 n**3 + 1/2*n**4.
n*(n - 3)*(n + 2)*(n + 3)/2
Let p = 68/103 - 678/1339. Factor 4/13*r + p*r**2 + 2/13.
2*(r + 1)**2/13
Let p(y) = y**2 - 1. Let k(v) = -4*v**2 + 16*v - 15. Let o(c) = k(c) + p(c). Suppose o(w) = 0. Calculate w.
4/3, 4
Let g be (-1*8/18)/((184/8)/(-138)). Let 2/3*a**2 + g*a + 2 = 0. Calculate a.
-3, -1
Let a(i) be the second derivative of -2/3*i**4 + 1/15*i**5 - 2*i**2 + 0 - 4*i - 8/3*i**3 + 1/30*i**6. Let k(b) be the first derivative of a(b). Factor k(l).
4*(l - 2)*(l + 1)*(l + 2)
Let m(v) = v**3 - 21*v**2 - 15*v - 8. Let l(u) = 10*u**2 + 8*u + 4. Let y(i) = 5*l(i) + 2*m(i). Let y(o) = 0. Calculate o.
-2, -1
Let n(g) be the second derivative of 2*g**7/5355 + 11*g**6/6120 + g**5/340 + 19*g**4/12 - 31*g. Let b(c) be the third derivative of n(c). Solve b(f) = 0 for f.
-1, -3/8
Suppose 0*g = 32*g - 128. Let k(m) be the second derivative of -1/25*m**5 - 8*m + 0 + 0*m**g + 2/15*m**3 + 0*m**2. Factor k(b).
-4*b*(b - 1)*(b + 1)/5
Let r(y) be the third derivative of 21*y**2 + 0*y - 9/10*y**5 - 1/12*y**6 + 0 - 8/3*y**3 - 5/2*y**4. Find s such that r(s) = 0.
-4, -1, -2/5
Let b(v) be the third derivative of 0*v + 9/2*v**3 + 0 + 1/20*v**5 + 21*v**2 + 3/4*v**4. Factor b(o).
3*(o + 3)**2
Let c(y) = -y**3 - 17*y**2 - 65*y + 15. Let q be c(-11). Let u(l) be the first derivative of -8 + 2*l**3 + 0*l + 15/4*l**q - 21/5*l**5 + 0*l**2. Factor u(t).
-3*t**2*(t - 1)*(7*t + 2)
Let z(w) = w**3 - 2*w**2 + w - 8. Let f be z(3). Factor 4*v - f*v**4 - 7*v + v + v**2 + 3*v**2 + 2*v**5.
2*v*(v - 1)**3*(v + 1)
Let b be ((-8)/(-16))/((-36)/(-27)). Factor b*f**2 - 3/8*f**3 + 0 - 3/8*f**4 + 0*f + 3/8*f**5.
3*f**2*(f - 1)**2*(f + 1)/8
Let v(p) be the second derivative of 1/4*p**5 + 0 + 125/2*p**3 + 625/2*p**2 + 9*p + 25/4*p**4. Factor v(c).
5*(c + 5)**3
Let i(n) = -n**3 - 8*n**2 - 6*n + 3. Let f be i(-7). Let j be (f - -7)*(-4)/(-3). Factor y + 0*y**3 - j*y + 3*y**3 + 3*y**2 - 3*y**4.
-3*y*(y - 1)**2*(y + 1)
Let f = -871 + 875. Let k(o) be the first derivative of 1/2*o**2 + 0*o + 2/3*o**3 - 4 + 1/4*o**f. What is r in k(r) = 0?
-1, 0
Let i(o) = o**4 + o**3 - 1. Let j(b) = -18*b**5 + 31*b**4 + 5*b**3 - 9. Let d(p) = -18*i(p) + 2*j(p). Solve d(h) = 0 for h.
0, 2/9, 1
Let s = 6257378/221 + -28314. Let d = 4/17 - s. Suppose 22/13*u + 34/13*u**3 - 42/13*u**2 - 10/13*u**4 - d = 0. What is u?
2/5, 1
Let d = 43 + -41. Find x, given that 26*x**2 - 11*x**2 + 15*x + 10 - 14*x**2 - 11*x**d = 0.
-1/2, 2
Suppose 4*l - 14*l = -12*l. Let q(d) be the third derivative of -1/150*d**5 + l*d + 5*d**2 + 1/12*d**4 - 4/15*d**3 + 0. Factor q(o).
-2*(o - 4)*(o - 1)/5
Let s(y) be the third derivative of -y**5/80 - 43*y**4/16 - 1849*y**3/8 - 352*y**2. What is o in s(o) = 0?
-43
Let l(y) = 45*y**2 - 30*y + 1. Let o(k) = -1. Let f be 1 + (-8 - (-1 - 2)). Let z(u) = f*o(u) + l(u). Factor z(a).
