 -12*a + 2*g. Factor 24/5*n**a + 162/5 + 216/5*n + 108/5*n**2 + 2/5*n**v.
2*(n + 3)**4/5
Suppose -5*u + 204 = 7*u. Suppose 9*p - u = 10. Factor -4/9*z + 2/9*z**2 + 0 + 2/9*z**p.
2*z*(z - 1)*(z + 2)/9
Let o be -6 + (1/(-5) - 930/(-150)). Let q(p) be the second derivative of 10*p + o*p**2 - 1/78*p**4 + 0 + 2/39*p**3. Find n, given that q(n) = 0.
0, 2
Let p(f) be the second derivative of -f**5/75 + f**4/30 + 4*f**3/15 - 8*f**2 - 11*f. Let u(l) be the first derivative of p(l). Let u(v) = 0. What is v?
-1, 2
Let i(k) = -k**3 + 30*k**2 - 31*k + 60. Let p be i(29). Factor 9 + 3/2*y**p - 21/2*y.
3*(y - 6)*(y - 1)/2
Let z be 6/33 + 8/(-44). Suppose 3*l = 7*l + 3*v - 17, z = l + 5*v. Factor f**3 + 4*f**l - 4*f**3 + f**3 - 2*f**3.
4*f**3*(f - 1)*(f + 1)
Let s(p) be the first derivative of -96/5*p**5 - 10/3*p**6 + 8*p - 40*p**4 - 6*p**2 + 35 - 104/3*p**3. Suppose s(j) = 0. What is j?
-2, -1, 1/5
Suppose -z + 6*o = 2*o - 68, -5*o + 32 = z. Let b be 39/z + (-6)/8 + 2. Factor -2*u**b + 2/3*u + 2/3 - 10/3*u**3 - 4/3*u**4.
-2*(u + 1)**3*(2*u - 1)/3
Let l(o) be the second derivative of -2/5*o**5 + 0 + o**4 + 0*o**3 - 2/15*o**6 + 0*o**2 + 16*o. Solve l(r) = 0 for r.
-3, 0, 1
Suppose 4*v + 37 = 2*j + 25, 0 = 4*j + 4*v. Factor 36*w**2 + 10*w - 34*w**j - 14 + 4*w - 2.
2*(w - 1)*(w + 8)
Let l be (1065/60 + -18)/(1/(-8)). Let q(r) be the second derivative of -l*r**2 + 1/3*r**4 + 0*r**3 + 0 + 10*r. Factor q(o).
4*(o - 1)*(o + 1)
Suppose -4*r - 5*w + 2 + 9 = 0, -3 = 3*w. Factor -h**4 + 8*h**3 + 3*h**4 - 4*h**2 - 10*h**r + 4*h**4.
-4*h**2*(h - 1)**2
Let h(k) be the third derivative of -k**5/60 + 4*k**4/3 + 34*k**3/3 + 23*k**2 - 1. Factor h(s).
-(s - 34)*(s + 2)
Let c(u) be the third derivative of -1/36*u**6 - 2/9*u**3 + 0*u**7 - 1/9*u**5 + 1/1008*u**8 + 0*u + 0 - 4*u**2 - 5/24*u**4. Factor c(m).
(m - 4)*(m + 1)**4/3
Let g(f) = -f**2 - 11*f - 3. Let b(w) = 5*w + 1. Let p be -4 + (-2 - -1 - -3). Let o(a) = p*g(a) - 5*b(a). Factor o(d).
(d - 1)*(2*d - 1)
Let y be (564/90 - 6)/(16/12). Factor -4/5*m + 1/5*m**3 + 4/5 - y*m**2.
(m - 2)*(m - 1)*(m + 2)/5
Factor 33 + 4*b + 45 - 8 - 35*b**2 + 31*b + 5*b**3 + 5.
5*(b - 5)*(b - 3)*(b + 1)
Suppose 253 = 10*t + t. Let y = t - 23. Suppose k**4 + 0*k + y*k**2 + 0*k**3 - 1/2*k**5 + 0 = 0. Calculate k.
0, 2
Let l be 2*(-4)/32 - 153/(-132). Let -4/11*d**4 + 0*d + 0 - 4/11*d**2 - l*d**3 = 0. What is d?
-2, -1/2, 0
Let o(q) be the third derivative of q**7/315 + 17*q**6/360 + 43*q**5/180 + 7*q**4/18 + 571*q**2. Find c such that o(c) = 0.
-4, -7/2, -1, 0
Let w be -5 + -8 + 18 + -2. Let q(n) be the second derivative of -3/40*n**5 + 0 - 4*n + 1/4*n**4 + 1/4*n**w - 3/2*n**2. Find u, given that q(u) = 0.
-1, 1, 2
Let q(w) be the second derivative of -w**4/54 - 4*w**3/27 + 32*w**2/9 - 57*w + 3. Factor q(a).
