
Let g = 1906/791 - 240/113. Find o, given that 2/7*o - g*o**2 + 0 = 0.
0, 1
Let k(j) = -j**3 - j**2 - j + 4. Let t = 10 - 10. Let a be k(t). Factor a*h**2 + 0*h**3 + 0*h + 4*h + h**3.
h*(h + 2)**2
Let l(p) be the first derivative of 360*p**2 - 14 + 5/12*p**4 - 20*p**3 - 2880*p. Factor l(z).
5*(z - 12)**3/3
Let k = 32/189 + 125/378. Determine u so that -3/2*u**3 + 0 - 3/2*u**2 - k*u - 1/2*u**4 = 0.
-1, 0
Let m(h) = 4*h**4 + 36*h**3 + 94*h**2 + 10*h - 142. Let f(u) = -u**2 + u - 1. Let x(g) = -2*f(g) - m(g). Determine z, given that x(z) = 0.
-4, -3, 1
Suppose -26 = -18*p + 46. Let b(j) be the first derivative of -1/20*j**5 + 0*j + 1/8*j**p - 1/12*j**3 - 3 + 0*j**2. Factor b(y).
-y**2*(y - 1)**2/4
Let y(r) = r**3 - r**2 + r + 2. Let u(d) = 4*d**3 + 24*d**2 + 4*d - 8. Let v(x) = -u(x) - 4*y(x). Factor v(g).
-4*g*(g + 2)*(2*g + 1)
Suppose -l = -6*l + 70. Let c be (-30)/(-25)*15/l. Factor 6/7*r - c - 1/7*r**2.
-(r - 3)**2/7
Let m = -473/2 - -237. Let g(b) be the second derivative of m*b**3 - 3/20*b**5 + 1/10*b**6 + 0 + 0*b**2 - 1/4*b**4 - 2*b. Solve g(c) = 0 for c.
-1, 0, 1
Let a(g) be the third derivative of -g**9/20160 - g**8/672 - 3*g**7/560 - 5*g**5/12 - g**4/12 - 18*g**2. Let u(x) be the third derivative of a(x). Factor u(h).
-3*h*(h + 1)*(h + 9)
Let j(v) = -4 + 6*v**3 - 4*v**3 - 5*v**4 + 4*v**2 - v**2. Let b(t) = -6*t**4 + 2*t**3 + 4*t**2 - 5. Let w(g) = 4*b(g) - 5*j(g). Suppose w(d) = 0. What is d?
0, 1
Let s(t) be the third derivative of -1/840*t**6 - 43*t**2 + 1/1470*t**7 + 0 + 0*t**4 + 0*t**3 + 0*t + 0*t**5. Let s(n) = 0. What is n?
0, 1
Factor -5/3*h**2 + 0 + 5*h.
-5*h*(h - 3)/3
Let j = 6 + -1. Let o(m) = -8*m**2 - 15*m + 6. Let l be o(-2). Let -2*g**4 - 2*g**4 - 8*g**j + l*g**5 = 0. Calculate g.
-1, 0
Let a(v) be the third derivative of -2/165*v**5 - 2/33*v**4 + 1/110*v**6 + 0 + 0*v + 1/1848*v**8 + 1/231*v**7 + 5*v**2 + 0*v**3. Factor a(l).
2*l*(l - 1)*(l + 2)**3/11
Determine l, given that 4*l**3 + 34*l**2 + 7*l**2 - 2*l**3 - 33*l**2 + 48*l + 20*l**2 = 0.
-12, -2, 0
Let f = 15832/9 - 1757. Factor 7/9*i**4 + 8/9 - 28/9*i - 2/3*i**2 + f*i**3.
(i - 1)*(i + 2)**2*(7*i - 2)/9
Let v(i) be the first derivative of i**8/1680 + i**7/210 + i**6/72 + i**5/60 - 8*i**3/3 + 9. Let d(g) be the third derivative of v(g). Factor d(z).
z*(z + 1)**2*(z + 2)
Let r be ((-12)/(-8))/((-6)/(-12)). Let d(k) be the first derivative of 2/9*k**2 - 2/9*k**3 + 0*k + r + 1/18*k**4. Factor d(c).
2*c*(c - 2)*(c - 1)/9
Let l(x) be the third derivative of 0 - 7/4*x**5 - 1/6*x**6 + 0*x - 145/24*x**4 - 5*x**3 - 13*x**2. Determine s so that l(s) = 0.
-3, -2, -1/4
Let g(d) be the third derivative of 5/9*d**4 + 18*d**2 + 0 - 1/90*d**5 - 100/9*d**3 + 0*d. Factor g(s).
-2*(s - 10)**2/3
Let r = -21 + 24. Factor r*i**2 + i**2 - 40*i - 100 - 7*i**2 - i**2.
