*2 - 29*k**2 + 10*k**2 - 16*k**5 - 8*k**3 - n + 24*k = 0. Calculate k.
-1, 1/4, 1
Let p(y) be the first derivative of y**4/22 - 2*y**3/33 - 2*y**2/11 + 1. Factor p(u).
2*u*(u - 2)*(u + 1)/11
Factor -5*u**4 - 19*u**4 - 12*u**3 + 8*u**3 - 64*u - 4*u**5 + 96*u**2.
-4*u*(u - 1)**2*(u + 4)**2
Let p(b) be the second derivative of -b**6/120 + b**5/40 - b**3/2 - 5*b. Let f(n) be the second derivative of p(n). Suppose f(q) = 0. What is q?
0, 1
Let b(f) be the third derivative of -2*f**5/15 - f**4/4 + f**3/3 + 15*f**2. Let b(z) = 0. What is z?
-1, 1/4
Let p be (22/(-12) - (-11)/33) + 3. Factor p*l + 1/2*l**4 - 1 + 1/2*l**2 - 3/2*l**3.
(l - 2)*(l - 1)**2*(l + 1)/2
Let b = -17/9 - -103/45. Find v, given that -2/5*v**4 - 6/5*v**3 + 0 - 6/5*v**2 - b*v = 0.
-1, 0
Let k be ((-2)/6)/((-8)/32). Factor 0*p**4 + 0 - 2/3*p**5 - 2/3*p + k*p**3 + 0*p**2.
-2*p*(p - 1)**2*(p + 1)**2/3
Let r(b) be the third derivative of b**6/12 - b**5/4 - 5*b**4/12 - 2*b**2. Suppose r(w) = 0. What is w?
-1/2, 0, 2
Let g(f) = -3*f**2 - 6*f. Suppose 1 + 4 = -p. Let z(m) = -m**3 + 5*m**2 + 11*m. Let k(o) = p*g(o) - 3*z(o). Factor k(d).
3*d*(d - 1)*(d + 1)
Let o(m) = -m**2 + 26*m - 67. Let q be o(23). Factor -2/11*a**q + 4/11*a - 2/11.
-2*(a - 1)**2/11
Determine v so that -16/5 - 12/5*v**2 - 32/5*v = 0.
-2, -2/3
Let s(g) be the second derivative of -1/63*g**7 + g - 1/15*g**5 - 1/9*g**4 + 0 + 1/15*g**6 + 1/3*g**3 - 1/3*g**2. Factor s(y).
-2*(y - 1)**4*(y + 1)/3
Let q(j) be the first derivative of -2/5*j + 5 - 2/5*j**3 + 1/10*j**4 + 3/5*j**2. Determine a so that q(a) = 0.
1
Let i(u) be the first derivative of -u**6/180 - u**5/45 - u**4/36 + 2*u**2 - 7. Let j(k) be the second derivative of i(k). Factor j(q).
-2*q*(q + 1)**2/3
Let k(o) = -4*o**2 - 6*o - 4. Let b(t) = 17*t**2 + 24*t + 16. Let v(c) = -2*b(c) - 9*k(c). Determine g, given that v(g) = 0.
-2, -1
Let g = -25 - -27. Factor 0 - 1/2*l + 1/2*l**g.
l*(l - 1)/2
Suppose -b = 2*r - 9, -r - 2*r = 3*b - 21. Let a = -3 + 4. Solve -3/2*j**3 - a - 7/2*j - 4*j**r = 0 for j.
-1, -2/3
Let x = 39115/7 + -5578. Let n = x - 67/7. Factor 4/7*w**3 - n*w**5 - 4/7*w**2 - 2/7*w + 2/7*w**4 + 2/7.
-2*(w - 1)**3*(w + 1)**2/7
Let m(c) be the first derivative of -c**4/10 + 2*c**3/45 - 3. Suppose m(x) = 0. Calculate x.
0, 1/3
Let q be (-4)/(-3) + 8/12. Suppose w = 4*k, -2*w = w + q*k. Factor w + 0*j - 5/2*j**3 - 3/2*j**4 - j**2.
-j**2*(j + 1)*(3*j + 2)/2
Let i(m) be the third derivative of -m**5/80 - m**4/8 - 12*m**2. Let i(r) = 0. Calculate r.
-4, 0
Let -13*d - 4*d**4 + 8 + 16*d**3 + 0*d - 3*d + 8 - 12*d**2 = 0. What is d?
-1, 1, 2
Let d(k) = -k**2 + 3*k + 5. Let t be d(4). Let z be (1 - t) + (-1)/(-2). Factor 0*y - 15/2*y**4 - 7/2*y**3 - z*y**2 - 9/2*y**5 + 0.
