e of p**6/320 - p**5/160 - p**4/64 + 3*p**3/2 + 18*p**2. Let g(r) be the first derivative of f(r). Factor g(c).
3*(c - 1)*(3*c + 1)/8
Let 0*z - 2/3*z**3 + 0 + 80/3*z**2 = 0. Calculate z.
0, 40
Let a(c) = -c**2 - 79*c - 75. Let o be a(-78). Factor -1/2 - 7/4*b**o - 3/4*b + 3*b**2.
-(b - 1)**2*(7*b + 2)/4
Let t(n) be the first derivative of 1/9*n**3 + n + 0*n**5 - 2 - 1/12*n**4 + 0*n**2 + 1/90*n**6. Let s(o) be the first derivative of t(o). Factor s(z).
z*(z - 1)**2*(z + 2)/3
Let u be 10/6 + ((-476)/51)/(-7). Determine o so that 2/7*o**u + 4/7 - 4/7*o + 1/7*o**4 - 3/7*o**2 = 0.
-2, 1
Let n(d) be the third derivative of d**8/13440 - d**7/1680 - d**6/60 + 7*d**5/12 - 32*d**2. Let t(b) be the third derivative of n(b). Solve t(l) = 0.
-2, 4
Let s = -570 + 11401/20. Let p(d) be the second derivative of -3/10*d**2 + 1/10*d**3 + s*d**4 + 0 + 7*d - 3/100*d**5. Factor p(i).
-3*(i - 1)**2*(i + 1)/5
Let y(c) = -11*c**2 - 347*c - 25921. Let r(i) = -2*i**2 - 5*i. Let b(z) = -15*r(z) + 3*y(z). Suppose b(o) = 0. What is o?
-161
Let j(v) be the first derivative of -1/3*v**2 + 1/6*v**4 + 24 + 4/3*v - 4/9*v**3. Factor j(p).
2*(p - 2)*(p - 1)*(p + 1)/3
Let f(b) be the first derivative of -5*b**4/54 + 4*b**3/9 - 4*b**2/9 - b + 14. Let i(n) be the first derivative of f(n). Solve i(v) = 0 for v.
2/5, 2
Let t(p) be the first derivative of p**6/12 - p**5/2 + 3*p**4/8 + 5*p**3/6 - p**2 - 92. Factor t(r).
r*(r - 4)*(r - 1)**2*(r + 1)/2
Suppose -48 = -v - 11*v. Factor -1/3*q**v + 1/3*q**2 - 1/3*q**3 + 0 + 1/3*q.
-q*(q - 1)*(q + 1)**2/3
Suppose -2*v = -5*v + 6*v. Let x(i) be the second derivative of 1/84*i**7 + 0*i**2 + 1/6*i**3 + 7/24*i**4 + v + 1/12*i**6 + 5*i + 9/40*i**5. Factor x(b).
b*(b + 1)**3*(b + 2)/2
Let f(v) be the first derivative of v**3 - 18 - 9/2*v**2 + 0*v. Suppose f(k) = 0. Calculate k.
0, 3
Let 20*k + 36*k**3 + 7*k**4 + 38*k**3 - 36*k**2 - 3*k**4 - 62*k**3 = 0. Calculate k.
-5, 0, 1
Factor 0 - 2/5*b + 9/5*b**2.
b*(9*b - 2)/5
Suppose -6*f = -3*f. Suppose 2*s - m - 1 = 0, s + 5*m - 23 = -6. Determine u, given that 0*u**s + 2 + f*u**2 + 3*u**2 + 9*u + 4 = 0.
-2, -1
Let q = -29 - -35. Let t(n) = n**3 - 6*n**2 + 2. Let f be t(q). Find v such that -6/11*v + 2/11*v**f + 4/11 = 0.
1, 2
Let w = -119 + 39. Let g = w + 80. Determine s so that 1/4*s**3 + 0*s**2 + g*s + 0 = 0.
0
Let n be ((-63)/(-25) + -1)/(282/470). Determine a, given that 16/15*a + 14/15*a**3 + n*a**2 - 8/15 = 0.
-2, -1, 2/7
Let p(v) = 6*v**2 + 63*v - 462. Let z be p(5). Let q be (1/(-2))/(1/(-4)). Determine n, given that 3/2*n**4 + 0 - 9/2*n**q + z*n + 0*n**3 = 0.
-2, 0, 1
Let l = 1637 - 1635. Solve 1/5*k**5 + 0 + 1/5*k - 3/10*k**l - 2/5*k**3 + 3/10*k**4 = 0.
-2, -1, 0, 1/2, 1
Let a(r) be the first derivative of -r**5/4 + 5*r**4/16 + 5*r**3/4 - 25*r**2/8 + 5*r/2 + 50. Factor a(z).