-4*(i + 5)**2
Let -2/3*d**3 + 0 - 8/3*d**2 + 0*d = 0. Calculate d.
-4, 0
Let q(v) be the second derivative of v**8/420 + v**7/840 - v**6/120 + 7*v**3/6 - 2*v**2 - 15*v - 2. Let d(g) be the second derivative of q(g). Factor d(m).
m**2*(m + 1)*(4*m - 3)
Let g(d) be the third derivative of 3*d**5 + 175*d**4/2 + 6125*d**3/6 + 6*d**2 + 21. Let g(z) = 0. What is z?
-35/6
Suppose -17*b = -23 - 28. Let y(z) be the second derivative of 0 - 7*z - 1/15*z**6 + 0*z**3 - b*z**4 + 27*z**2 + 4/5*z**5. Factor y(k).
-2*(k - 3)**3*(k + 1)
Let v(q) be the second derivative of 1/63*q**7 + 7*q + 0 - 1/45*q**6 + 0*q**2 + 0*q**3 + 0*q**5 + 0*q**4. Suppose v(c) = 0. What is c?
0, 1
Let a(q) = -q**3 + 3*q**2 + 17*q + 10. Let k be a(6). Let j(p) be the first derivative of -3/20*p**4 + 0*p**2 + 0*p**3 + k + 0*p. Factor j(t).
-3*t**3/5
Factor 10*v + 5/4*v**4 + 0 - 25/4*v**3 + 5/2*v**2.
5*v*(v - 4)*(v - 2)*(v + 1)/4
Let m(s) = 4*s. Let a be m(3). Let z(v) = -11*v - 130. Let y be z(-12). Factor -d**4 + y*d**2 - 16*d**3 - 4*d**2 + a*d**3 + 7*d**3.
-d**2*(d - 2)*(d - 1)
Suppose -m + 27 = 5*k, -3*k + 13 = -2. Let y = 0 + m. Factor 9*x**2 + y*x**3 - 6*x**2 - 3*x**4 - 3*x + x**3.
-3*x*(x - 1)**2*(x + 1)
Let c(f) = -125*f**3 - 965*f**2 - 3515*f - 4355. Let y(o) = -9*o**3 - 69*o**2 - 251*o - 311. Let p(v) = 4*c(v) - 55*y(v). Suppose p(t) = 0. Calculate t.
-7, -3
Let f(l) = 11*l**2 + 35*l - 55. Let g(s) = 5*s**2 + 17*s - 26. Let c(w) = 4*f(w) - 9*g(w). Factor c(n).
-(n - 1)*(n + 14)
Let x(m) be the first derivative of -5*m**3/3 - 5*m**2 + 40*m + 22. What is h in x(h) = 0?
-4, 2
Let k(v) = -12*v**3 + 16*v**2 + 16*v + 32. Let t(m) = m**3 - 2. Suppose -q - 2 = -1. Let b(w) = q*k(w) - 16*t(w). Factor b(u).
-4*u*(u + 2)**2
Let n be 12/7 - (-28)/98. Determine v, given that -12*v**n + 3*v**2 - v**3 - 250 - 24*v + 230 = 0.
-5, -2
Let u be 125/(-750) - 15/(-18). Factor 4/3*c - 1/3*c**3 - 8/3 + u*c**2.
-(c - 2)**2*(c + 2)/3
Factor -1/5*y**2 - 8/5 - 6/5*y.
-(y + 2)*(y + 4)/5
Factor -2*i**3 + 0 + 2*i - 2/5*i**4 + 2/5*i**2.
-2*i*(i - 1)*(i + 1)*(i + 5)/5
Let z(p) be the third derivative of -5*p**8/336 - 13*p**7/42 - 7*p**6/8 + 13*p**5/12 + 55*p**4/12 + 62*p**2. Solve z(q) = 0.
-11, -2, -1, 0, 1
Find p such that -2*p - 25*p**2 - 15*p**3 - 14*p + p**4 + 6*p + 4*p**4 + 5*p**5 = 0.
-1, 0, 2
Let t(i) be the second derivative of 0 + 9/8*i**4 + 1/5*i**6 + 1/4*i**3 - 20*i + 33/40*i**5 - 3/4*i**2. Factor t(s).
3*(s + 1)**3*(4*s - 1)/2
Let y(h) be the third derivative of h**5/42 + h**4/7 + h**3/3 - h**2 + 15*h. Factor y(b).
2*(b + 1)*(5*b + 7)/7
Let o(t) be the second derivative of 3*t**5/20 + 7*t**4/2 + 30*t**3 + 108*t**2 - 28*t - 1. Suppose o(j) = 0. What is j?
-6, -2
Let m(q) be the second derivative of -q**5/150 - q**4/30 + 28*q**3/45 + 194*q. What is l in m(l) = 0?
