2/3*f**3 + f - 1/3 + f**4 - g*f**2 - 1/3*f**5 = 0. What is f?
-1, 1
Let z be -3*((-5)/(-1) - 3). Let v = z + 10. Factor 5*q**2 + 2*q**4 + q - 4*q**2 + 6*q**3 + 2*q**v + q**5 + 3*q**2.
q*(q + 1)**4
Determine n, given that -31*n + 24*n**3 - n - 8*n**2 + 2*n**5 + 9*n**4 + 5*n**4 = 0.
-4, -2, 0, 1
Let g be (1/8)/(45/4). Let n(m) be the third derivative of 0*m**4 + 0 + 3*m**2 - g*m**5 + 0*m + 0*m**3. Factor n(o).
-2*o**2/3
Factor -2*d - 3/2 - 1/2*d**2.
-(d + 1)*(d + 3)/2
Suppose -u + 2 = -4*s, 3*s - 2*s - 5*u = -10. Suppose -m + s*m + 6 = 0. Factor r**2 - 2*r**2 + 2 - 5*r + m*r.
-(r - 2)*(r + 1)
Factor -10/9*j**3 - 8/9 + 2/9*j**4 + 2/3*j**2 + 10/9*j.
2*(j - 4)*(j - 1)**2*(j + 1)/9
Let z(h) = -6*h**2 + 9*h + 33. Let a(m) = 5*m**2 - 9*m - 32. Let p(n) = 3*a(n) + 2*z(n). Factor p(w).
3*(w - 5)*(w + 2)
Let g(d) = -3*d - 9. Let u be g(-6). Let l be ((-2)/12)/((-2)/u). Factor -l*x**2 + 0 + 0*x**3 + 1/4*x**4 - 1/2*x.
x*(x - 2)*(x + 1)**2/4
Let f(l) be the second derivative of -5*l**4/12 + 5*l**3 - 25*l**2/2 - 4*l + 11. Let f(u) = 0. Calculate u.
1, 5
Let c(j) be the first derivative of 4*j**5/25 + 3*j**4/5 + 8*j**3/15 + 5. Determine q, given that c(q) = 0.
-2, -1, 0
Factor 4 - 2 - 2*q + 6*q - 3*q - q**2.
-(q - 2)*(q + 1)
Let g(v) be the third derivative of -2*v**7/105 + v**6/15 + 4*v**5/15 - 4*v**4/3 - v**2. Let g(n) = 0. Calculate n.
-2, 0, 2
Let b(z) be the first derivative of -z**4/2 - 4*z**3 - 9*z**2 - 9. Find x such that b(x) = 0.
-3, 0
Suppose 0 = -726*c + 720*c + 18. Factor -6*m - 1/2*m**3 - c*m**2 - 4.
-(m + 2)**3/2
Let q(c) = -2*c**2 - 7*c. Let m(i) = -i**2 - i - 1. Let r(z) = 12*m(z) - 4*q(z). Factor r(p).
-4*(p - 3)*(p - 1)
Let d = 9 + -7. Suppose -16 = -5*b + 2*t - d, 4 = -b - 3*t. Solve 0 - 1/5*k**b + 2/5*k - 1/5*k**3 = 0 for k.
-2, 0, 1
Let a be 4/20*1 - (-3 + 3). Let 0 - a*y**3 + 1/5*y**2 - 1/5*y**4 + 1/5*y = 0. Calculate y.
-1, 0, 1
Let l(w) be the first derivative of w**4/12 + 2*w**3/3 + 3*w**2/2 + 29. Find d such that l(d) = 0.
-3, 0
Let f be (-2)/(2/37) - 0. Let i = f - -112/3. Factor i*y**2 + 1/3 - 2/3*y.
(y - 1)**2/3
Suppose 8*o**5 + 0 + 57/2*o**3 + 28*o**4 + o + 19/2*o**2 = 0. Calculate o.
-2, -1, -1/4, 0
Let s(j) be the second derivative of -1/27*j**3 - 1/54*j**4 + 1/135*j**6 + 0*j**2 + 1/90*j**5 + 0 - 2*j. Factor s(k).
2*k*(k - 1)*(k + 1)**2/9
Let b(m) = m**4 - m. Let k(o) = -8*o**4 + o**3 + 5*o**2 + 4*o - 2. Let l(v) = 5*b(v) + k(v). Find f such that l(f) = 0.
-1, -2/3, 1
Let u = 10 + -28. Let w be 3/(-3) + u/(-6). Factor -3/2*l**w + 3 - 3/2*l.
-3*(l - 1)*(l + 2)/2
Let d(j) be the first derivative of 0*j**2 + 1/10*j**4 + 3*j - 2 - 2/15*j**3 - 1/50*j**5. Let z(q) be the first derivative of d(q). Let z(r) = 0. What is r?
