4*a - 1/4*a**3 - 1/2 + 0*a**2 = 0.
-2, 1
Solve -19/10*r + 11/5*r**3 + 11/10*r**4 - 1/2 - 3/10*r**5 - 3/5*r**2 = 0.
-1, -1/3, 1, 5
Suppose 0 = 4*a - 2*a - 8. Let u = a - -4. Solve -2*v**2 + v**2 + 18*v**5 - 7*v**2 + 12*v**4 - 22*v**3 + u*v = 0 for v.
-1, 0, 2/3
Let k(s) be the third derivative of s**7/735 - s**6/210 + s**5/210 + 2*s**2. Factor k(y).
2*y**2*(y - 1)**2/7
Let f(w) be the third derivative of -w**10/15120 + w**8/3360 - 5*w**4/24 + w**2. Let q(t) be the second derivative of f(t). Factor q(x).
-2*x**3*(x - 1)*(x + 1)
Let s(u) = -72*u**4 - 146*u**3 + 18*u + 10. Let w(v) = -v - 1. Let x(a) = s(a) + 10*w(a). Solve x(p) = 0 for p.
-2, -1/4, 0, 2/9
Let c(y) = -y**3 + 7*y**2 + 8*y + 2. Let u be c(8). Let r = 2/411 + 182/137. Factor r*p**u + 0*p + 0 - 2/3*p**3.
-2*p**2*(p - 2)/3
Let y(l) = 6*l**2 - 17*l - 5. Let h(b) = -9*b**2 + 25*b + 7. Suppose -6 = 3*k - 3*p, -8*p = -3*k - 3*p. Let i(a) = k*h(a) - 7*y(a). Factor i(c).
3*c*(c - 2)
Find a such that -1/2*a**4 - 3/2*a**2 - 8*a - 21/2*a**5 + 37/2*a**3 + 2 = 0.
-1, 2/7, 2/3, 1
Let i = 289/8 + 147/8. Suppose 18*w**2 - i*w**3 + 63*w**4 + 0 - 2*w - 49/2*w**5 = 0. Calculate w.
0, 2/7, 1
Let w = 188/5 + -373/10. Let o(k) be the second derivative of 0*k**2 + 1/12*k**4 + 3/10*k**5 + 0 + 2/21*k**7 + 0*k**3 + 3*k + w*k**6. Solve o(q) = 0 for q.
-1, -1/4, 0
Find a such that 59*a**4 - 4*a**5 - 118*a**4 + 8*a**3 + 55*a**4 = 0.
-2, 0, 1
Let t(i) = -i**2 - 21*i + 60. Let k be t(-21). Let 64/3*u**2 + k*u**3 + 63/2*u**5 + 0 + 8/3*u + 72*u**4 = 0. Calculate u.
-2/3, -2/7, 0
Let m = -4578/5 + 916. Factor m*w**4 + 0*w - 4/5*w**3 + 0 - 6/5*w**2.
2*w**2*(w - 3)*(w + 1)/5
Let h(a) be the third derivative of a**8/10080 - a**7/630 + a**6/90 + a**5/12 + 3*a**2. Let s(f) be the third derivative of h(f). Find v, given that s(v) = 0.
2
Let a(i) = 5*i**3 + 5*i**2 - 5*i. Let c(w) = 5*w**3 + 6*w**2 - 6*w. Let u(n) = -6*a(n) + 5*c(n). Solve u(h) = 0.
0
Let m(y) = y**3 - 9*y**2 + 9*y - 8. Let i be m(8). What is f in -10/3*f**3 + i - f**4 - 3*f**2 - 2/3*f = 0?
-2, -1, -1/3, 0
Let c = -257/7 - -37. Solve c*w**2 + 0 + 4/7*w = 0.
-2, 0
Solve -4/9*c**2 - 2/9*c + 2/9*c**3 + 4/9 = 0.
-1, 1, 2
Let p(g) be the first derivative of 242*g**3/27 + 44*g**2/3 + 8*g - 13. Let p(s) = 0. What is s?
-6/11
Let h(n) = -2*n - 14 + n + n + 2*n. Let k be h(7). Determine r, given that -2/3*r**3 - 2*r**4 + 0*r + k*r**2 + 8/3*r**5 + 0 = 0.
-1/4, 0, 1
Let c(u) = -u**2 - 4*u - 1. Let v(k) = -k. Suppose -3*j - 2 = -4*j - s, 5*j + 2*s - 1 = 0. Let w(g) = j*c(g) + 6*v(g). Solve w(x) = 0.
1
Let t(u) = 2*u - 5 - 2*u + u. Let l be t(8). What is j in -2/5*j**2 + 2/5*j**l + 0 + 0*j = 0?
0, 1
Suppose -z + 3 + 0 = 0. Suppose 2*t = -3*t + 10. Factor 2*d**2 - 2*d**4 - 3*d**z - t*d**3 + 2*d**5 + 3*d**3.