-2*(a - 4)*(a + 8)/9
Let 535*q**3 + 1266*q**2 - 1080 + 5*q**5 - 821*q + 90*q**4 + 281*q - 276*q**2 = 0. What is q?
-6, -1, 1
Let j = -556 + 558. Let h(g) be the second derivative of 1/90*g**5 - 4/27*g**3 - 4/9*g**j + 0 + 11*g + 1/54*g**4. Let h(b) = 0. What is b?
-2, -1, 2
Solve 2/3*f**4 + 94/3*f**2 + 32*f**3 + 0*f + 0 = 0 for f.
-47, -1, 0
Let a(z) be the third derivative of z**7/1260 - z**6/45 + 7*z**5/180 + z**4/9 - 5*z**3/12 + 22*z**2 - 3. Solve a(v) = 0.
-1, 1, 15
Let r = 1003 - 1001. Let 0 - 8/3*v - 8*v**4 + 4/3*v**3 + 20/3*v**r = 0. What is v?
-1, 0, 1/2, 2/3
Suppose s - 4*c - 10 = -2*s, c = s - 3. Find p such that 4*p**s - 4*p - 77*p**3 - 2*p**4 - 2*p**4 + 81*p**3 = 0.
-1, 0, 1
Suppose -3 = v - 6. Suppose 3*k + 12 = 6*l - v*l, -5*l = -3*k - 20. Factor 10*j**4 + 35*j**4 - 26*j**3 - 18*j**5 + 4*j**2 - 5*j**l.
-2*j**2*(j - 1)**2*(9*j - 2)
Suppose 0 = -l + 4*l - 27. Suppose 6 = 2*y + 4*r, r + 2*r - l = -3*y. Solve 18*n**2 - 2*n - 3*n + n - 8*n + 3*n**4 - 12*n**y + 3 = 0 for n.
1
Let x(n) = -2*n**5 - 28*n**4 - 54*n**3 + 78*n**2 + 6*n. Let k(v) = -6*v**5 - 83*v**4 - 161*v**3 + 233*v**2 + 17*v. Let g(r) = 6*k(r) - 17*x(r). Factor g(z).
-2*z**2*(z - 1)*(z + 6)**2
Let n = -997 - -681. Let u = n - -318. Factor 5/4*k**3 + 5/4*k**u - 5/4*k - 5/4.
5*(k - 1)*(k + 1)**2/4
Let c be ((-12)/(-8) + -2)/((-4)/56). Suppose d + 2*l + c = 2*d, -l = -3*d + 11. Factor 1 - 1/2*j**d + 0*j**2 + 3/2*j.
-(j - 2)*(j + 1)**2/2
Let s(b) = -3*b**4 + 6*b**3 - 3*b**2 + 5*b. Let t be 6 - (-6 - -3 - -4). Let l(m) = -3*m**4 + 5*m**3 - 2*m**2 + 4*m. Let w(g) = t*l(g) - 4*s(g). Factor w(a).
-a**2*(a - 1)*(3*a + 2)
Let s = -20 - -25. Suppose -10 = 3*t - s*t. Find p such that -3*p**5 - 3*p**t + 6*p**5 + 2*p**3 - p - p**5 = 0.
-1, 0, 1
Suppose 66748 = -7*s + 66769. Factor -6/5*g**2 - 3/5*g**s + 0 + 9/5*g.
-3*g*(g - 1)*(g + 3)/5
Let f(x) be the third derivative of 1/21*x**4 - 1/42*x**5 - 7*x**2 + 0 + 1/420*x**6 + 0*x**3 + 0*x. Find k such that f(k) = 0.
0, 1, 4
Solve -1746*p**2 - 11236 - 384*p + 29668 + 1748*p**2 = 0.
96
Let f be (8 + 100/(-10))/(-4). Let l(j) be the first derivative of -1/3*j**3 + 11 + j - 1/4*j**4 + f*j**2. Let l(m) = 0. Calculate m.
-1, 1
Suppose q = -25 + 22, -3*d - 15 = 5*q. Factor -4/7*l**3 + 8/7 + d*l**2 + 12/7*l.
-4*(l - 2)*(l + 1)**2/7
Suppose 0 = 2*p + 7*p - 756. Factor -p*j + 168*j + 2*j**3 - 76*j + 8*j**2.
2*j*(j + 2)**2
Let w be 1*9 - (-67 + 76). Let u(y) be the second derivative of -y + 3/5*y**5 - 4/3*y**4 + 8/15*y**6 - 2*y**3 + w*y**2 + 0. Factor u(b).
4*b*(b - 1)*(b + 1)*(4*b + 3)
Let z(s) be the first derivative of s**4/12 - 16*s**3/9 - 35*s**2/6 - 6*s + 76. Factor z(b).
