 + k**3/9 - 5*k + 7. Let c(n) be the first derivative of a(n). Factor c(i).
-i*(7*i - 2)/3
Suppose 6*f - 4 = -4. What is m in 0*m + 0*m**2 + 3/2*m**3 + 3*m**4 + 3/2*m**5 + f = 0?
-1, 0
Let n(w) = -w**2 + w - 1. Let s(c) = -8*c**2 - 2 - 6*c + 16*c - 7. Let b(l) = 21*n(l) - 3*s(l). Determine r so that b(r) = 0.
1, 2
Let g(j) be the second derivative of j**6/120 - j**5/40 - j**4/16 + j**3/3 - j**2/2 - 12*j. Factor g(k).
(k - 2)*(k - 1)**2*(k + 2)/4
Let n(o) = -51*o**2 - 12*o + 9. Let q(t) = -25*t**2 - 6*t + 4. Let x(d) = 4*n(d) - 9*q(d). Solve x(s) = 0.
-2/7, 0
Let l(u) = -8*u**2 - 3*u + u + 0*u - 4 - u**3 - 6. Let v be l(-8). Find x such that 8*x**3 + 4*x - v*x**5 - 2*x - 4*x**2 - 4*x + 4*x**4 = 0.
-1, -1/3, 0, 1
Let w = 193/470 + -1/94. Let 0 + w*n + 2/5*n**2 = 0. What is n?
-1, 0
Let f(p) be the first derivative of -3*p**4/4 - 3*p**3 + 12*p - 2. Factor f(o).
-3*(o - 1)*(o + 2)**2
Let q(p) = -p**3 - p**2 - 3. Let t(z) = 5*z**3 + 5*z**2 + 17. Let c(i) = 34*q(i) + 6*t(i). Factor c(d).
-4*d**2*(d + 1)
Let n(h) be the third derivative of 7*h**2 + 1/105*h**7 + 1/20*h**6 + 0*h**3 - 1/4*h**4 + 0 - 1/30*h**5 + 0*h. Factor n(f).
2*f*(f - 1)*(f + 1)*(f + 3)
Let s = 1814/3 - 602. What is h in s*h**2 + 16/9*h**3 + 2/9 + 4/3*h = 0?
-1/2
Let c(u) = -3*u**2 + 12*u + 2. Let n be c(4). Factor 8/7 - 2/7*g**3 + 10/7*g**n - 16/7*g.
-2*(g - 2)**2*(g - 1)/7
Let a be 87/15 - (-1)/5. Factor 4*s**3 - 7 + 6*s + 11 - a*s**3.
-2*(s - 2)*(s + 1)**2
Let k(y) be the first derivative of -y**8/840 + y**7/420 + y**6/90 - 4*y**3/3 - 1. Let q(f) be the third derivative of k(f). Let q(u) = 0. Calculate u.
-1, 0, 2
Let d(r) = -r**3 + 8*r**2 - 8*r + 7. Suppose 5*g - 4*m - 28 = 27, 19 = 2*g - m. Let q be d(g). Factor z**3 + 0 + q*z - z + z**2 - 1.
(z - 1)*(z + 1)**2
Factor 8/9 - 4/9*a**3 + 4/9*a - 8/9*a**2.
-4*(a - 1)*(a + 1)*(a + 2)/9
Let d(t) be the third derivative of t**5/300 - t**4/30 - 36*t**2. Factor d(r).
r*(r - 4)/5
Let s = 3 + -6. Let p be (s/4)/(3/(-2)). Factor 1/2*y**2 + p - y.
(y - 1)**2/2
Suppose -5*d - 5*k - 10 = 0, 3*d + 5*k = 5*d - 31. Determine n, given that 2/7*n**d + 2/7*n**2 + 0*n + 0 = 0.
-1, 0
Solve 4 - 64/3*v**3 - 100/3*v + 224/3*v**2 = 0.
1/4, 3
Let o(h) be the first derivative of -2*h**3/5 + 4*h**2/5 + 8*h/5 + 11. Factor o(a).
-2*(a - 2)*(3*a + 2)/5
Let l = 206 + -204. Factor -3/5*q**l - 3/5*q**3 - 1/5*q**4 - 1/5*q + 0.
-q*(q + 1)**3/5
Let y(l) = 7*l**3 + 4*l**2 - 5*l + 6. Let j(a) = -8*a**3 - 5*a**2 + 5*a - 6. Let i(f) = 6*j(f) + 7*y(f). Suppose i(m) = 0. What is m?
-2, 1, 3
Suppose r - 8 = -5. Let r*z + 120 - 120 - 3*z**3 = 0. Calculate z.
-1, 0, 1
Suppose 5*l - 38 = -3*v + 3*l, v - 16 = -4*l. Let p be (v/14)/(5/7). Let 2/5 - 2/5*x**3 + p*x**2 - 6/5*x = 0. What is x?
