o + 14. Suppose -s*x + 10 = -8. Let 3/2*m**x + 0 + 3/2*m - 3*m**2 = 0. Calculate m.
0, 1
Suppose -4*x = -4*s - 8, 5*s + 2*x = 2*s + 4. Suppose 4/9*k + 2/9*k**2 + s = 0. Calculate k.
-2, 0
Let m(g) be the third derivative of g**5/150 + g**4/60 - 11*g**2. Factor m(s).
2*s*(s + 1)/5
Factor 16/3*a + 32/3 + 2/3*a**2.
2*(a + 4)**2/3
Let n(c) be the third derivative of -c**5/100 + 3*c**4/20 - 9*c**3/10 - 3*c**2. Factor n(k).
-3*(k - 3)**2/5
Solve 2/9*m**3 + 2/3*m**2 - 2/3*m**4 - 4/9*m + 2/9*m**5 + 0 = 0.
-1, 0, 1, 2
Factor 2*s**3 + 10*s + 16*s**2 + 36 - 6*s + 19*s + 19*s.
2*(s + 2)*(s + 3)**2
Let u(p) be the first derivative of p**6/120 - p**4/8 + p**3/3 + 3. Let b(z) be the third derivative of u(z). Factor b(c).
3*(c - 1)*(c + 1)
Let r(u) be the third derivative of -u**6/240 - u**5/40 + 5*u**3/6 - 5*u**2. Let z(p) be the first derivative of r(p). Factor z(v).
-3*v*(v + 2)/2
Let o(l) = 2*l - 21. Let s(i) = -i + 11. Let z(w) = -3*o(w) - 5*s(w). Let r be z(5). Factor -1/5*n**5 + 2/5*n**r + 1/5 + 1/5*n**4 - 1/5*n - 2/5*n**2.
-(n - 1)**3*(n + 1)**2/5
Let s be 0/1*(-2)/4. Suppose 5*k - 3*c - 3 - 10 = 0, 4*c = 4*k - 12. Determine n so that 3*n**4 + s*n**2 - 3*n**4 - 2*n**3 + k*n - n**2 + n**4 = 0.
-1, 0, 1, 2
Suppose 11*s - 12*s + 3 = 3*f, 5*s = -5*f + 15. Factor 2/15*l**s + 0*l - 2/5*l**2 + 8/15.
2*(l - 2)**2*(l + 1)/15
Let t(v) be the third derivative of 0*v**4 - 1/35*v**7 + 0*v + 0 - 1/112*v**8 - 1/40*v**6 + 5*v**2 + 0*v**5 + 0*v**3. Factor t(w).
-3*w**3*(w + 1)**2
Let z(s) be the first derivative of s**6/2 + 12*s**5/5 + 3*s**4/2 - 4*s**3 - 9*s**2/2 + 14. Factor z(l).
3*l*(l - 1)*(l + 1)**2*(l + 3)
Suppose 155 + 4*s**3 - 2*s**5 - 4*s**2 + 2*s**4 - s - s - 153 = 0. What is s?
-1, 1
Let f be (-6)/(-45) + 129/45. Let y(j) be the second derivative of 0 - 1/3*j**f + 1/21*j**7 + 3*j + 0*j**5 + 0*j**2 + 2/15*j**6 - 1/3*j**4. Factor y(i).
2*i*(i - 1)*(i + 1)**3
Let j(d) = -5*d**3 - 18*d**2 - 13*d. Let v(k) = -3*k**3 - 9*k**2 - 6*k. Let a(z) = -3*j(z) + 7*v(z). Let a(s) = 0. Calculate s.
-1, -1/2, 0
Let m be -1*(-5)/(-20) + 12/16. Determine u, given that -2*u**4 - 2*u**2 - m*u - 1/2*u**5 - 3*u**3 + 0 = 0.
-1, 0
Suppose -3*b**4 - b**4 + 16 + 52*b**2 + 48*b + 24*b**3 + 8*b**4 = 0. Calculate b.
-2, -1
Suppose -t + 6*t - 10 = -5*q, -5*t = 2*q - 1. Suppose 3*s - 4*s + q*s - s**2 = 0. Calculate s.
0, 2
Let k(s) be the first derivative of -1/14*s**4 - 2/21*s**3 - 4 + 2/7*s + 1/7*s**2. Factor k(h).
-2*(h - 1)*(h + 1)**2/7
Let y(w) = -5*w + 2 + w**3 + 7*w + 1. Let v(r) = -2*r**3 - 3*r - 5. Let p(f) = -6*v(f) - 10*y(f). Suppose p(h) = 0. Calculate h.
-1, 0, 1
Determine u so that -124*u**2 + 3*u**2 - 44*u - 10 + 6 = 0.