0, 1, 2
Let 16*b + 18*b - 3*b**3 - 18 - 14*b**2 + b**3 = 0. Calculate b.
-9, 1
Suppose 22 = 5*r + 132. Let y = -22 - r. Factor -2/9*x**2 + y - 2/9*x**4 - 4/9*x**3 + 0*x.
-2*x**2*(x + 1)**2/9
Suppose -2/5 + 8/15*h - 2/15*h**2 = 0. Calculate h.
1, 3
Let w(m) be the first derivative of -2*m**5/45 - 5*m**4/18 - 2*m**3/3 - 7*m**2/9 - 4*m/9 - 15. Let w(c) = 0. What is c?
-2, -1
Let n(g) = -1. Let t(c) = -c. Let o(m) = -m**2 - 3*m + 5. Let k be o(-4). Let x be t(k). Let i(w) = -w**3 + w**2 - 1. Let p(l) = x*n(l) + i(l). Factor p(r).
-r**2*(r - 1)
Suppose -4*k = 2*k - 24. Let z(n) be the third derivative of 0 + 1/6*n**k - n**2 + 1/3*n**3 + 0*n + 1/30*n**5. Factor z(h).
2*(h + 1)**2
Let y(b) be the third derivative of 0 + 0*b - 1/3*b**3 + 2*b**2 - 1/6*b**4 - 1/30*b**5. Factor y(t).
-2*(t + 1)**2
Let g(f) be the second derivative of f**6/60 + f**5/20 + f**4/24 + 19*f. Factor g(i).
i**2*(i + 1)**2/2
Factor 57*b + 48*b**3 + 16*b**2 - 28*b**4 - 57*b.
-4*b**2*(b - 2)*(7*b + 2)
Let q(v) = -7*v + v**3 + 2*v**2 + 2 - 5 + 3*v**2. Let a be q(-6). Factor -2*j**3 - 2*j**2 - 4*j + 4*j**a + 2*j**4 + 2*j.
2*j*(j - 1)*(j + 1)**2
Suppose -2*n + 10 + 0 = 0. Suppose -n*p + 7 = -8. Factor -3*l + 4 + l - p*l**2 + l**2.
-2*(l - 1)*(l + 2)
Let o(m) = -2*m**4 + 6*m**3 - 9*m**2 + 2*m - 3. Let b(u) = 10*u - 8 - 9*u**4 + 0*u**4 - u**4 - 6 - 44*u**2 + 30*u**3. Let v(f) = 3*b(f) - 14*o(f). Factor v(p).
-2*p*(p - 1)**3
Factor 15*t - 3*t + 16 + 2 + 2*t**2.
2*(t + 3)**2
Let u = -16 - -22. Suppose -o**4 - o**4 + 2*o**2 - u*o**3 - 3*o**2 - 3*o**2 = 0. What is o?
-2, -1, 0
Suppose -278 + 48 = -5*k. Let b = k - 137/3. Find f such that 0 - b*f - 1/3*f**2 = 0.
-1, 0
Let n be 0 + 1 - 1 - -2. Let g be (19 - 16)/(3/2). Find r, given that 3*r**3 - 5 - 5*r**g - n*r**2 + 17 - 2*r**2 = 0.
-1, 2
Let d = -5 + 7. Let l(o) be the second derivative of 1/6*o**4 + 0 - d*o + 1/3*o**3 + 0*o**2. Solve l(g) = 0.
-1, 0
Let f(u) be the third derivative of u**5/12 + 5*u**4/12 - 5*u**3/2 + 4*u**2. Factor f(o).
5*(o - 1)*(o + 3)
Suppose 5*u + 5*a - 45 = 0, 7*a - 5*a = 6. Let m(b) be the third derivative of -1/28*b**4 + 1/21*b**3 + 1/70*b**5 + 3*b**2 - 1/420*b**u + 0 + 0*b. Factor m(s).
-2*(s - 1)**3/7
Let o(t) be the third derivative of -1/168*t**8 + 0*t**5 - 9*t**2 - 1/60*t**6 + 0*t + 0 + 0*t**4 + 2/105*t**7 + 0*t**3. Find h, given that o(h) = 0.
0, 1
Let n(f) = f**2 - f + 1. Let o(p) = -3. Let g(y) = 3*n(y) + o(y). Factor g(w).
3*w*(w - 1)
Let f(q) be the third derivative of -q**10/453600 + q**8/30240 - q**6/2160 + q**5/30 - 6*q**2. Let o(z) be the third derivative of f(z). Factor o(r).
-(r - 1)**2*(r + 1)**2/3
Let g = -109 + 109. Factor -2/9*j**5 + 0 - 4/9*j**2 + 2/9*j + g*j**3 + 4/9*j**4.
