etermine o, given that -1/3*o - 1/3*o**2 + a = 0.
-1, 0
Let p(j) = -j**3 - 5*j**2 - j - 3. Let a be p(-5). Solve 4*r**3 - a*r**5 - 26*r**4 + 26*r**4 - 2*r = 0.
-1, 0, 1
Suppose y - 28 = -3*y + 5*g, 20 = -5*g. Factor 1/4 + 1/4*p - 1/4*p**y - 1/4*p**3.
-(p - 1)*(p + 1)**2/4
Factor 16*b - 289/4*b**3 - 221/4*b**2 - 1.
-(b + 1)*(17*b - 2)**2/4
Let f(p) be the third derivative of -p**8/13440 + p**7/840 - p**6/120 + p**5/30 - p**4/24 + 3*p**2. Let m(z) be the second derivative of f(z). Factor m(j).
-(j - 2)**3/2
Solve 59 - 203 + 6*a**3 + 132*a - 2*a**3 - 40*a**2 = 0.
3, 4
Let q(m) be the first derivative of m**4/24 + m**3/4 - 8*m + 7. Let z(x) be the first derivative of q(x). Determine c, given that z(c) = 0.
-3, 0
Let m = 2 - -8. Suppose 0 = -m*u + 6*u. Find z, given that 0*z + 1/6*z**3 + 1/6*z**2 + u = 0.
-1, 0
Factor -31 + 162 + 44*o**2 + 49 + 156*o + 4*o**3.
4*(o + 3)**2*(o + 5)
Let v(b) = 3*b**2 - 12*b - 13. Let w(g) = 4*g**2 - 18*g - 20. Let l(h) = -7*v(h) + 5*w(h). Determine r so that l(r) = 0.
-3
Let u = -159/5 - -32. Let s(a) be the first derivative of -2/5*a - u*a**2 + 1/10*a**4 + 1 + 2/15*a**3. Let s(k) = 0. Calculate k.
-1, 1
Factor 2/9*o - 2/9*o**3 + 2/9*o**2 - 2/9.
-2*(o - 1)**2*(o + 1)/9
Let q(m) = m**2 + 3*m + 4. Let k be q(-6). Let t be 4/(-22) - (-8)/k. Factor 0*f + 0 - t*f**4 + 2/11*f**3 + 0*f**2.
-2*f**3*(f - 1)/11
Let u(q) be the third derivative of q**6/360 - q**4/24 + q**3/6 - 5*q**2. Let i(m) be the first derivative of u(m). Solve i(c) = 0.
-1, 1
Let c(z) = -z + 1. Let a be c(-1). Let f(g) be the first derivative of 1/4*g**4 - g**3 + 3/5*g**5 + a - g**2 + 1/6*g**6 + 0*g. Factor f(w).
w*(w - 1)*(w + 1)**2*(w + 2)
Suppose -2*l = 4*z + 5 - 1, -z + l + 2 = 0. Factor 2/3*m**5 + 0*m**4 + 0 + 0*m**2 - 2/3*m**3 + z*m.
2*m**3*(m - 1)*(m + 1)/3
Let g(z) be the first derivative of 2*z**3/21 + 3*z**2/7 + 4*z/7 + 5. Determine c, given that g(c) = 0.
-2, -1
Let i be (4/4)/((-2)/(-54)). Let d = i - 80/3. Suppose -4/3 - d*u**2 + 4/3*u = 0. What is u?
2
Let o(w) = -4*w**4 + 15*w**3 - 8*w**2 + 3. Let p(i) = 4*i**4 - 14*i**3 + 8*i**2 - 2. Let m(z) = -2*o(z) - 3*p(z). Let m(r) = 0. What is r?
0, 1, 2
Let s(u) = u. Let c be s(4). Let g = 7 - 2. What is d in -4*d - 2*d**3 - 2*d**2 + g*d + 5 + d**4 - c + d**5 = 0?
-1, 1
Suppose 0 = 2*n - l + 1, 5 = -3*n + 5*l - 0. Suppose 0 = -3*a - n*a. Factor a + 1/5*m - 1/5*m**2.
-m*(m - 1)/5
Suppose 22 = 3*h - 2*f, 4*h = 2*h + f + 14. Let c be (h/81)/(4/12). Find v such that -2/9*v**5 + c*v**2 + 2/3*v**4 + 0 - 2/3*v**3 + 0*v = 0.
0, 1
Let z(o) be the second derivative of -o**6/75 - o**5/50 + o**4/30 + o**3/15 - o. What is a in z(a) = 0?
-1, 0, 1
Let o(t) be the second derivative of -3*t**5/20 - 3*t**4/4 - 3*t**3/2 - 3*t**2/2 + 10*t. What is r in o(r) = 0?