-5*(z - 1)**3*(z + 2)/4
Factor 24*y**2 - 151 - 79*y**2 + 248*y + 28*y**2 - 101 + 31*y**2.
4*(y - 1)*(y + 63)
Let f = -9243691484/2219 + 4165701. Let q = -2/317 - f. Factor 1/7*h**2 + q*h + 2/7.
(h + 1)*(h + 2)/7
Let h be (2/6)/(1/3). Let f(s) = -s**2. Let j(a) = 55*a - 10. Let y(g) = -4*g - 1. Let c(u) = -j(u) - 10*y(u). Let q(x) = h*c(x) + 5*f(x). Factor q(n).
-5*(n - 1)*(n + 4)
Let c(d) = d**4 + 1. Let r(j) be the third derivative of 2*j**7/35 - j**6/10 + 2*j**5/15 + 4*j**3/3 + 13*j**2. Let w(g) = 8*c(g) - r(g). Factor w(a).
-4*a**2*(a - 2)*(a - 1)
Let o(h) be the second derivative of -53*h - 3*h**2 - 3/2*h**3 + 0 - 1/4*h**4. Find z such that o(z) = 0.
-2, -1
Suppose -3*m = 2*d - 27, 0 = -3*d + m - 6*m + 43. Let z(c) be the first derivative of d + 4*c**5 - 5*c**5 - 7. Let z(h) = 0. What is h?
0
Let s(z) be the third derivative of z**7/945 - z**6/60 + z**5/10 - z**4/4 - 52*z**2. What is r in s(r) = 0?
0, 3
Let b(w) = -w - 9. Let f be b(-12). Factor 7*h + 0*h**f + 5*h**4 - 5*h**2 - 3*h**3 - 2*h - 2*h**3.
5*h*(h - 1)**2*(h + 1)
Suppose 0 = -3*n - 2*w - 28, -5*n = 3*w - 5*w + 52. Let t be 144/160 + 4/n. Find p such that 5/4*p**2 + 0 - t*p = 0.
0, 2/5
Let k(z) be the first derivative of 7*z**6/360 - 11*z**5/240 + z**4/24 + 14*z**3/3 - 1. Let a(y) be the third derivative of k(y). Solve a(o) = 0.
2/7, 1/2
Suppose 0 = -5*u + 31*u + 30*u. Let k(h) be the first derivative of 0*h + u*h**3 + 14 - h**4 + 0*h**2 - 2/3*h**6 + 8/5*h**5. Suppose k(f) = 0. What is f?
0, 1
Let d(f) be the first derivative of 3*f**4/20 + 12*f**3/5 - 129*f**2/10 + 18*f - 10. Suppose d(u) = 0. Calculate u.
-15, 1, 2
Suppose -13*d = -10*d - 12. Suppose n = d*b - b + 16, -5*n + 4*b + 36 = 0. Let -1/2*z**3 + 0*z + 1/4*z**n + 0 + 0*z**2 = 0. What is z?
0, 2
Let c(q) be the first derivative of 0*q**5 - q + 0*q**4 + 0*q**3 + 4 + 0*q**2 + 1/15*q**6. Let n(t) be the first derivative of c(t). Factor n(u).
2*u**4
Let q = 68 + -63. Let a be ((-2)/q)/((-84)/70). Determine h, given that 2*h**2 + a*h**3 + 4*h + 8/3 = 0.
-2
Let o(t) be the first derivative of -2*t**3/21 + 5*t**2/7 + 12*t/7 + 457. Factor o(c).
-2*(c - 6)*(c + 1)/7
Let m(c) = c + 28. Let j be m(-20). Determine p, given that -2 - 2*p**4 + 67*p - 2*p**5 - 77*p + j - 4*p**2 + 12*p**3 = 0.
-3, -1, 1
Suppose 2 + 2 = z, -2*l + 5*z = -84. Factor 1 + 2 + l*i**2 + 95*i**2 + 42*i.
3*(7*i + 1)**2
Let s(z) be the third derivative of 0*z + 5*z**2 + 0 + 0*z**3 + 1/48*z**4 + 1/240*z**5. Factor s(b).
b*(b + 2)/4
Let x(b) = 10*b**2 - 75*b + 131. Let n(g) = -22*g**2 + 151*g - 263. Let i(k) = 3*n(k) + 7*x(k). Factor i(h).
4*(h - 16)*(h - 2)
Let q = 30 - 26. Let x(f) = f - 1. Let o be x(q). Find y, given that o*y + y**2 - 5 - 6*y**2 - 13*y = 0.
