Let d(a) be the third derivative of -a**7/210 - 3*a**6/80 - 3*a**5/40 - 119*a**2. Factor d(g).
-g**2*(g + 3)*(2*g + 3)/2
Determine u, given that -3*u**3 - 1 + 89*u**2 - 233*u**2 - 1 + 2 = 0.
-48, 0
Let c = -6 - -12. Let f(r) be the second derivative of -1/3*r**3 + 0*r**2 + 0 - 2*r - 5/12*r**4 + 11/20*r**5 - 2/15*r**c. Factor f(t).
-t*(t - 2)*(t - 1)*(4*t + 1)
Let l(r) be the first derivative of r**9/252 + r**8/420 - r**7/105 + 14*r**3/3 - 8. Let b(i) be the third derivative of l(i). Factor b(t).
4*t**3*(t + 1)*(3*t - 2)
Let u(m) be the second derivative of -1/4*m**5 - 5/2*m**3 - 5/2*m**2 + 0 - 25*m - 5/4*m**4. Let u(c) = 0. What is c?
-1
Suppose -69*t - 32*t = 0. Factor 0*a**2 + 2/23*a**3 + t - 2/23*a.
2*a*(a - 1)*(a + 1)/23
Let f(q) be the first derivative of q**9/1008 + q**8/280 - q**7/56 - q**6/20 - q**3/3 + 15*q**2 - 40. Let w(k) be the third derivative of f(k). Factor w(a).
3*a**2*(a - 2)*(a + 1)*(a + 3)
Let r = -2/1263 + 562/421. Let 16/3*n**2 + 4/3 + 2/3*n**5 - 14/3*n - 4/3*n**4 - r*n**3 = 0. What is n?
-2, 1
Let n be (-1 - -1)/(28 + -26). Determine v, given that 0 + 2/7*v**5 + 24/7*v**4 + n*v + 96/7*v**3 + 128/7*v**2 = 0.
-4, 0
Let n(f) be the second derivative of -f**4/90 - 14*f**3/9 - 245*f**2/3 - 83*f. Solve n(c) = 0.
-35
Suppose 5/2 + 15/2*g + 15/2*g**2 + 5/2*g**3 = 0. Calculate g.
-1
Let 11*x**3 + 36*x - 9 + 20*x - 33 - 46*x**2 - 9*x**3 + 30*x = 0. Calculate x.
1, 21
Let b(m) be the second derivative of -m**6/10 + 9*m**5/20 - 2*m**3 - 355*m. Suppose b(a) = 0. Calculate a.
-1, 0, 2
Let x(v) be the third derivative of -v**11/27720 - v**10/50400 - v**5/5 - 8*v**2. Let l(t) be the third derivative of x(t). Let l(w) = 0. Calculate w.
-1/4, 0
Let s be (-1)/2*(21 - 3). Let h be (7/14)/(s/(-12)). Find y such that -h*y**2 + 0*y + 0 = 0.
0
Let m(k) be the third derivative of -2*k**2 + 0*k**3 + 1/6*k**4 + 3*k - 1/10*k**5 + 0 + 0*k**6 + 1/105*k**7. Factor m(j).
2*j*(j - 1)**2*(j + 2)
Factor 96*j - 24*j**3 + 64 + 4*j**4 - 23*j**2 - 25*j**2 - 30*j**2 + 82*j**2.
4*(j - 4)**2*(j + 1)**2
Let x(a) = 12*a**2 - 428*a + 444. Let g(d) = 4*d**2 - 142*d + 148. Let p(h) = -14*g(h) + 5*x(h). Factor p(t).
4*(t - 37)*(t - 1)
Suppose 0 = -2*f + 70 - 62. Let b(z) = -2*z**4 + 8*z**3 - 14*z**2 + 4. Let k(g) = -2*g**4 + 7*g**3 - 13*g**2 + 5. Let t(h) = f*k(h) - 5*b(h). Factor t(p).
2*p**2*(p - 3)**2
Let w(v) be the first derivative of -4*v**5 - 14*v**4 - 176*v**3/15 - 16*v**2/5 - 445. Suppose w(o) = 0. What is o?
-2, -2/5, 0
Let r(n) be the second derivative of n**5/70 + 13*n**4/84 - n**3/6 - 219*n + 1. Factor r(p).
p*(p + 7)*(2*p - 1)/7
Let h(z) = -2*z**2 + 44*z - 38. Let m be h(21). Solve 0*l - 8/9*l**m - 10/9*l**3 + 0 - 4/9*l**2 - 2/9*l**5 = 0 for l.
-2, -1, 0
Let a be 2117/2030 + (-5)/(-50). Let 4/7*x**3 + 0 - 12/7*x**2 + a*x = 0. Calculate x.
