9
Let n(h) be the first derivative of -h**6/6 - h**5 - 9*h**4/4 - 7*h**3/3 - h**2 - 216. Factor n(g).
-g*(g + 1)**3*(g + 2)
Let g(o) = 5*o**2 - 6*o + 1. Let i(l) = -20*l**2 + 25*l - 5. Suppose 0 = -23*a + 21*a - 8. Let k(d) = a*i(d) - 15*g(d). Factor k(u).
5*(u - 1)**2
Factor 342 - s**2 + 340 + 6*s - 687.
-(s - 5)*(s - 1)
Let x = 47 - 32. Let o be (-15)/5 + 81/x. Let -7/5*z**3 + o*z**2 - 2/5 - 3/5*z = 0. Calculate z.
-2/7, 1
Let l be (-1)/4*(-1 + 0 + 0). Let x = -320 + 641/2. Solve -x + l*z**2 + 1/4*z = 0 for z.
-2, 1
Suppose 4*c + 20 = 0, 5*c - 7 = x - 48. Let j be (x/30)/(4/10). What is t in -j*t**4 - 2/3*t**3 + 0*t**2 + 0 + 0*t - 2/3*t**5 = 0?
-1, 0
Let h(v) be the third derivative of -5*v**4/24 + 9*v**3/2 + 2*v**2 - 58*v. Let c be h(5). Solve -1/3*o**2 - 5/3 + c*o = 0.
1, 5
Let j(u) be the first derivative of -3*u**5 - 14 + 0*u**2 - 1/2*u**6 - 6*u**4 - 4*u**3 + 0*u. Factor j(r).
-3*r**2*(r + 1)*(r + 2)**2
Let w(y) be the third derivative of -y**6/780 - y**5/195 - 23*y**2 + 5*y. Factor w(f).
-2*f**2*(f + 2)/13
Let p(b) be the second derivative of b**6/10 - b**4/4 + 7*b. Factor p(n).
3*n**2*(n - 1)*(n + 1)
Let i(x) = 16*x**5 - 32*x**4 + 55*x**3 - 25*x**2 + 7. Let f(q) = 2*q**5 - 2*q**4 + q**3 + q**2 + 1. Let m(w) = -14*f(w) + 2*i(w). Factor m(k).
4*k**2*(k - 4)**2*(k - 1)
Let s(f) = 8*f**2 - 83*f - 79. Let t(y) = 2*y**2 - y + 1. Let h(z) = -s(z) + 3*t(z). Solve h(j) = 0.
-1, 41
Suppose 5*i - 22 = 4*y, -2*y + 7*y = 3*i - 21. Let d be (-170)/(-34) + (-11)/2 + 62/28. Factor 4/7 - p**i - d*p.
-(p + 2)*(7*p - 2)/7
Suppose 60*r = 56*r. Let s be 1 + -1 - 6/(-4). Factor s*u**2 + 3*u + r.
3*u*(u + 2)/2
Let l(v) be the first derivative of 8/39*v**3 + 1/26*v**4 + 0*v**2 + 0*v - 3. Factor l(n).
2*n**2*(n + 4)/13
Let 3/2 + 25/2*r**2 + 11*r + 3*r**3 = 0. What is r?
-3, -1, -1/6
Let f(t) be the first derivative of -t**6/6 - t**5/2 + 5*t**4/12 + 5*t**3/3 + 10*t + 2. Let s(w) be the first derivative of f(w). Factor s(o).
-5*o*(o - 1)*(o + 1)*(o + 2)
Let w(u) be the second derivative of 8*u**2 + 4/3*u**3 + 0 - 7/12*u**4 + 21*u + 1/20*u**5. Suppose w(t) = 0. What is t?
-1, 4
Let l(c) = -4*c**4 - 7*c**3 - 9*c**2 + 22*c - 11. Let s(x) = -18*x**4 - 34*x**3 - 44*x**2 + 108*x - 54. Let f(q) = -14*l(q) + 3*s(q). Factor f(r).
2*(r - 2)*(r - 1)**2*(r + 2)
Let u(w) be the first derivative of -2*w**7/175 - 9*w**6/200 - w**5/50 - 9*w**2/2 - 28. Let n(m) be the second derivative of u(m). Find r, given that n(r) = 0.
-2, -1/4, 0
Let n(a) be the second derivative of -73*a**5/160 - a**4/48 + 73*a**3/48 + a**2/8 - 131*a. Solve n(r) = 0.
-1, -2/73, 1
Let g be (8/12)/((-3)/(-9)). Let u(k) = 5*k - 4 + g*k**2 + 0 + 7*k + 0. Let p(i) = 3*i**2 + 12*i - 3. Let a(d) = 5*p(d) - 6*u(d). Let a(z) = 0. Calculate z.