1
Let h(v) be the first derivative of v**6/9 + 8*v**5/15 + v**4 + 8*v**3/9 + v**2/3 - 5. Suppose h(a) = 0. Calculate a.
-1, 0
Let c(l) be the third derivative of l**8/33600 - l**6/1200 + l**5/300 - l**4/6 + 2*l**2. Let y(a) be the second derivative of c(a). Factor y(o).
(o - 1)**2*(o + 2)/5
Suppose -6*d + 6 = -3*d. Let o(i) be the third derivative of 1/240*i**5 - 1/12*i**3 + 3*i**d - 1/96*i**4 + 0*i + 0. Factor o(x).
(x - 2)*(x + 1)/4
Determine v so that 0 + 5/2*v**2 + 2*v + 1/2*v**3 = 0.
-4, -1, 0
Let s = 127/255 - 5/51. Let q = 547/5 - 109. What is y in 0 - 6/5*y**4 - q*y**2 - s*y + 2*y**3 = 0?
-1/3, 0, 1
Let n(g) = 6*g**2 - 2*g - 4. Let x(y) = -13*y**2 + 4*y + 9. Let c(b) = 7*n(b) + 3*x(b). Factor c(m).
(m - 1)*(3*m + 1)
Factor 77*n**4 - 3*n - 25*n**4 + 9*n**2 - 25*n**4 - 24*n**4 - 9*n**3.
3*n*(n - 1)**3
Let n(c) = -c**4 + 3*c**3 + c**2 - 3*c - 4. Let z(k) = k**4 - 4*k**3 + 4*k + 5. Let p(j) = -3*n(j) - 2*z(j). Factor p(i).
(i - 2)*(i - 1)*(i + 1)**2
Let w = 16 + -16. Let b(m) be the second derivative of w + 3*m + 1/10*m**5 - 1/3*m**3 - 1/15*m**6 + 0*m**2 + 1/6*m**4. Solve b(j) = 0 for j.
-1, 0, 1
Let w be (-13)/(-21) + 3/(-9). Find o, given that 0*o**4 + 0*o + 2/7*o**5 - w*o**3 + 0 + 0*o**2 = 0.
-1, 0, 1
Let x(i) be the third derivative of i**5/630 + i**4/21 + 4*i**3/7 + 5*i**2. Factor x(v).
2*(v + 6)**2/21
Let x(z) be the second derivative of -121*z**4/27 - 88*z**3/27 - 8*z**2/9 + 35*z. Suppose x(h) = 0. What is h?
-2/11
Let x = -13 + 1. Let a be (2/24)/(x/(-32)). Factor 0*d - 2/9*d**2 + a.
-2*(d - 1)*(d + 1)/9
Let c(i) = i**2. Let u(f) = 12*f**2 - 9*f + 1. Let a(y) = -4*c(y) + u(y). Factor a(l).
(l - 1)*(8*l - 1)
Let z = -1/454 + 915/3178. Suppose 0 + z*j**2 + 0*j = 0. What is j?
0
Let q(z) be the second derivative of -1/8*z**2 + 1/12*z**3 - 1/48*z**4 - 2*z + 0. Let q(t) = 0. Calculate t.
1
Let v(i) = 3*i**2 - 6*i + 3. Let w(j) = 2*j**2 - 9*j - 3. Let n(s) = -2*s**2 + 10*s + 4. Let g(x) = 5*n(x) + 6*w(x). Let r(a) = 7*g(a) - 5*v(a). Factor r(z).
-(z - 1)**2
Let a(y) be the third derivative of y**7/2940 + y**6/420 + y**5/210 + 5*y**3/6 + 5*y**2. Let r(d) be the first derivative of a(d). Factor r(v).
2*v*(v + 1)*(v + 2)/7
Let g = 41/180 - 1/36. Let w(n) be the second derivative of 0*n**2 + 0*n**4 - g*n**5 + 3/5*n**6 - 1/3*n**7 + 0*n**3 + 0 - 2*n. Determine d so that w(d) = 0.
0, 2/7, 1
Let l(v) be the first derivative of -v**6/21 + 4*v**5/35 + v**4/14 - 4*v**3/21 + 14. Suppose l(m) = 0. Calculate m.
-1, 0, 1, 2
Let d(b) = 8*b**3 + 7*b**2 - 8*b. Let z(u) = -7*u**3 - 6*u**2 + 7*u. Let i(a) = 6*d(a) + 7*z(a). Factor i(r).
-r*(r - 1)*(r + 1)
Let f(s) = s**3 - 17*s**2 + 16*s - 3. Let w be f(16). Let n(q) = q**2 + q - 1. Let y be n(w). Factor 0 - 2/9*t**4 + 2/9*t**2 + 0*t - 2/9*t**3 + 2/9*t**y.
2*t**2*(t - 1)**2*(t + 1)/9
Suppose k = 3*s - 7, -3*k = s + 4 - 13. Solve -3*n**3 + 2*n**5 - n**s + 2*n**3 = 0 for n.