-1
Let n = -6/47 - -230/329. Let -2/7*l - 2/7*l**3 + n*l**2 + 0 = 0. Calculate l.
0, 1
Let m(c) be the third derivative of c**7/1050 + c**6/600 + 7*c**2. Factor m(k).
k**3*(k + 1)/5
Let q(u) be the third derivative of u**8/1120 - u**7/1260 - u**6/180 - 5*u**4/24 + 4*u**2. Let i(x) be the second derivative of q(x). Factor i(t).
2*t*(t - 1)*(3*t + 2)
Let w(j) be the first derivative of j**8/5880 + j**7/980 + j**6/420 + j**5/420 - j**3 - 2. Let v(d) be the third derivative of w(d). Factor v(h).
2*h*(h + 1)**3/7
Let i = -8 - -13. Let p(o) = -8*o**2 - o + i*o + 1 + 12. Let y(z) = -z**2 + 1. Let m(r) = -2*p(r) + 18*y(r). Determine q, given that m(q) = 0.
-2
Let x(l) be the third derivative of -l**6/420 + l**5/210 - 11*l**2. Suppose x(q) = 0. Calculate q.
0, 1
Let w(v) = v**3 + 4*v**2 - 6*v. Let i be w(-5). Let k be ((-2)/(-7))/(i - 4). Factor 2/7*h**5 + 4/7*h**2 - k*h**4 + 2/7*h - 4/7*h**3 - 2/7.
2*(h - 1)**3*(h + 1)**2/7
Suppose 4*u + a = -3, -13 = 4*u + 5*a + 2. Let g(o) = o**3 + 14*o**2 + 21*o - 36. Let r be g(-12). Factor 0*s**2 + 4/5*s**3 - 2/5*s + u*s**4 - 2/5*s**5 + r.
-2*s*(s - 1)**2*(s + 1)**2/5
Let t(h) be the third derivative of -h**8/2184 - h**7/1365 + h**6/260 + h**5/78 + h**4/78 - 6*h**2. Factor t(c).
-2*c*(c - 2)*(c + 1)**3/13
Let g(v) be the third derivative of v**7/70 + v**6/20 - 2*v**5/5 - 9*v**4/4 - 9*v**3/2 - 3*v**2. Determine p, given that g(p) = 0.
-3, -1, 3
Let y be (0 - (-4)/(-10))*135/(-216). Let -1/4*j**5 - y*j**2 + 1/4*j**4 + 0 + 1/4*j**3 + 0*j = 0. Calculate j.
-1, 0, 1
Find t such that -17*t**2 - 48*t**3 - 8*t + 22*t**5 + 61*t**2 - 6*t**5 - 4*t**4 = 0.
-2, 0, 1/4, 1
Let v(h) be the second derivative of -2*h + 0*h**4 - 1/6*h**3 + 0 - h**2 + 1/60*h**5. Let x(i) be the first derivative of v(i). Factor x(w).
(w - 1)*(w + 1)
Factor 1/5*z**3 + 0 + 0*z - 1/5*z**2.
z**2*(z - 1)/5
Let j be 6/(-8)*(14 - (-4960)/(-336)). Factor 6/7*m**4 - j*m**3 + 0*m + 0 + 0*m**2 - 2/7*m**5.
-2*m**3*(m - 2)*(m - 1)/7
Let r = -2 + 4. Let z = 71 + -141/2. Find f, given that 1/2*f**r - z + 0*f = 0.
-1, 1
Let h(o) = 19*o - 112. Let s be h(6). Let 0 + 0*d + 0*d**4 + 0*d**s + 1/3*d**5 - 1/3*d**3 = 0. Calculate d.
-1, 0, 1
Let a(p) = 3*p**2 + p. Let r be a(-1). Let 2*y**3 + 6*y**4 - r*y + 0*y**2 + 0*y - y**2 - 5*y**4 = 0. Calculate y.
-2, -1, 0, 1
Let 1/2*n + 1/2*n**4 + 0 - 1/2*n**3 - 1/2*n**2 = 0. Calculate n.
-1, 0, 1
Factor -7/2*d**3 - 1/2*d**5 - 3/2*d**2 + 0*d - 5/2*d**4 + 0.
-d**2*(d + 1)**2*(d + 3)/2
Let w = -38 + 42. Find b such that 8/5*b + 8/5*b**3 - 2/5*b**w - 2/5 - 12/5*b**2 = 0.
1
Let i(m) be the third derivative of -1/150*m**5 + 1/120*m**4 - 1/600*m**6 - m**2 + 0 + 1/525*m**7 + 0*m + 0*m**3. Solve i(q) = 0 for q.