1, 3
Let i(x) = x**4 + 2*x**3 - 25*x**2 + 13*x. Let h(v) = -2*v**4 - 4*v**3 + 74*v**2 - 38*v. Let d(r) = -3*h(r) - 10*i(r). Factor d(p).
-4*p*(p - 1)**2*(p + 4)
Let f(g) be the first derivative of 7 - 1/14*g**2 + 1/7*g - 2/21*g**3. Find r, given that f(r) = 0.
-1, 1/2
Let d(v) be the second derivative of v**7/105 - 2*v**6/75 + v**5/50 + 404*v. Let d(n) = 0. What is n?
0, 1
Let t(s) be the second derivative of 1/96*s**4 - 6*s + 0 - 1/8*s**2 - 1/48*s**3. Suppose t(q) = 0. What is q?
-1, 2
Suppose 89 = 6*r + 17. Determine u so that r*u - 2 - 8 - 4*u**2 + 2 = 0.
1, 2
Let g = -2176/7 - -19633/63. Solve 7/9*l**2 - g - 1/9*l**3 + 1/9*l = 0.
-1, 1, 7
Let n = -9907/4 - -2477. Factor -1/2*m**2 + 1/4 + 1/4*m + n*m**4 + 1/4*m**5 - 1/2*m**3.
(m - 1)**2*(m + 1)**3/4
Let z(v) be the second derivative of v**6/90 + v**5/3 + 25*v**4/6 - 5*v**3/6 + 8*v. Let w(u) be the second derivative of z(u). Suppose w(h) = 0. Calculate h.
-5
Let n(q) be the third derivative of -q**5/20 - 9*q**4/8 - 10*q**3 + 170*q**2. Determine v, given that n(v) = 0.
-5, -4
Let q(p) be the first derivative of 0*p**3 - 4 + 2/35*p**5 + 1/14*p**4 + 0*p + 0*p**2. Factor q(r).
2*r**3*(r + 1)/7
Let x(c) be the first derivative of -5*c**4/2 + 95*c**3/3 - 45*c**2/2 + 153. Suppose x(f) = 0. What is f?
0, 1/2, 9
Find f such that -1/7*f**5 - 29/7*f**2 + 3/7*f**3 + 18/7*f + 0 + 9/7*f**4 = 0.
-2, 0, 1, 9
Solve 3/5*m**2 + 7260 + 132*m = 0.
-110
Let n(u) be the third derivative of u**5/60 + u**4/24 + 171*u**2. Find h such that n(h) = 0.
-1, 0
Let q(j) be the third derivative of 0*j - 1/390*j**5 + 1/26*j**4 + 9*j**2 + 0 - 3/13*j**3. Factor q(h).
-2*(h - 3)**2/13
Let a(j) be the third derivative of j**8/168 - j**7/105 - j**6/60 + j**5/30 + 628*j**2. Factor a(r).
2*r**2*(r - 1)**2*(r + 1)
Solve 175/4*s**3 - 877/8*s**2 - 81/2 - 49/8*s**4 + 225/2*s = 0 for s.
1, 18/7
Let h(n) be the second derivative of -2*n**7/63 - 13*n**6/135 - 7*n**5/90 - 2*n + 171. Find t such that h(t) = 0.
-7/6, -1, 0
Let u = -2/919 - -943/11028. Let s(c) be the second derivative of -8*c + 0*c**2 - 1/6*c**3 + 0 + u*c**4. Factor s(j).
j*(j - 1)
Factor 0*c**2 + 9*c**2 - 3*c**2 + 2*c**4 - 90*c**3 + 98*c**3.
2*c**2*(c + 1)*(c + 3)
Let c(w) = -w**2 + 11*w - 4. Let r be c(9). Let o = 17 - r. Solve a**3 - o*a**3 + 0*a**3 - 2*a**3 + 4*a**5 = 0 for a.
-1, 0, 1
Let c(m) be the first derivative of -m**5/30 - 7*m**4/24 - 13*m**3/18 + m**2/4 + 3*m + 140. Factor c(x).
-(x - 1)*(x + 2)*(x + 3)**2/6
Let f(d) be the second derivative of -3*d**5/40 - 5*d**4/4 - 17*d**3/4 - 6*d**2 - 98*d. Find t, given that f(t) = 0.
-8, -1
Let z(h) = 13*h**3 - 61*h**2 - 48*h + 101. Let t(y) = 45*y**3 - 213*y**2 - 168*y + 354. Let r(g) = 5*t(g) - 18*z(g). Factor r(n).
-3*(n - 4)*(n - 1)*(3*n + 4)
Let k(i) be the third derivative of i**5/80 + i**4/16 - i**3 + 4*i**2 - 1. Suppose k(x) = 0. Calculate x.