-2/11
Let p(j) = -j**2 + 7*j - 4. Let v be p(6). Suppose 0 = -a - 5*g + 5 + 5, -3 = -a + 2*g. Factor 3*h**2 + h**a + 5*h**3 + 7*h**4 - 2*h**2 + v*h**5.
h**2*(h + 1)**2*(3*h + 1)
Find t such that -1/3*t**4 + 0*t + 0 + t**3 - 2/3*t**2 = 0.
0, 1, 2
Suppose 4*b - 3*c - 6 = 0, -5*b - 8*c + 3*c - 10 = 0. Suppose b = -j + 5*j - 12. Factor 0 + 0*d - 1/4*d**4 + 1/4*d**2 - 1/4*d**j + 1/4*d**5.
d**2*(d - 1)**2*(d + 1)/4
Let d(i) = i + 8. Let j be d(-3). Let k(m) be the first derivative of 1 + 0*m**3 - m + 1/5*m**j + m**2 - 1/2*m**4. Find l such that k(l) = 0.
-1, 1
Let t(s) = -s + 3 - 5 - 4 - 2. Let h be t(-11). Let -11*n**3 + 8 + 2*n + 3*n - 6*n**2 + h*n**3 - 2*n**4 + 3*n = 0. Calculate n.
-2, -1, 1
Let x = -6 - -11. Find p such that -p**x - p**3 - 2*p**4 - 2*p**2 + 2*p**5 + 4*p**4 = 0.
-2, -1, 0, 1
Let k(o) = 3*o**3 + 2*o**2 + o + 2. Let a(x) = 10*x**3 + 6*x**2 + 3*x + 7. Suppose 6*p - 28 = 2*p. Let z(s) = p*k(s) - 2*a(s). Suppose z(d) = 0. What is d?
-1, 0
Let t(o) = -o**3 + 5*o**2 - 3*o + 4. Let b(p) = p**3 - 10*p**2 + 8*p + 13. Let m be b(9). Let y be t(m). Factor -9*j**4 - 2 - 2*j + j**4 + 2*j**3 + 2 + y*j**2.
-2*j*(j - 1)*(j + 1)*(4*j - 1)
Let l be 1/2 - 10/(-4). Suppose 4*m - 7 = p, 2*m + 3*p - 5 = m. Determine u so that -2*u**2 - u**3 - m*u**l + u**3 = 0.
-1, 0
Let u(y) = -6*y**4 + 14*y**3 - 6*y**2 - 11*y + 9. Let f(c) = 3*c**4 - 7*c**3 + 3*c**2 + 5*c - 4. Let s(g) = -10*f(g) - 4*u(g). Solve s(d) = 0 for d.
-2/3, 1
Let x(l) be the second derivative of l**7/14 - l**6/10 - 3*l**5/20 + l**4/4 - 5*l. Determine p so that x(p) = 0.
-1, 0, 1
Let o(q) be the first derivative of -q**8/1176 + q**6/140 + q**5/105 - 3*q**2/2 + 2. Let b(i) be the second derivative of o(i). Factor b(t).
-2*t**2*(t - 2)*(t + 1)**2/7
Let h(p) be the first derivative of p**5/3 - 5*p**3/9 + 35. Factor h(l).
5*l**2*(l - 1)*(l + 1)/3
Factor -22/25*t - 16/25*t**2 + 8/25*t**3 - 6/25.
2*(t - 3)*(2*t + 1)**2/25
Let v(m) be the first derivative of m**5/20 + m**4/2 + 2*m**3 + 2*m**2 + 4. Let n(c) be the second derivative of v(c). Suppose n(j) = 0. What is j?
-2
Solve 1/6 + 1/2*d**2 + 1/2*d + 1/6*d**3 = 0 for d.
-1
Let d(l) be the second derivative of 3*l**4/16 - 7*l**3/8 + 3*l**2/4 - 10*l. Factor d(z).
3*(z - 2)*(3*z - 1)/4
Let u(w) be the second derivative of -w**5/10 + w**4/3 - 2*w. Factor u(b).
-2*b**2*(b - 2)
Suppose -5*r + 81 = -0*f + 3*f, 0 = 3*f + 4*r - 78. Factor 32*t**3 + f*t**2 + t + 14*t**4 + 0*t**4 + 3*t.
2*t*(t + 1)**2*(7*t + 2)
Suppose 0 = 5*o - 4*b + 6, -o + 2 = -2*o + b. Suppose -3*r = 5*x + o*r + 10, -34 = -3*x + 5*r. Factor -1 - 4 + x + 2*k**2.
2*(k - 1)*(k + 1)
Let n = -1 + 6. Suppose 2*t + a = 60, 10*t - 144 = n*t - 4*a. What is p in 4 - 8*p**3 - p**3 + t*p + 58*p**3 + 77*p**2 = 0?
-1, -2/7
Suppose 0 = 3*t - 0 - 3. Suppose -l + t = -3. Let 2/5*r + 14/5*r**3 + 6/5*r**l + 0 + 2*r**2 = 0. Calculate r.