5*(3*a - 1)**2
Let s(u) be the second derivative of u**5/140 - u**4/21 + u**3/14 + u - 2. Suppose s(r) = 0. What is r?
0, 1, 3
Let 4 - 15/2*o**4 - 8*o**3 + 21*o + 37/2*o**2 + 2*o**5 = 0. What is o?
-1, -1/4, 2, 4
Solve 3137*w**2 - 5*w**3 - 1529*w**2 - 1498*w**2 + 115*w = 0.
-1, 0, 23
Suppose w = -505*t + 506*t + 8, 4*w + 16 = -4*t. Determine a, given that -22*a - 121/2*a**w - 2 = 0.
-2/11
Let w(y) = -y**3 - 4*y**2 - 9*y - 14. Let g be w(-3). Let l be 17/4 + -4*(5 - g). Factor -1/4*u**3 + 0*u + 0 - l*u**4 + 0*u**2.
-u**3*(u + 1)/4
Let a = 3093 - 3091. Solve 0 - 2/7*g + 0*g**a + 2/7*g**3 = 0 for g.
-1, 0, 1
Let x(v) be the third derivative of v**8/168 + 4*v**7/105 + v**6/15 - v**5/15 - 5*v**4/12 - 2*v**3/3 - 282*v**2. What is z in x(z) = 0?
-2, -1, 1
Let z(x) = x**2 + x - 1. Let m(r) = 2*r**3 - 5*r**2 + 31*r - 19. Let j(u) = -2*m(u) + 18*z(u). Factor j(f).
-4*(f - 5)*(f - 1)**2
Let s = 55 - 53. Factor 24*i - 13 - 15*i**s + 4*i**3 - i**3 + 2 - 1.
3*(i - 2)**2*(i - 1)
Factor 4/3*w**2 + 0 - 2/3*w**3 + 2*w.
-2*w*(w - 3)*(w + 1)/3
Factor 1/7*u**2 - 3/7 - 4/7*u + 2/7*u**3.
(u + 1)**2*(2*u - 3)/7
Suppose -303*y = -308*y + 20. Suppose -2*h + 2 = 4*r, -3*h - h = y*r - 8. Let -4/3*b**h + 1/3*b**2 + 4/3*b - 1/3 = 0. What is b?
-1, 1/4, 1
Determine k so that -26*k**3 + 898*k - 70*k**3 + 2*k**4 - 1354*k - 1660*k + 1242*k**2 = 0.
0, 2, 23
Suppose 0 - 4*j**2 + 6*j + 2/3*j**3 = 0. Calculate j.
0, 3
Let d(q) be the first derivative of q**3 + 27*q**2/2 + 42*q - 85. Factor d(j).
3*(j + 2)*(j + 7)
Let v be (-2)/5 - (-1)/(10/(-206)). Let c be 10/9*(-1 + v/(-15)). Solve -14/9*k**4 + 0*k**2 - c*k**3 + 0*k + 0 = 0 for k.
-2/7, 0
Let o(q) be the second derivative of q**6/15 + q**5/5 + q**4/6 - 16*q. Solve o(v) = 0 for v.
-1, 0
Let i(s) be the first derivative of -40 + 3/4*s**4 - 3/5*s**5 + 0*s**2 - 1/3*s**3 + 0*s + 1/6*s**6. Factor i(n).
n**2*(n - 1)**3
Factor -127*j - 7*j**2 - 3*j**3 + 97*j + 10*j**3 - 16 + 5*j**4 + 5*j**3.
(j + 1)**2*(j + 2)*(5*j - 8)
Determine r so that 6*r**3 + 34*r - 40*r - 2*r**4 + 0*r**3 + 3 - r**4 = 0.
-1, 1
Determine l so that 6*l - 10/3*l**3 + 2*l**2 + 2/3*l**4 + 0 = 0.
-1, 0, 3
Factor 9*v**2 + 6*v + 0 + 3/4*v**4 + 9/2*v**3.
3*v*(v + 2)**3/4
Let n(h) be the first derivative of -14 + 5/11*h**2 - 12/11*h - 2/33*h**3. Let n(k) = 0. Calculate k.
2, 3
Let q(h) be the first derivative of 8365427*h**4/4 - 41209*h**3 + 609*h**2/2 - h + 388. Factor q(b).
(203*b - 1)**3
Let l(a) be the first derivative of -2/15*a**3 + 12/5*a + 1/5*a**2 + 12. Find c such that l(c) = 0.
-2, 3
Let b(a) = -a**2 - 88*a + 770. Let m be b(8). Factor l**3 + 1/2 - l - 1/2*l**4 + 0*l**m.