2*d**2*(d - 1)**2*(d + 1)
Let s(k) be the third derivative of 0 - 1/27*k**3 + 0*k + 0*k**4 + 1/270*k**5 - k**2. Factor s(r).
2*(r - 1)*(r + 1)/9
Let y = 382 + -1141/3. Factor -5/3*a**3 - 3*a**2 + y*a + 2/3 + 7/3*a**4.
(a - 1)**2*(a + 1)*(7*a + 2)/3
Factor -3*r**5 + 8*r**3 + r**5 + 45*r**4 - 45*r**4.
-2*r**3*(r - 2)*(r + 2)
What is g in -11/2*g**3 - 2 - 2*g**4 + 3/2*g**2 + 8*g = 0?
-2, 1/4, 1
Let z(g) be the first derivative of -g**8/105 - g**7/42 - g**6/90 - g**3 - 3. Let r(q) be the third derivative of z(q). Factor r(f).
-4*f**2*(f + 1)*(4*f + 1)
Let l(m) be the first derivative of 3*m**4/2 + 4*m**3/3 + 5. Factor l(q).
2*q**2*(3*q + 2)
Suppose 2*j + 3*j - 20 = 0. Suppose 3*w + 6 = 2*x, -w + j*w + 6 = x. Factor 8/3*h**4 - 2/3*h**5 + 0*h + 4/3*h**2 + x - 10/3*h**3.
-2*h**2*(h - 2)*(h - 1)**2/3
Let a(p) = -2*p**2 - 4*p. Let r(t) = 4*t + 6. Let j be r(-2). Let u be a(j). Let 0*q + 0 + 2/3*q**5 + 4/3*q**3 - 2*q**4 + u*q**2 = 0. What is q?
0, 1, 2
Determine o so that 2*o**5 - 36*o**2 - 14407*o - 6*o**3 + 14407*o + 8*o**4 = 0.
-3, 0, 2
Suppose -20 = -5*d - 5*z, -18 = -4*d - 2*z - 3*z. Find u such that 0 - 8/5*u - 378/5*u**3 - 343/5*u**5 - 637/5*u**4 - 92/5*u**d = 0.
-1, -2/7, 0
Let l(q) be the second derivative of q**6/75 + q**5/50 + 2*q. Factor l(u).
2*u**3*(u + 1)/5
Let r(z) = -21*z**4 - 15*z**3 + 3*z**2 + 15*z. Let a = 46 + -64. Let c(f) = -f**4 - f**3 + f. Let q(n) = a*c(n) + r(n). Factor q(p).
-3*p*(p - 1)**2*(p + 1)
Let t = 8 + -6. Solve -2*u**2 + t*u + 2*u - u**3 + 0*u**2 - u**3 = 0.
-2, 0, 1
Let j = -4/11 + 19/22. Let -q + 0*q**2 + q**3 + j - 1/2*q**4 = 0. Calculate q.
-1, 1
Let i(y) be the second derivative of -2/45*y**6 + 1/9*y**3 + 0*y**2 + 0*y**5 + 0 - 6*y - 1/63*y**7 + 1/9*y**4. Factor i(j).
-2*j*(j - 1)*(j + 1)**3/3
Let x(h) = -5*h**4 - 26*h**3 - 30*h**2 - 26*h - 11. Let t(b) = -b**3 - b - 1. Let f(v) = -6*t(v) + x(v). Factor f(p).
-5*(p + 1)**4
Suppose 0 = -4*b - 3*c + 20, 0 = -3*b - c + 6*c - 14. Factor 3*z + 5*z**2 - 3*z + z - 3*z**b.
z*(2*z + 1)
Let m(j) be the second derivative of j**6/480 + j**5/160 - 5*j**3/6 + 4*j. Let i(w) be the second derivative of m(w). Factor i(x).
3*x*(x + 1)/4
Let p(x) be the first derivative of x**4/72 - x**2/12 + 4*x - 2. Let g(y) be the first derivative of p(y). Let g(s) = 0. Calculate s.
-1, 1
Let f(r) be the second derivative of 0 - 1/3*r**4 + 2*r**2 + 1/3*r**3 - 1/10*r**5 + 4*r. Factor f(k).
-2*(k - 1)*(k + 1)*(k + 2)
Let i = -1243 + 3731/3. Determine q so that 16/3*q**2 - 32/3*q**5 - 16*q**3 - i*q + 0 + 64/3*q**4 = 0.
0, 1/2
Let x(m) = 4*m**5 + 4*m**4 + 3*m**3 + 7*m**2 - 2*m + 3. Let t(g) = -3*g**5 - 4*g**4 - 4*g**3 - 6*g**2 + g - 2. Let q(l) = -6*t(l) - 4*x(l). Factor q(j).
2*j*(j + 1)**4
Let p = 11/10 + 1/10. Factor -2/5*d**4 - 6/5*d**2 + p*d**3 + 0 + 2/5*d.
