)*(z + 1)**2/9
Let c = -1956/11 - -178. Suppose 2*q = -3*q. Factor -2/11*w**5 + 6/11*w**4 - 6/11*w**3 + 0 + c*w**2 + q*w.
-2*w**2*(w - 1)**3/11
Let i(h) = -h**2 + 19*h + 5. Let p be i(19). Let -964*f**4 - 1836*f**4 - 580*f**3 + 235*f**2 - 5 + 9104*f**5 + 10*f - 1104*f**p = 0. What is f?
-1/5, 1/4
Let w be (-3)/(-30) + 2/(-20). Let l(a) be the second derivative of -7/20*a**5 + 6*a - 3/4*a**4 + 0*a**2 + w - 1/3*a**3. Let l(v) = 0. Calculate v.
-1, -2/7, 0
Factor -9*m**2 + 18*m**3 + 29*m**2 - 3*m**4 - 35*m**2.
-3*m**2*(m - 5)*(m - 1)
Let o = -113 - -113. Suppose -3*k**3 + o*k - 2*k**2 + 2 + 5*k - k - k = 0. Calculate k.
-1, -2/3, 1
Let a(h) be the third derivative of -11*h**6/40 + 16*h**5/5 - 19*h**4/2 - 8*h**3 - h**2 - 33*h. Factor a(o).
-3*(o - 4)*(o - 2)*(11*o + 2)
Suppose 0 = -3*s + w - 0 - 6, -15 = 5*w. Let n be (-6 + 60/16)/s. Solve 0 + 3/4*c - n*c**2 = 0.
0, 1
Let d(z) be the third derivative of -z**5/120 - 7*z**4/48 + 5*z**3/2 - 13*z**2 - 2*z. Solve d(m) = 0 for m.
-10, 3
Factor -529/4 - 23/2*i - 1/4*i**2.
-(i + 23)**2/4
Factor 4/17*f - 14/17*f**3 + 0 + 26/17*f**2.
-2*f*(f - 2)*(7*f + 1)/17
Factor 4/5*t**3 - 1/5*t**4 + 0*t + 0 - 3/5*t**2.
-t**2*(t - 3)*(t - 1)/5
Let q(z) be the second derivative of -z**7/72 + z**6/16 - z**5/12 + z**4/2 - 10*z. Let f(r) be the third derivative of q(r). Factor f(c).
-5*(c - 1)*(7*c - 2)
Let i be (-2)/3*(105/(-14))/(-1). Let d(m) = 3*m**3 + 13*m**2 - 7*m - 9. Let x(t) = 3*t**3 + 14*t**2 - 8*t - 9. Let n(y) = i*d(y) + 4*x(y). Factor n(s).
-3*(s - 1)*(s + 1)*(s + 3)
Let o(t) be the first derivative of -5*t**4/4 - 835*t**3/3 + 1685*t**2/2 - 845*t - 449. Find q, given that o(q) = 0.
-169, 1
Let s(b) be the second derivative of b**7/105 - b**6/30 + b**5/50 + b**4/15 - 2*b**3/15 + b**2/10 - 11*b + 1. Solve s(g) = 0 for g.
-1, 1/2, 1
Let k(b) be the second derivative of -b**6/1620 + b**5/270 + b**4/36 + 13*b**3/2 - 6*b. Let o(x) be the second derivative of k(x). Factor o(f).
-2*(f - 3)*(f + 1)/9
Let r(v) be the second derivative of v**5/80 + 37*v**4/48 + 323*v**3/24 - 361*v**2/8 + 69*v. Determine x so that r(x) = 0.
-19, 1
Let k(v) be the third derivative of 77*v**6/600 + 97*v**5/300 + v**4/15 - 