(b - 18)*(b + 1)**2/3
Let s(f) be the third derivative of 7/36*f**4 - 1/10*f**5 - 1/315*f**7 + 0 - 7*f**2 + 1/36*f**6 - 2/9*f**3 + 0*f. Factor s(y).
-2*(y - 2)*(y - 1)**3/3
Let k(n) be the second derivative of n**7/21 + 4*n**6/35 - 39*n**5/70 - 16*n**4/21 + 4*n**3/7 + 193*n. Solve k(s) = 0.
-3, -1, 0, 2/7, 2
Let x = -21 + 25. Let i(k) = 6*k**2 + 19*k - 14. Let p(y) = -5*y**2 - 20*y + 15. Let a(z) = x*p(z) + 5*i(z). Solve a(n) = 0 for n.
-2, 1/2
Suppose -t - m = -13, -6*t = -2*t + 5*m - 56. Let j = t + -9. Factor 1/2*i**2 + 0*i + j*i**3 + 0 - 1/2*i**4.
-i**2*(i - 1)*(i + 1)/2
Let s be 0 + 16/(-72) + 60/27. Let c(k) be the third derivative of 0*k + 1/14*k**4 + s*k**2 + 1/210*k**5 + 3/7*k**3 + 0. What is n in c(n) = 0?
-3
Suppose 4*g + 0*g + 5*g**3 + 9*g - 15*g**2 + 2*g - 5 = 0. Calculate g.
1
Let q(i) be the second derivative of i**5/45 - 2*i**4/27 + 2*i**3/27 - i - 61. Factor q(k).
4*k*(k - 1)**2/9
Let g = -23/258 + 65/86. Factor -4*k - g*k**2 - 6.
-2*(k + 3)**2/3
Let j = 167/385 + -18/77. Factor j*q**5 - 4/5*q + 3/5*q**3 - 4/5*q**2 + 0 + 4/5*q**4.
q*(q - 1)*(q + 1)*(q + 2)**2/5
Let y(n) = n**2 - 2*n - 1. Let u(j) = -j**2 - 64*j + 1158. Let r(h) = -u(h) - 2*y(h). Determine g, given that r(g) = 0.
34
Let f(n) = -n**2 + 6*n + 16. Let b be f(7). Let s be (6/4)/(b/12). Determine g so that -3/2 - 3/4*g + 3/4*g**3 + 3/2*g**s = 0.
-2, -1, 1
Let q(k) be the first derivative of -3/2*k**2 - 1/16*k**4 + 2 - 2*k - 1/2*k**3. What is h in q(h) = 0?
-2
Let r be -2 + 5 + -2 + 52/(-64). Let s(b) be the third derivative of 3/40*b**5 + 0 - r*b**4 - 3*b**2 - 1/80*b**6 + 1/4*b**3 + 0*b. Determine h so that s(h) = 0.
1
Let p(w) = 39*w**3 + 507*w**2 + 363*w - 909. Let f(v) = 3*v**3 + 39*v**2 + 28*v - 70. Let m(r) = -27*f(r) + 2*p(r). Factor m(g).
-3*(g - 1)*(g + 2)*(g + 12)
Let y = -20 + 24. Suppose -5*l - p = -y*p, 5*p = 4*l. Factor 1/3*u**3 + 1/6 - 1/6*u**4 - 1/3*u + l*u**2.
-(u - 1)**3*(u + 1)/6
Let z be (-1 - -3)*(-66)/12. Let q = z + 15. Determine g, given that -2*g**q + 4/3*g + 2*g**2 - 2/3*g**3 + 0 - 2/3*g**5 = 0.
-2, -1, 0, 1
Let l be (-6)/12 + (-1)/(-29). Let j = 1/29 - l. Factor 3/2 + j*s**2 - 2*s.
(s - 3)*(s - 1)/2
Factor -3/7*d**4 + 108/7*d**2 - 486/7*d + 6/7*d**3 + 81.
-3*(d - 3)**3*(d + 7)/7
Suppose p = -0 + 2. Factor -d**2 - d**p + 3*d**2.
d**2
Let b(q) be the third derivative of 1/60*q**4 + 0*q**3 + 0*q + 1/300*q**5 + 0 + 10*q**2. Factor b(s).
s*(s + 2)/5
Let f = -103332/7 + 14764. Let -52/7*l - 46/7*l**2 - f - 12/7*l**3 = 0. Calculate l.
-2, -4/3, -1/2
Let m(w) be the third derivative of -w**5/660 - w**4/132 + 5*w**3/22 + 88*w**2. Factor m(q).
-(q - 3)*(q + 5)/11
Let a(d) be the second derivative of d**4/30 + d**3/15 + 51*d + 7. Factor a(p).
2*p*(p + 1)/5
Factor 7*i**2 + 28*i + 1061 - 72*i - 36*i - 5*i**2 - 261.
2*(i - 20)**2
Let w(x) be the first derivative of 2*x**3/57 + 2*x**2 +