-y**2*(y + 1)*(3*y + 1)**2/2
Let y(z) be the third derivative of -z**8/112 + 3*z**7/35 - 7*z**6/20 + 4*z**5/5 - 9*z**4/8 + z**3 - 24*z**2. What is u in y(u) = 0?
1, 2
Let i(m) be the first derivative of -m**5/35 - m**4/14 + m**2/7 + m/7 - 2. Factor i(k).
-(k - 1)*(k + 1)**3/7
Let 10*t**5 - 972*t**2 + 3*t**3 + 967*t**2 + 5*t**4 - 18*t**3 + 5*t = 0. Calculate t.
-1, 0, 1/2, 1
Let c(q) be the first derivative of -2*q**6/3 + 36*q**5/5 - 21*q**4 + 76*q**3/3 - 12*q**2 - 32. Suppose c(f) = 0. What is f?
0, 1, 6
Let c(m) = -m**2 - 5*m + 6. Let q(b) = -b**2 - 4*b + 5. Let n be 16/(-24) - (-14)/(-6). Let v = n - 2. Let s(h) = v*c(h) + 6*q(h). Let s(f) = 0. Calculate f.
0, 1
Factor -1/3*k**2 + 0 - 2/3*k.
-k*(k + 2)/3
Suppose 0 = -0*v + v - 5*o - 29, 4*v + 5*o = 41. Let c = -11 + v. Determine s, given that 2*s - 18*s**2 - 63*s**4 + 49/2*s**5 + 0 + 109/2*s**c = 0.
0, 2/7, 1
Let f(b) be the first derivative of -3 + 1/9*b**3 + 0*b - 1/6*b**2. Determine y, given that f(y) = 0.
0, 1
Let n = -1 - 0. Let c be 1*(5 + -2 + n). Factor -2*t - 2*t**c + 0 + 0.
-2*t*(t + 1)
Let o be (0 - -3)*20/6. Suppose 2*s + 26 = 5*p, -4*p + 5*s + o = -21. Factor b + 0*b + 3*b**2 - p*b**2.
-b*(b - 1)
Let v be 12*((-10)/6)/(-5). Suppose -2*u**2 + v*u**5 + 0*u**5 - 7*u**3 + 20*u**4 - 15*u**4 = 0. Calculate u.
-2, -1/4, 0, 1
Let f(j) = -5*j**2 + 4*j. Let u = 3 + -6. Let v(s) = -4*s**2 + 5*s. Let t(q) = u*v(q) + 2*f(q). Let l(g) = g**2 - 3*g. Let h(r) = 5*l(r) - 2*t(r). Factor h(d).
d*(d - 1)
Let n(l) be the second derivative of -l**9/52920 + l**7/8820 + l**4/4 + l. Let d(y) be the third derivative of n(y). Factor d(x).
-2*x**2*(x - 1)*(x + 1)/7
Let f(y) be the first derivative of y**5/25 + 9*y**4/10 + 97*y**3/15 + 72*y**2/5 + 64*y/5 + 19. Let f(a) = 0. Calculate a.
-8, -1
Let x(r) be the third derivative of -r**6/210 + r**5/35 - r**4/14 + 2*r**3/21 - 2*r**2. Factor x(o).
-4*(o - 1)**3/7
Let o(b) = -7*b**4 - 6*b**3 - 4*b**2 + 6*b - 7. Let i(k) = -k + 1 - 6*k**2 + 3*k**2 + k**2 + k**3 + k**4 + 3*k**2. Let u(a) = -6*i(a) - o(a). Factor u(v).
(v - 1)**2*(v + 1)**2
Let s(k) be the second derivative of -k**4/90 + 4*k**3/45 - k**2/5 + 15*k. Factor s(m).
-2*(m - 3)*(m - 1)/15
Let m be 1 - (0 + 1 + 11). Let n(x) = -50*x**3 - 31*x**2 - 11*x. Let p(k) = 10*k**3 + 6*k**2 + 2*k. Let d(h) = m*p(h) - 2*n(h). Find z, given that d(z) = 0.
-2/5, 0
Suppose 0*x = -4*x. Let s = -7 - -11. Determine m so that x*m**s + m**2 - 3*m**2 + 2*m**4 = 0.
-1, 0, 1
Let t(k) be the first derivative of -1/21*k**6 + 0*k**2 + 0*k**3 + 0*k - 2/35*k**5 + 5 + 1/7*k**4. Find j, given that t(j) = 0.
-2, 0, 1
Let k be 4/(-26) - (-448)/1560. Let x(z) be the third derivative of 0*z - 1/20*z**6 + 0*z**3 + 1/3*z**4 - k*z**5 + 0 - 2*z**2. What is m in x(m) = 0?
-2, 0, 2/3
Let q(v) be the third derivative of 0*v + 1/16*v**4 + 0 + 1/8*v**3 + 1/80*v**5 - 3*v**2. Factor q(w).