-(l - 1)**3*(l + 1)/2
Let q = 16 + -14. Let m = q - -5. Find v, given that -m + v**4 - 35*v - 6*v**3 + 0 - 2 + 8*v**2 + 41*v = 0.
-1, 1, 3
Let x(o) be the third derivative of -o**6/1140 - 62*o**5/95 - 3844*o**4/19 - 1906624*o**3/57 - 4*o**2 - 34*o. Factor x(h).
-2*(h + 124)**3/19
Let k be (5/(-2))/((-2)/336*-4). Let w be 11/((-220)/k)*(-4)/(-18). Factor w*z - 1 + 1/2*z**2.
(z + 3)*(3*z - 2)/6
Let y(f) be the first derivative of f**4/18 - 10*f**3/27 + 4*f**2/9 - 183. Factor y(k).
2*k*(k - 4)*(k - 1)/9
Let d be ((-20)/(-8))/1*(-20)/(-25). Let r be 1/4 + 6/(-88). Solve 6/11*v - r - 4/11*v**d = 0.
1/2, 1
Let w be 14 - 0 - (-2)/8*-16. Factor 135 - 127 + 44*m + 84*m**2 + 6*m**4 + w*m**4 + 64*m**3.
4*(m + 1)*(m + 2)*(2*m + 1)**2
Let b be (-26)/(-40) + 4*3/(-30). Let k(m) be the first derivative of -1/2*m**2 - 1/5*m**5 + 1/3*m**3 + b*m**4 - 2 + 0*m. Factor k(t).
-t*(t - 1)**2*(t + 1)
Let k(y) be the first derivative of -y**4/12 + y**2/2 + 2*y/3 - 274. Factor k(d).
-(d - 2)*(d + 1)**2/3
Let w(n) = -37*n**2 + 586*n + 99. Let t be w(16). Factor -54/5 - 38/15*s**2 - 66/5*s - 2/15*s**t.
-2*(s + 1)*(s + 9)**2/15
Determine f, given that -2/3*f**2 + 0 - 32/3*f = 0.
-16, 0
Let c = 75/2 - 112/3. Let f(n) be the second derivative of -9*n + c*n**3 + 1/12*n**4 + 0 + 0*n**2. Solve f(x) = 0 for x.
-1, 0
What is o in -11*o**2 + 20*o**3 + 10*o + 29*o**3 - 48*o**3 = 0?
0, 1, 10
Let t(r) be the third derivative of 0*r**3 + 1/12*r**5 + 5/12*r**4 + 0*r + 0 - 6*r**2. Factor t(l).
5*l*(l + 2)
Let s = 16 - 12. Suppose -4*h + 20 = -5*g + g, 2*h = -g + s. Solve -10 + 65*n - 100*n**2 + 11*n**3 + 41*n**3 - 7*n**h = 0 for n.
2/9, 1
Suppose 6*p - 109 - 95 = 0. Let b = p + -34. Factor b + 8/3*w**4 + 10/3*w**3 - 4/3*w**2 - 2*w.
2*w*(w + 1)**2*(4*w - 3)/3
Let r(g) be the second derivative of g**8/8960 - g**7/1680 - 11*g**4/12 - 15*g. Let j(c) be the third derivative of r(c). Determine f so that j(f) = 0.
0, 2
Let j = 790 - 788. Factor -4*s**3 - 2*s**4 - 2*s - 2/5 - 2/5*s**5 - 4*s**j.
-2*(s + 1)**5/5
Suppose 6*g + 2*r - 758 = g, -2*g = r - 304. Let c be (-4)/1 - (-630)/g. Factor 0 - c*x**4 + 0*x + 1/5*x**2 + 0*x**3.
-x**2*(x - 1)*(x + 1)/5
Let d(g) = g + 9. Let z be d(-12). Let f be z - -5 - (-32)/(-20). Factor -1/5*u - 1/5*u**2 + f.
-(u - 1)*(u + 2)/5
Let w(h) be the second derivative of 5*h**4/72 + 25*h**3/36 - 5*h**2/2 + 189*h - 1. Factor w(c).
5*(c - 1)*(c + 6)/6
Let x(a) = a**3 - 10*a**2 - 11*a + 12. Let d be x(11). Factor 28*u**3 + 8*u**3 - d*u**2 + 0*u**3 - 20*u**4 - 7*u**4.
-3*u**2*(3*u - 2)**2
Find t, given that -4311*t - 8700*t**3 - 2*t**5 + 10748*t**2 + 13824*t**2 + 405*t**4 + 7938 - 19755*t - 147*t**4 = 0.
1, 63
Suppose 14/5*q**2 + 0 + 12/5*q + 2/15*q**4 + 16/15*q**3 = 0. What is q?
-3, -2, 0
Let v(k) be the third derivative of k**5/90 + 5*k**4/6 + 25*k**3 + 39*k**2 + 1. Let v(b) =