-1, -1/3, 0
Let o(w) be the third derivative of 0*w**3 + 1/84*w**8 + 1/6*w**4 + 0*w + 1/5*w**6 + 0 - 8/105*w**7 + 10*w**2 - 4/15*w**5. Suppose o(q) = 0. What is q?
0, 1
Let m(t) be the first derivative of -t**6/4 + t**5/10 + t**4/4 - 58. Suppose m(q) = 0. What is q?
-2/3, 0, 1
Let y be (-14)/(-4) - ((-84)/(-4))/7. Let b(l) be the first derivative of y*l - 3 - 1/6*l**3 + 0*l**2. Factor b(v).
-(v - 1)*(v + 1)/2
Suppose 3*u - 4 = -m, 24 = 3*u + 5*m + 4. Suppose g + 12 = 4*p, u = 2*p - 3*g - 0*g - 6. Suppose 10/3*v**2 + 2/3 + 4/3*v**p + 8/3*v = 0. What is v?
-1, -1/2
Let l(i) be the second derivative of i**7/105 - i**6/20 + i**5/10 - i**4/12 - i**2/2 - 2*i. Let s(u) be the first derivative of l(u). Factor s(n).
2*n*(n - 1)**3
Let j(u) be the third derivative of -u**8/840 + 2*u**7/175 - 13*u**6/300 + 2*u**5/25 - u**4/15 + 5*u**2. Determine m, given that j(m) = 0.
0, 1, 2
Let v(r) = -r**3 + r**2 + 1. Let i(d) = 7*d**4 + 22*d**3 + 31*d**2 + 4*d. Let g = -1 + 0. Let k(w) = g*i(w) + 4*v(w). Factor k(a).
-(a + 1)**2*(a + 2)*(7*a - 2)
Let t(l) be the second derivative of -l**7/84 + l**6/10 - 13*l**5/40 + l**4/2 - l**3/3 - 4*l. Factor t(c).
-c*(c - 2)**2*(c - 1)**2/2
Let p(i) be the second derivative of 0*i**2 + 1/18*i**4 - 5*i + 0 + 0*i**3 - 1/20*i**5. Factor p(x).
-x**2*(3*x - 2)/3
Let d(v) be the second derivative of 0*v**2 + 2*v + 1/54*v**4 + 1/27*v**3 + 0. Factor d(z).
2*z*(z + 1)/9
Let r be (-2)/(-11) + (-1390)/22. Let m be (-7)/(-3)*(-6)/r. Factor 0*k + 0 - m*k**2 + 2/9*k**3.
2*k**2*(k - 1)/9
Let j(v) be the third derivative of -v**7/280 - v**6/40 + v**5/40 + 3*v**4/8 - 9*v**3/8 + 17*v**2. Factor j(h).
-3*(h - 1)**2*(h + 3)**2/4
Let i be ((-702)/(-15))/((-2)/(-5)). Let b be ((-13)/i)/((-1)/12). Factor 2/3*s**4 + 0 + 0*s + 2/3*s**2 - b*s**3.
2*s**2*(s - 1)**2/3
Factor -22/7*p**2 - 6*p**3 - 34/7*p**4 - 4/7*p + 0 - 10/7*p**5.
-2*p*(p + 1)**3*(5*p + 2)/7
Factor 0*o**3 - o**4 + o**2 - 1/2*o + 1/2*o**5 + 0.
o*(o - 1)**3*(o + 1)/2
Let b = -120 + 122. Factor -13/2*v**b + 13/4*v + 15/4*v**3 - 1/2.
(v - 1)*(3*v - 1)*(5*v - 2)/4
Let o(u) be the first derivative of -u**6/30 + u**5/25 + u**4/10 + 9. Factor o(c).
-c**3*(c - 2)*(c + 1)/5
Let k(c) = -195*c**3 + 1092*c**2 - 1260*c - 675. Let s(g) = 15*g**3 - 84*g**2 + 97*g + 52. Let z(i) = -2*k(i) - 27*s(i). Determine f so that z(f) = 0.
-2/5, 3
Let a = -1198 - -1201. Solve 22/5*z**a + 8/5*z - 24/5*z**5 + 0 - 46/5*z**4 + 8*z**2 = 0 for z.
-2, -2/3, -1/4, 0, 1
Let y(z) be the first derivative of 2*z**6/15 - 4*z**5/5 + 5*z**4/3 - 4*z**3/3 + 2*z - 3. Let h(r) be the first derivative of y(r). Solve h(c) = 0 for c.
0, 1, 2
Let f = -1 - -3. Suppose -h**2 - 3*h**5 - 9*h**4 + f*h**2 - 4*h**2 - 9*h**3 = 0. Calculate h.
-1, 0
Let m = 0 + 2. Factor 3*j + 0 - 6 + 7*j