-2*d*(d - 1)**3/5
Suppose -4*r = -3*i, 2*i + 2*i - 7 = 3*r. Factor 3*q + 14*q**2 - 6*q**4 + i*q**3 - 2*q + 3*q.
-2*q*(q - 2)*(q + 1)*(3*q + 1)
Let v = 28 + -16. Suppose -3*n + v = -0*n - w, 5*n = -3*w + 34. Factor 3/5*r - 6/5*r**3 - 6/5*r**2 + 3/5 + 3/5*r**n + 3/5*r**4.
3*(r - 1)**2*(r + 1)**3/5
Solve -12*z**2 - 4*z + 2*z**3 + z**3 + 12*z + z = 0.
0, 1, 3
Let p = 11 - 0. Let i(x) = 4 + 6*x**2 + p*x + 8*x + 2*x**2. Let s(g) = -4*g**2 - 10*g - 2. Let j(a) = 4*i(a) + 7*s(a). Factor j(k).
2*(k + 1)*(2*k + 1)
Let -12/5 - 3/5*h**2 - 3*h = 0. Calculate h.
-4, -1
Let a(r) be the second derivative of r**6/540 - r**5/270 - r**4/108 + r**3/27 + 9*r**2/2 + 4*r. Let y(d) be the first derivative of a(d). Factor y(z).
2*(z - 1)**2*(z + 1)/9
Let i(f) be the third derivative of -2*f**7/105 + 2*f**6/15 - 4*f**5/15 - 11*f**2. Factor i(q).
-4*q**2*(q - 2)**2
Let n(j) be the third derivative of -3*j**5/20 + 11*j**4/24 - j**3/3 + 4*j**2. Factor n(u).
-(u - 1)*(9*u - 2)
Let r(x) be the third derivative of 0*x - 8/27*x**3 + 0 - 1/27*x**4 - x**2 + 1/135*x**5 + 1/540*x**6. Determine p so that r(p) = 0.
-2, 2
Let u(m) be the first derivative of m**4 - 16/3*m**3 - 4 - 1/3*m**6 + 4/5*m**5 - 4*m + 7*m**2. Factor u(o).
-2*(o - 1)**4*(o + 2)
Let c be -1*(0 - 2/(-2)). Let m be 3/18 + c/(-2). Suppose m + 7/3*h + 5/3*h**2 = 0. What is h?
-1, -2/5
Let r(s) be the first derivative of 1/18*s**4 + 0*s + 1/9*s**2 + 2 - 4/27*s**3. Factor r(b).
2*b*(b - 1)**2/9
Let w(i) = i**3 + i**2 - 2*i + 1. Let o be w(1). Suppose 2*r + 6*r = 16. Factor -r*x**2 + 0 - 2 + o - x**2 + 4*x.
-(x - 1)*(3*x - 1)
Suppose -6 = -0*q - 3*q. What is r in -15*r**3 + 2 + q*r + r**2 + 13*r**3 - 3*r**2 = 0?
-1, 1
Let o(j) = -2*j**4 + j**3 + 2*j**2 + 5*j + 3. Let u(s) = s**4 - s**3 - s**2 - s - 1. Suppose 0 = -4*y - 4. Let i(k) = y*o(k) - 3*u(k). Factor i(h).
-h*(h - 2)*(h - 1)*(h + 1)
Suppose -2*j + 3*k - 2*k + 3 = 0, 5*k = 2*j + 1. Suppose j*i - 7*i = 0. Factor 1/2*c**2 + i*c - 1/2.
(c - 1)*(c + 1)/2
Factor 6*m**2 - 2*m**2 + 2 - 18.
4*(m - 2)*(m + 2)
Let m = 3349/3 + -1116. Factor -m*a**3 + 2/3*a**2 + 0 - 1/3*a.
-a*(a - 1)**2/3
Suppose v = 11 - 2. Determine l, given that 3*l**5 + 2*l**4 + 10*l - l**3 - v*l - 3*l**3 - 2*l**2 = 0.
-1, 0, 1/3, 1
Let g(z) = z**5 - z**4 + 8*z**2 + z + 3. Let l(x) = -x**5 + x**4 + x**3 - 7*x**2 - 2. Let w(m) = -2*g(m) - 3*l(m). Suppose w(p) = 0. What is p?
-2, 0, 1
Let f(a) be the third derivative of -a**7/42 + a**6/24 - 4*a**2. Find x, given that f(x) = 0.
0, 1
Factor -5*t**2 - 4 - 1/2*t**3 - 17/2*t.
-(t + 1)**2*(t + 8)/2
Suppose 5*a - 5 = -2*i, -i - 5*a + 3 = -2. Factor -3/2*x**3 - 1/2*x**2 - x**4 + i + 0*x.
-x**2*(x + 1)*(2*x + 1)/2
Factor -2*a + 2/9*a**2 + 0.
2*a*(a - 9)/9
Let v be -1 - (50/(-8))/5. 