-1, 0, 1/2, 1
Let q(i) = 4*i**4 + 16*i**3 + 19*i**2 + 11*i + 4. Let x(d) = -4*d**4 - 16*d**3 - 20*d**2 - 12*d - 4. Let w(k) = 4*q(k) + 5*x(k). Suppose w(g) = 0. Calculate g.
-1
Let c(h) = -15*h**2 + 30*h - 20. Let a(q) = -7*q**2 + 15*q - 10. Let k(t) = -5*a(t) + 2*c(t). Suppose k(b) = 0. What is b?
1, 2
Factor -1/3*c**2 - 1/3*c + 0.
-c*(c + 1)/3
Suppose -g - 8 = -5*g. Suppose 2*p = -g*u + 5*p + 9, -3*p - 9 = -5*u. Find a, given that -a**3 + u - 1/2*a**4 + 0*a - 1/2*a**2 = 0.
-1, 0
Let d(v) be the third derivative of v**7/35 + v**6/12 - v**5/6 - 5*v**4/12 + 2*v**3/3 + 3*v**2. Determine i, given that d(i) = 0.
-2, -1, 1/3, 1
Let x be (-3)/15*(2 + -3). Let g(a) be the second derivative of 0 + a - 1/30*a**4 - 2/15*a**3 - x*a**2. Suppose g(c) = 0. Calculate c.
-1
Let o(h) be the first derivative of 1 + 0*h**2 + 0*h - 1/2*h**4 - 4/3*h**3. Factor o(p).
-2*p**2*(p + 2)
Determine p, given that 4/19*p + 14/19*p**4 + 0 + 32/19*p**3 + 22/19*p**2 = 0.
-1, -2/7, 0
Factor 12/7 + 2487/7*h**2 - 4050/7*h**3 - 324/7*h + 1875/7*h**4.
3*(h - 1)**2*(25*h - 2)**2/7
Let p be (-1 - -1)/(0 + -1). Let c be (-51)/(-15) - (-2)/(-5). Factor 1/4*m**2 - 1/4*m**c + 0 + p*m.
-m**2*(m - 1)/4
Let f(n) be the first derivative of n**8/1680 - n**6/180 + n**4/24 + n**3/3 + 3. Let v(g) be the third derivative of f(g). Suppose v(s) = 0. Calculate s.
-1, 1
Let i(v) be the third derivative of v**5/12 - 5*v**4/24 - 5*v**3/3 + 4*v**2. Factor i(k).
5*(k - 2)*(k + 1)
Let n(z) = -2*z - 2. Let q be n(-2). Let c be (-4)/35 - q/(-5). Factor -2/7*f - c*f**3 + 0 + 4/7*f**2.
-2*f*(f - 1)**2/7
Let x(p) be the third derivative of p**5/300 - p**4/40 - 44*p**2. Find d such that x(d) = 0.
0, 3
Let c(m) be the second derivative of m**6/105 - m**5/70 - m**4/42 + m**3/21 - 22*m. Suppose c(l) = 0. What is l?
-1, 0, 1
Factor 3/2*q**2 + 0 + q + 1/2*q**3.
q*(q + 1)*(q + 2)/2
Factor 0 + 38/7*d**4 + 4/7*d - 2*d**5 - 30/7*d**3 + 2/7*d**2.
-2*d*(d - 1)**3*(7*d + 2)/7
Let d(s) be the first derivative of -s**6/600 + s**4/40 - 4*s**3/3 - 2. Let y(v) be the third derivative of d(v). What is b in y(b) = 0?
-1, 1
Suppose 0*q + 0*q = -q. Let l(a) be the second derivative of a**2 + 7/6*a**3 - a + 3/20*a**5 + 2/3*a**4 + q. Factor l(r).
(r + 1)**2*(3*r + 2)
Suppose -6*v = -7*v + 18. Let a be 0 + -1 + v/15. Factor 3/5*z - a*z**2 - 2/5.
-(z - 2)*(z - 1)/5
Let y(j) be the first derivative of 1/7*j**2 + 0*j**3 + 0*j - 1/14*j**4 - 9. Factor y(b).
-2*b*(b - 1)*(b + 1)/7
Let -4*h + 7*h + 5*h - 2*h + 3*h**2 = 0. What is h?
-2, 0
Let a(l) be the first derivative of 1/3*l**3 - 1/4*l**4 + 1/4*l**2 - 1/10*l**5 - 1 - 1/2*l + 1/12*l**6. Let a(n) = 0. Calculate n.
-1, 1
Let i(g) be the first derivative of g**4/4 - 3*g**3 + g**2/2 - 11*g - 2. Let q(h) = 2*h**2 + 2. Suppose -2 = 5*t + 8. Let w(f) = t*i(f) - 11*q(f). Factor w(p).
-2*p*(p + 1)