0, 1, 2
Let s(z) be the second derivative of -z**4/12 + 2*z**3 + 13*z**2/2 + z - 4. Solve s(t) = 0 for t.
-1, 13
Let a(b) be the third derivative of 1/390*b**5 - 14*b**2 - 1/156*b**4 + 0*b + 0 - 2/13*b**3. Factor a(y).
2*(y - 3)*(y + 2)/13
Let g(m) be the second derivative of m**3/3 - 4*m**2 - 12*m. Let r be g(6). Factor -95*x + 95*x + 20*x**r - 8*x**2 + 12*x**3.
4*x**2*(x + 1)*(5*x - 2)
Let n(k) be the first derivative of 3*k**4/8 - 15*k**3/2 + 36*k**2 + 96*k + 144. Factor n(r).
3*(r - 8)**2*(r + 1)/2
Suppose 2 = -l - 8. Let f be (-26)/l + (-3)/5. Let 0*z + 0*z**3 + 0 + 1/4*z**f - 1/4*z**4 = 0. Calculate z.
-1, 0, 1
Let m(k) = 8*k**2 - 92*k - 41. Let h(i) = -2*i**2 + 31*i + 14. Let d(q) = -7*h(q) - 2*m(q). Let d(w) = 0. What is w?
-16, -1/2
Suppose t - 7*y + 14 = -3*y, -t = 5*y - 22. Factor -11*l**3 + 15*l**t - 11*l + 6*l + l**3.
-5*l*(l - 1)*(2*l - 1)
Let x = -1558 - -1564. Let g(m) be the second derivative of 1/105*m**x + 5*m + 0 - 2/7*m**3 + 4/21*m**4 - 9/7*m**2 + 3/35*m**5. Factor g(n).
2*(n - 1)*(n + 1)*(n + 3)**2/7
Let s(q) = 11240*q**3 + 12100*q**2 + 868*q + 20. Let b(j) = j**3 + 4*j**2 + j + 1. Let l(g) = 4*b(g) - s(g). Factor l(f).
-4*(f + 1)*(53*f + 2)**2
Let b be ((-6)/18)/(4/(-72)). Let w(j) = -11*j**2 + 46*j - 66. Let i(m) = -m**2 + m - 1. Let l(q) = b*i(q) - w(q). Factor l(z).
5*(z - 6)*(z - 2)
Factor 23 + 37*g - 42 + g**2 + 19.
g*(g + 37)
Let m be 5 - (-202)/5 - (-2)/(-5). Suppose -5*g = m - 70. Determine n so that 5/4*n**4 - 5/4*n**2 + 1/2*n + 7/4*n**g + 0 - 9/4*n**3 = 0.
-1, 0, 2/7, 1
Let z(k) = -k**3 + k**2 + 3*k - 3. Suppose l - 4 = 2*l. Let a(o) be the second derivative of 2*o**3/3 - 2*o**2 + 12*o. Let f(i) = l*z(i) + 3*a(i). Factor f(w).
4*w**2*(w - 1)
Let -294/11*h**2 - 552/11*h**4 + 0*h + 144/11*h**5 + 0 + 700/11*h**3 = 0. Calculate h.
0, 7/6, 3/2
Suppose k + 111 = 2*a, 66 = a + k - 5*k. Let q = -54 + a. Factor 0*h + q + 2/3*h**2 + 2/3*h**3.
2*h**2*(h + 1)/3
Let z = 59/14 + -281/70. Let h(b) be the first derivative of -9 + 1/5*b**2 - 1/15*b**3 - z*b. Let h(u) = 0. Calculate u.
1
Let b(j) be the third derivative of j**6/180 + 19*j**5/45 - 714*j**2. Solve b(m) = 0 for m.
-38, 0
Let k be 6*4*5/30. Suppose -3*b = -2*b + 2*p + 4, k*p = -3*b - 6. Factor -3/2*s**b + 0 - 3*s.
-3*s*(s + 2)/2
Let c be -10 - (68 - -12)/(-8). Factor -16/3*g**3 + 2/3*g**2 + 32/3*g**4 + 0 + c*g.
2*g**2*(4*g - 1)**2/3
Suppose 106 - 72 = 35*u - 106. Let 0 + 4/3*n**5 - 8/3*n - 4*n**2 + 4/3*n**3 + 4*n**u = 0. Calculate n.
-2, -1, 0, 1
Let a = -78 + 83. Suppose -5*m + 3*v - 6 = 0, -a*m + 0*m = 5*v - 10. Factor z - 1/3*z**2 + m.
-z*(z - 3)/3
Let i(b) be the first derivative of b**6/6 + 3*b**5/4 - 5*b + 11. Let f(x) be the first derivative of i(x). Factor f(g).