-1
Let c(d) be the second derivative of 0 + 0*d**2 - 1/12*d**4 + 27*d - 1/6*d**3. Factor c(g).
-g*(g + 1)
Let j(w) be the third derivative of w**6/60 + 43*w**5/30 + 10*w**4/3 - 28*w**3 + 608*w**2. Find h, given that j(h) = 0.
-42, -2, 1
Let -184 + 4*i**2 + 30*i**2 - 30*i**2 + 84*i = 0. Calculate i.
-23, 2
Let n(z) be the second derivative of 10*z + 5/8*z**2 + 0 + 0*z**3 - 5/48*z**4. Suppose n(q) = 0. Calculate q.
-1, 1
Let g(n) be the third derivative of -n**6/30 - 2*n**5/3 - 14*n**4/3 - 16*n**3 - 21*n**2 - 13. Factor g(z).
-4*(z + 2)**2*(z + 6)
Let g(n) = n**2. Let c(p) = -28*p + 46*p + 23*p**2 + 62*p - 36*p**3 + 32 + 2*p**2. Let z(u) = -c(u) + g(u). Let z(k) = 0. Calculate k.
-2/3, 2
Let x(y) = -5*y**2 - 410*y - 7970. Let l(z) = z - 3. Let w(t) = 10*l(t) + x(t). Factor w(r).
-5*(r + 40)**2
Let m = -138 + 11726/85. Let i = 227/595 - m. Factor -i*p**3 + 0 - p**2 - 2/7*p.
-p*(p + 2)*(3*p + 1)/7
Determine k so that -360/11 - 2/11*k**2 + 184/11*k = 0.
2, 90
Let l = 5 - -5. Suppose -8 = n - l. Suppose -7*k + 5*k**n - 12 + k**2 - k - 2*k**2 = 0. Calculate k.
-1, 3
Let b(f) be the third derivative of f**7/840 + f**6/120 - f**5/40 - f**4/24 + 5*f**3/24 + 129*f**2. Find j such that b(j) = 0.
-5, -1, 1
Let u be (189/(-70))/((-33)/55). Factor 25/2 + 15/2*n + 1/2*n**3 - u*n**2.
(n - 5)**2*(n + 1)/2
Let a = -70 + 66. Let m be (-104)/(-15) + -6 + a/30. Find b such that -4/5*b**2 + m*b**4 + 0 + 0*b**3 + 0*b = 0.
-1, 0, 1
Let g(y) = 31*y**4 - 1382*y**3 + 17323*y**2 + 12012*y + 2028. Let z(b) = b**4 + b**3 + b**2. Let m(j) = g(j) - 4*z(j). Factor m(f).
3*(f - 26)**2*(3*f + 1)**2
Let k = -18833/5 + 3767. Solve 1/5*g**2 + k*g + 0 = 0.
-2, 0
Let p(z) = -4*z**2 + 14*z - 20. Let q(d) be the second derivative of 5*d**4/12 - 5*d**3/2 + 21*d**2/2 + 7*d. Let s(x) = 6*p(x) + 4*q(x). Factor s(c).
-4*(c - 3)**2
Let a(k) = -k**2 + 34*k + 152. Let g be a(38). Factor -2/7*v**4 - 6/7*v**3 + 8/7*v**2 + 0 + g*v.
-2*v**2*(v - 1)*(v + 4)/7
Let c = -2/28865 + 57736/86595. Suppose 0*d - 5*d + 10 = 0. Solve 2/3*y - 2/3*y**3 - c*y**d + 2/3 = 0.
-1, 1
Let t(l) be the second derivative of -55/12*l**4 + 0*l**2 + 25/6*l**3 - 27*l + 0 + 7/4*l**5 - 1/6*l**6. What is k in t(k) = 0?
0, 1, 5
Let d(a) be the second derivative of 1/12*a**3 + 0 + 1/32*a**4 + a**2 + 1/240*a**5 - 4*a. Let l(z) be the first derivative of d(z). Suppose l(p) = 0. What is p?
-2, -1
Let c(v) be the second derivative of -3*v**5/80 - 5*v**4/4 - 17*v**3/8 + 57*v**2/4 + 121*v. Let c(b) = 0. Calculate b.
-19, -2, 1
Let z(s) = -s**2. Let j(l) = 7*l**2 - 16*l - 48. Let t(y) = j(y) + 3*z(y). Solve t(r) = 0.
-2, 6
Suppose -8 = 2*w + n, 26 = 7*w - 12*w - n. Let x be 0/((-8)/w*12/(-8)). Factor -16/5*u**3 + 8/5*u**2 + 4/5*u**5 + 12/5*u + x*u**4 - 8/5.
4*(u - 1)**3*(u +