-1, 0, 1
Let q(b) be the second derivative of -7*b**4/6 - 4*b**3/27 + 4*b**2/9 - 14*b. Factor q(i).
-2*(7*i + 2)*(9*i - 2)/9
Let w(b) = -5*b**5 + 3*b**4 - 6*b**3 - 6*b**2 + 11*b + 11. Let r(p) = -3*p**5 + 2*p**4 - 4*p**3 - 4*p**2 + 7*p + 7. Let f(m) = 8*r(m) - 5*w(m). Factor f(x).
(x - 1)**2*(x + 1)**3
Let s(i) = -2*i**2 + 8 - 1 + 5 - 4 - 12*i. Suppose 0*x = x + 18. Let r(t) = t - 1. Let h(l) = x*r(l) - 2*s(l). Factor h(a).
2*(a + 1)*(2*a + 1)
Suppose -3*v + 7*v - 12 = 0. Factor l - 2*l**3 + l**4 + 3*l**v + l**5 - 2*l**2 - 4*l**3 + l**3 + 1.
(l - 1)**2*(l + 1)**3
Let l be (-12)/(0 + -5 - -2). Let -16/3*n**3 + 4/3*n + 0 + 2/3*n**2 + 10/3*n**l = 0. Calculate n.
-2/5, 0, 1
Let r(j) be the first derivative of 2*j - 7/3*j**3 + 1 - 5/2*j**2. Factor r(k).
-(k + 1)*(7*k - 2)
Let o(r) be the second derivative of -r**5/160 + r**4/48 + r**3/48 - r**2/8 + 9*r. Factor o(g).
-(g - 2)*(g - 1)*(g + 1)/8
Let z(v) = 2*v**2 + 18*v + 4. Let y be z(-9). Let 1/4*c**5 - 7/4*c**2 + 1/2*c + 0 - 5/4*c**y + 9/4*c**3 = 0. What is c?
0, 1, 2
Let d(a) be the first derivative of -3*a**5/35 + a**4/14 + 3*a**3/7 - 4*a/7 - 4. Let d(k) = 0. What is k?
-1, 2/3, 2
Let r(z) be the third derivative of -5*z**8/2184 + z**7/455 + 17*z**6/780 - 19*z**5/390 + 4*z**3/39 + 2*z**2. Find m, given that r(m) = 0.
-2, -2/5, 1
Suppose -10*s = -8*s. Let i(g) be the third derivative of 1/150*g**5 + s - 1/15*g**3 + 1/300*g**6 + 0*g - 2*g**2 - 1/60*g**4. Factor i(x).
2*(x - 1)*(x + 1)**2/5
Factor -6 + 4*m - 2*m + 7*m - 3*m**2.
-3*(m - 2)*(m - 1)
Let v = -1/5283 - -19378/36981. Let t = -5/21 + v. Factor -t*f**2 + 2/7*f - 2/7*f**3 + 2/7.
-2*(f - 1)*(f + 1)**2/7
Let d = -13 - -18. Let f be ((-8)/(-6)*3)/2. Factor 6*g**3 - 2*g**5 + 4*g**f + 4*g**4 - 2*g**5 + g + 5*g**d.
g*(g + 1)**4
Let o be (10/2 - 4)*0. Suppose -7 = -2*g - 3. Factor x + o + 3/2*x**3 - 5/2*x**g.
x*(x - 1)*(3*x - 2)/2
Suppose -14 = -4*x - 6. Factor x*z + 0*z**5 + 0*z**2 + z**4 + 3*z**5 - z**2 - 5*z**3.
z*(z - 1)*(z + 1)**2*(3*z - 2)
Suppose 2*t - 14 = -q, -5*q = -0*t - 5*t + 5. Let z(x) be the third derivative of -1/3*x**3 + 1/30*x**5 - 1/12*x**q + x**2 + 0 + 0*x + 1/60*x**6. Factor z(l).
2*(l - 1)*(l + 1)**2
Let a(j) be the first derivative of 18*j - 3 + 2/3*j**3 - 6*j**2. Factor a(w).
2*(w - 3)**2
Let r = 891 - 6211/7. Find u, given that -82/7*u**3 + 8*u**5 + 26/7*u + 4/7 + 22/7*u**2 - r*u**4 = 0.
-1, -2/7, -1/4, 1
Let j(a) = -3*a**3 + 8*a**2 + 3*a - 4. Let x(o) = -14*o**2 + 33 - 3*o**2 + 6*o**3 - 5*o - o - 26. Let u(z) = 5*j(z) + 2*x(z). Suppose u(t) = 0. What is t?
-1, 1, 2
Find u, given that -1 + 1/4*u**5 + 5/4*u**4 + 7/4*u**3 - 2*u - 1/4*u**2 = 0.
-2, -1, 1
Let v(w) be t