5*g**3*(g + 3)
Let h(d) be the second derivative of -d**4/36 - 7*d**3/18 - d**2 - 2*d - 53. Suppose h(q) = 0. What is q?
-6, -1
Let x(i) be the first derivative of -i**6/9 + 7*i**5/30 - i**4/9 + 21*i + 20. Let f(w) be the first derivative of x(w). Factor f(r).
-2*r**2*(r - 1)*(5*r - 2)/3
Suppose 3*v - 3*o = 15, o = -3*v - 2*o - 3. Suppose 6 + v = 2*k. What is w in 27*w + 2 + k + 21*w**4 - 12*w - 27*w**2 - 15*w**3 = 0?
-1, -2/7, 1
Let h be (-1)/11 - (-2507)/1199. Let y be (2/8)/(3/4). Let 0 + o**3 + o**h + y*o**4 + 1/3*o = 0. Calculate o.
-1, 0
Suppose -7*k + 4*k = -30. Let j be (-8)/(-30) - (-4)/k. Factor 4/3*s**3 - 4/3*s - 2/3 + j*s**2.
2*(s - 1)*(s + 1)*(2*s + 1)/3
Let o = 1 + 2. Let g = o - 0. Let z(f) = 13*f**3 - 19*f**2 + 10*f - 4. Let x(j) = -12*j**3 + 18*j**2 - 9*j + 3. Let h(s) = g*z(s) + 4*x(s). Factor h(u).
-3*u*(u - 1)*(3*u - 2)
Let s = 14 + -6. Suppose 2*f = -2*f + s. Suppose 5 - 4 - o**2 - 2*o - 4 + f = 0. What is o?
-1
Factor -1/11*n**2 + 10/11*n - 9/11.
-(n - 9)*(n - 1)/11
Suppose 4*u + 7 = 4*f - 9, -24 = u + 3*f. Let l be 6/u + 104/84. Determine a so that 2/7*a + 0 - l*a**2 = 0.
0, 1/2
Let z be -2 + 1/(2/4). Suppose -b**3 + z*b**4 + 2*b**4 - 11*b**3 + 2*b**4 = 0. What is b?
0, 3
Let j(k) be the third derivative of -k**5/100 - 17*k**4/4 - 1445*k**3/2 + 36*k**2 - 2. What is i in j(i) = 0?
-85
Factor 20/3 + 14/3*z + 2/3*z**2.
2*(z + 2)*(z + 5)/3
Let s(o) be the second derivative of 3*o**5/20 - 24*o**3 + 192*o**2 + 156*o. Determine x so that s(x) = 0.
-8, 4
Suppose 0 = -22338*w + 22240*w + 196. Determine a so that -13/4*a + 169/8 + 1/8*a**w = 0.
13
Suppose -5*b + 5*i = 10, -7*i + 25 = -2*i. Factor -5*d**b + 5*d**3 + 2*d**3 - 21*d + 15*d**2 - 5*d**3 + 9.
-3*(d - 3)*(d - 1)**2
Let m(y) = 10*y**3 - 35*y**2 + 20*y - 13. Let q be m(3). Factor 11/5*p**q - 12/5*p**3 - p**4 + 6/5*p + 0.
-p*(p - 1)*(p + 3)*(5*p + 2)/5
Let a = 1831/14 + -1819/14. Determine n, given that -a*n - 3/7*n**2 - 3/7 = 0.
-1
Find z such that 8 - 2/9*z**3 + 110/9*z**2 + 2/9*z**5 - 14/9*z**4 - 56/3*z = 0.
-3, 1, 2, 6
Let t(b) be the second derivative of -b**5/10 - b**4 - 3*b**3 - 4*b**2 - 3*b + 21. Let t(d) = 0. Calculate d.
-4, -1
Let i(s) = -10*s + 544. Let o be i(54). Factor -26/9*v**3 - 8/3*v**2 + 0 - 2/9*v**5 - 8/9*v - 4/3*v**o.
-2*v*(v + 1)**2*(v + 2)**2/9
Let t(b) be the second derivative of -b**4/4 - 7*b**3/2 - 9*b**2 - 37*b + 2. Factor t(o).
-3*(o + 1)*(o + 6)
Suppose 7*s - 36 = 4*s. Let q = s - -8. Find h, given that 2*h**2 + 10*h**2 + 4 + 4*h**3 + 5 - q*h - 1 - 4*h**4 = 0.
-2, 1
Let p(l) be the first derivative of l**6/1980 - l**5/220 + l**4/66 - 8*l**3/3 - 11. Let i(t) be the third derivative of p(t). What is g in i(g) = 0?
1, 2
Let a(c) be the first derivative of -c**3/3 + c**2/2 + 12