-2*j*(j - 1)**3*(j + 1)/9
Let x(l) be the first derivative of -2*l**3/39 + 3*l**2/13 + 8*l/13 + 1. Suppose x(n) = 0. What is n?
-1, 4
Let c(t) = 2*t + 6. Let l be c(-3). Let p(u) be the second derivative of 2*u + 2/5*u**2 + l + 2/15*u**3 + 1/60*u**4. Factor p(d).
(d + 2)**2/5
Suppose 25 = -i + 6*i. Let f(v) be the first derivative of -9/10*v**4 + 2/5*v**2 - 2/15*v**3 + 1 + 0*v - 1/3*v**6 + 26/25*v**i. Factor f(b).
-2*b*(b - 1)**3*(5*b + 2)/5
Let u(o) = 5*o**3 - 6*o**2 - 9*o + 16. Let i(t) = t**2 - t - 1. Let v(m) = 6*i(m) + u(m). Factor v(c).
5*(c - 1)**2*(c + 2)
Let n = 169 - 88. Let k be 64/126 + (-18)/n. Find l such that -2/7*l**2 + 2/7 + k*l - 2/7*l**3 = 0.
-1, 1
Suppose 23 - 8 = 3*u. Factor u*a + 2 - 3*a**3 + 4*a**3 - 8*a.
(a - 1)**2*(a + 2)
Let y(i) be the second derivative of i**5/8 + i**4/24 - 13*i. Factor y(d).
d**2*(5*d + 1)/2
Let g = -64/5 - -197/15. Suppose 2/3*z - z**2 - 1/3*z**5 - g*z**3 + 0 + z**4 = 0. What is z?
-1, 0, 1, 2
Solve -d + 6*d**3 + 68 - 10*d**2 - 60 - 7*d = 0.
-1, 2/3, 2
Let t(q) be the second derivative of q**7/1365 - q**6/260 + q**5/195 - q**2/2 - q. Let h(z) be the first derivative of t(z). Let h(o) = 0. What is o?
0, 1, 2
Let u = -2/765 - -13784/5355. Factor -27/7 - 3/7*t**2 + u*t.
-3*(t - 3)**2/7
Let h(n) be the third derivative of n**7/3780 - n**6/540 + n**5/180 + n**4/12 - 3*n**2. Let q(k) be the second derivative of h(k). Let q(o) = 0. Calculate o.
1
Let s(q) be the third derivative of -q**5/108 - 11*q**4/72 + 7*q**3/27 - 23*q**2. Let s(f) = 0. Calculate f.
-7, 2/5
Let y(x) be the third derivative of -x**6/360 - x**5/45 - 5*x**4/72 - x**3/9 + 13*x**2. What is d in y(d) = 0?
-2, -1
Let s(f) = -f**3 + f**2 - f. Let d(q) = 20*q**3 - 32*q**2 + 34*q + 32. Let b(c) = -2*d(c) - 36*s(c). Factor b(l).
-4*(l - 4)**2*(l + 1)
Factor 3*v**3 + 0*v**3 + 6*v**4 + 6*v - 7*v**2 - 8*v**2.
3*v*(v - 1)*(v + 2)*(2*v - 1)
Let f(d) be the second derivative of -d**6/180 - d**5/60 + d**4/6 + d**3/2 + 5*d. Let z(j) be the second derivative of f(j). Solve z(p) = 0.
-2, 1
Let f(y) be the second derivative of -y**4/48 + y**3/6 - y**2/2 + 2*y. Find u, given that f(u) = 0.
2
What is n in -1/5*n + 1/5*n**2 + 1/5*n**3 + 0 - 1/5*n**4 = 0?
-1, 0, 1
Let l(r) = -r**2 - 1. Let k(g) = -2*g**2 + 11*g - 15. Let p(b) = -k(b) + 3*l(b). Factor p(z).
-(z - 1)*(z + 12)
Let u(k) be the third derivative of k**8/504 - 2*k**7/105 + k**6/15 - 4*k**5/45 - 15*k**2. Suppose u(f) = 0. What is f?
0, 2
Let l be (-10)/2*6/5. Let s(r) = r**2 + 4*r - 8. Let b be s(l). Suppose -4*a + b*a**2 - 2*a**3 + a + a = 0. What is a?
0, 1
Let h(n) = 26*n**4 + 14*n**3 - n**2 - 6. Let j(o) = -105*o**4 - 55*o**3 + 5*o**2 + 25. Let g(b) = -25*h(b) - 6*j(b). Determine u, given that g(u) = 0.
-1/2, 0
Let p(c) be the third derivative of -c**5/30 + 8*c**2. Factor p(n).
-2*n**2
Factor 0*u + 0 - 2/9*u**3 + 8/9*u**4 + 0*u**2 - 2/3*u**5.
-