-4, 2
Suppose 3/5*o**2 + 2 - 17/5*o = 0. Calculate o.
2/3, 5
Let t(q) be the third derivative of 0 - 1/6*q**4 + 1/30*q**5 + 0*q + 5*q**2 + 0*q**3. Factor t(v).
2*v*(v - 2)
Suppose n - 8 + 4 = 0. Let t be n/24*9/3. Factor -1 + h**2 - t*h**3 + 1/2*h.
-(h - 2)*(h - 1)*(h + 1)/2
Let i(b) be the second derivative of b**6/60 + b**5/40 - b**4/12 + 41*b. Determine r, given that i(r) = 0.
-2, 0, 1
Let t(w) be the first derivative of -1/9*w**3 + 1/12*w**4 - 1/6*w**2 - 1 + 1/3*w. Factor t(i).
(i - 1)**2*(i + 1)/3
Let d(v) = 66*v - 1383. Let n be d(21). Solve 8/5*h**n + 92/15*h**2 + 8*h + 10/3 + 2/15*h**4 = 0 for h.
-5, -1
Let q(h) = -6*h**4 - 25*h**3 + h**2 + 114*h - 84. Let f(m) = -2*m**4 - 8*m**3 + 38*m - 28. Let t(y) = -17*f(y) + 6*q(y). Suppose t(a) = 0. Calculate a.
-7, -2, 1
Let u(l) be the first derivative of -3*l**5/10 + 7*l**4/6 + 7*l**3/3 - 3*l**2 - 4*l + 3. Let j(k) be the first derivative of u(k). Solve j(a) = 0 for a.
-1, 1/3, 3
Let f(z) be the second derivative of z**6/10 - 57*z**5/20 + 20*z**4 + 50*z**3 - 4*z - 3. Find i, given that f(i) = 0.
-1, 0, 10
Let r(n) be the first derivative of -n**5 + 5*n**3 - 5*n**2 + 58. Factor r(f).
-5*f*(f - 1)**2*(f + 2)
Suppose 183*t - 530*t = 0. Solve 0 - 1/7*r**5 + t*r - 3/7*r**4 + 0*r**2 + 4/7*r**3 = 0 for r.
-4, 0, 1
Let c(p) be the second derivative of -p**7/36 - 11*p**6/45 - 11*p**5/40 + 8*p**4/9 + 5*p**3/9 - 32*p. Solve c(t) = 0.
-5, -2, -2/7, 0, 1
Suppose -3*y + 2*y - 6*y = 0. Let g = 59 - 59. Factor 0*a**4 + 0*a**2 - 1/2*a**3 + 1/2*a**5 + y + g*a.
a**3*(a - 1)*(a + 1)/2
Let f be (-8)/10 - (-918)/810. Let m(b) be the second derivative of -1/6*b**6 + f*b**3 - 9/20*b**5 + 1/6*b**7 - 3*b + 0*b**2 + 5/12*b**4 + 0. Factor m(o).
o*(o - 1)**2*(o + 1)*(7*o + 2)
Determine a so that 0*a**3 + 14*a**3 - 32*a**4 + 47*a + 12*a**5 + a**3 + 9*a**3 - 51*a = 0.
-1/3, 0, 1
Find h such that -3*h - 19/2*h**2 + 0 + 73/2*h**3 - 11*h**4 = 0.
-2/11, 0, 1/2, 3
Let g be 0 + 1 + 1 + 2/2. Suppose 0*c - g = -3*v + c, -5*v = -2*c - 4. Factor 0*k + 14/9*k**3 + 4/9*k**v + 0 + 10/9*k**4.
2*k**2*(k + 1)*(5*k + 2)/9
Suppose -786 + 2086 = 13*f. Let i be (12/(-135))/((-10)/f). Factor -2/9*q**2 - i*q - 2/3.
-2*(q + 1)*(q + 3)/9
Let l(u) be the third derivative of 7*u**7/15 - 7*u**6/15 + 2*u**5/15 - 16*u**2 + 1. Suppose l(i) = 0. Calculate i.
0, 2/7
Let b = -281415 + 37427979/133. Let d = -20/19 - b. Solve -1/7*q**4 - 4/7*q + 4/7 - 3/7*q**2 + d*q**3 = 0 for q.
-1, 1, 2
Let b(d) be the third derivative of -1/1176*d**8 + 9*d**2 - 1/35*d**6 - 1/28*d**4 - 1/21*d**5 + 0*d + 0*d**3 + 0 - 2/245*d**7. What is s in b(s) = 0?
-3, -1, 0
Suppose 5*a + 3*v - 141 = 0, -5*a + v = -4*v - 125. Factor -3*k - 25*k**2 