3*(w + 1)**2/4
Let 1/4*u**2 + 7/2*u + 49/4 = 0. What is u?
-7
Suppose 0 = -4*d + 237 + 4215. Let i = 7855/7 - d. Let 0 + 8/7*u**2 + i*u**3 + 0*u + 22*u**4 + 14*u**5 = 0. What is u?
-1, -2/7, 0
Let l be 1*33/6 - 5. Factor -l*s**2 - 1/2*s + 1/2*s**3 + 1/2.
(s - 1)**2*(s + 1)/2
Let t(q) be the third derivative of 1/90*q**5 + 0*q**4 + 0*q**3 + 1/180*q**6 + q**2 + 0*q + 0. Factor t(o).
2*o**2*(o + 1)/3
Solve 3/2*q - 1 - 1/2*q**2 = 0.
1, 2
Let x(m) be the third derivative of -m**8/26880 - m**7/10080 + m**6/2880 + m**5/480 + m**4/4 + 6*m**2. Let f(u) be the second derivative of x(u). Factor f(t).
-(t - 1)*(t + 1)**2/4
Let o(h) = 18*h + 9. Let w be o(-5). Let k be 6/(-2)*144/w. Find s such that 2/3 - 11/3*s - 7/3*s**3 + k*s**2 = 0.
2/7, 1
Let w(i) = -i**4 - i**3 + i**2 + i. Let o(z) = -5*z**5 + 35*z**4 + 45*z**3 - 55*z**2 - 20*z. Let x(p) = o(p) + 30*w(p). Factor x(c).
-5*c*(c - 1)**3*(c + 2)
Let u = 34087/15 - 2275. Let t = u - -16/5. Suppose -7/3*h**3 - t - h + 4*h**2 = 0. Calculate h.
-2/7, 1
Factor i**2 + 1/2*i - 1/4*i**4 - 1/2*i**3 - 3/4.
-(i - 1)**2*(i + 1)*(i + 3)/4
Let k be (12/21)/((-1)/(-24)). Let x = -466/35 + k. Let x*b - 2/5*b**2 + 2/5 - 2/5*b**3 = 0. What is b?
-1, 1
Let d be 0 - ((-30)/36 + (-4)/(-6)). Let u(n) be the second derivative of -1/3*n**3 + n**2 - d*n**4 + 3*n + 0 + 1/10*n**5. Determine f, given that u(f) = 0.
-1, 1
Let u(c) be the first derivative of 4*c**5/15 - 4*c**4/3 - 26. Determine v, given that u(v) = 0.
0, 4
Let l be 3/18 + (2 - 7/(-14)). Let v be 40/9 - (-2)/9. Factor -v*x**2 - l + 32/3*x.
-2*(x - 2)*(7*x - 2)/3
Let d(j) be the first derivative of -j**2 - 2*j + 2/3*j**3 + 1/2*j**4 + 9. Factor d(g).
2*(g - 1)*(g + 1)**2
Suppose -4*s + 5 = -3. Suppose -b = y + 4, b - 4 = -3*y + 4*y. Suppose 0*n**3 + 0*n + 1/4*n**4 - 1/4*n**s + b = 0. Calculate n.
-1, 0, 1
Let f = -1/39 - -5/26. Let a(z) be the second derivative of 0 + 0*z**2 + 1/12*z**4 + f*z**3 - 3*z. Factor a(l).
l*(l + 1)
Determine b so that -5 + 2 + 4 - 2*b - b**2 - 2*b**2 = 0.
-1, 1/3
Factor 2/5*o - 1/5 - 2/5*o**3 + 1/5*o**4 + 0*o**2.
(o - 1)**3*(o + 1)/5
Let f = 9043/8520 + 3/568. Determine o so that -56/5*o - 322/5*o**3 - 98/3*o**4 - f - 628/15*o**2 = 0.
-1, -2/5, -2/7
Let w(d) = -d**3 + 14*d**2 - 30*d + 75. Let p be w(12). Let 0*l**4 - 4/9 - 8/9*l**p + 2/3*l + 4/9*l**2 + 2/9*l**5 = 0. What is l?
-2, -1, 1
Let w be 4/16 + 54/8. Factor 0 - 2*r**4 + 6*r - 2*r**2 - 3 + w - 6*r**3.
-2*(r - 1)*(r + 1)**2*(r + 2)
Factor 30*v**2 + 12 - 35*v**2 + 17 - 4 - 20*v.
-5*(v - 1)*(v + 5)
Let r be (-1 + -1)*(-1)/6. Factor 1/3*b**3 + 1/3*b**2 - r*b**5 - 1/3*b**4 + 0 + 0*b.
-b**2*(b - 1)*(b + 1)**2/3
Factor 3/2*y**4 + 3/4*y**3 + 3/4*y**5 + 0*y + 0 + 0*y**2.
3*