-7, 0, 4
Suppose 44 = -8*y + 44. Solve y*q**2 - 2/7*q**3 + 0 + 2/7*q = 0 for q.
-1, 0, 1
Let u(r) be the second derivative of r**4/36 + r**3/9 - 4*r**2/3 - 124*r. Determine k so that u(k) = 0.
-4, 2
Let f = -64/7 - -135/14. Let x(l) be the second derivative of 0*l**2 + f*l**3 + 3*l - 1/2*l**4 + 0 + 3/20*l**5. Factor x(u).
3*u*(u - 1)**2
What is g in 801/8*g**3 + 72 + 9/8*g**5 + 531/2*g**2 + 69/4*g**4 + 294*g = 0?
-4, -3, -1/3
Let w(j) = -3*j + 8. Let y be w(2). Let h(u) be the first derivative of -1/5*u - y + 1/5*u**2 - 1/15*u**3. Factor h(o).
-(o - 1)**2/5
Let f(d) be the second derivative of d**6/150 + d**5/50 - d**4/60 - d**3/15 + 2*d. Determine j so that f(j) = 0.
-2, -1, 0, 1
Let g(z) be the second derivative of -1/45*z**6 - 4*z + 2/9*z**4 + 0 + 1/30*z**5 - 1/126*z**7 + 7/18*z**3 + 1/3*z**2. Solve g(j) = 0.
-1, 2
Let j(y) = 3*y**2 + 21*y - 12. Let h(t) = 6*t**2 + 42*t - 20. Let k(l) = -3*h(l) + 5*j(l). Factor k(r).
-3*r*(r + 7)
Solve -32/13*k**4 - 62/13*k**3 - 28/13*k**2 + 0 + 2/13*k = 0 for k.
-1, 0, 1/16
Let z(w) = -17 - 12 + 10*w + 0 - 7*w. Let r be z(11). Factor 2/11*t**3 - 2/11*t**2 + 0*t - 2/11*t**5 + 0 + 2/11*t**r.
-2*t**2*(t - 1)**2*(t + 1)/11
Let y(v) be the first derivative of -v**5/15 + 5*v**4/12 + 31*v**3/9 + 43*v**2/6 + 6*v + 51. Factor y(k).
-(k - 9)*(k + 1)**2*(k + 2)/3
Let n(x) = -12*x**2 + 51*x - 8. Let v be n(4). Factor 0 + 0*k - 2/5*k**v - 2/5*k**2 - 4/5*k**3.
-2*k**2*(k + 1)**2/5
Suppose 3/4*d**5 - 32*d**3 + 7*d**4 + 93/2*d**2 - 115/4*d + 13/2 = 0. Calculate d.
-13, 2/3, 1
Find j such that 3/2*j**3 - 1/2*j**4 - 2*j + 0 + 0*j**2 = 0.
-1, 0, 2
Let q(x) = x. Let f(y) = 7225*y**3 - 6885*y**2 - 344*y - 4. Let d(l) = 3*f(l) + 24*q(l). Solve d(k) = 0.
-2/85, 1
Let u = -29607 - -29609. Factor -3/7*p**u - 6/7 + 9/7*p.
-3*(p - 2)*(p - 1)/7
Let n = -2/63 + 31/315. Let w(p) be the third derivative of 3*p**2 - 1/12*p**4 + 0*p + 0*p**3 + 0 + n*p**5 - 1/60*p**6. What is b in w(b) = 0?
0, 1
Let w(v) = v**3 + 4*v**2 - 99*v - 33. Let c be w(-12). Factor 3*o**2 - 1/2*o**c + 4 - 6*o.
-(o - 2)**3/2
Let -204 - 64*o - 94 - 175 + 217 - 4*o**2 = 0. Calculate o.
-8
Suppose 4*y - c = -5*c + 12, 0 = 4*y - 2*c - 12. Factor 2*j**5 + 0*j**3 - 16*j**y + j**5 + j**5.
4*j**3*(j - 2)*(j + 2)
Suppose -9 = -4*t - 1. Factor 12*o + 13*o**2 - 8 + t*o**2 - 9*o**3 - 4.
-3*(o - 2)*(o + 1)*(3*o - 2)
Let y(l) = -l**3 - l + 1. Let i(v) = 2*v**4 + 45*v**3 + 236*v**2 + 365*v + 157. Suppose -2*m = -1 + 5. Let b(z) = m*i(z) - 10*y(z). Factor b(d).
-4*(d + 1)**2*(d + 9)**2
Factor -2*y**2 + 24*y + 5*y**2 + 55 - 33 - y**2.
2*(y + 1)*(y + 11)
Let s = -179 - -134. Let y be (-10)/(-12)*(-36)/s. Factor 0 + 8/3*u**2 - 8/3*u - y*u**3.
-2*u*(u - 2)**2/3
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