4*i**3 + 20*i**2 + 61*i - 3*i + 6*i + j.
-4*(i - 1)*(5*i + 2)**2
Suppose 34 = 2*b + 10. Let h = b + -9. Determine r, given that 32/5*r**2 + 4/5 - 14/5*r**h - 22/5*r = 0.
2/7, 1
Let d = -2/199 + 211/1194. Let u(c) be the third derivative of -1/10*c**5 + 0*c**3 + 1/60*c**6 + 0*c + 0 + 2*c**2 + d*c**4. Factor u(m).
2*m*(m - 2)*(m - 1)
Let b = 10 - 6. Let g be 2/b*(3 + 1). Solve 4 + 10*q - 6*q**2 + 8*q**2 + g*q**3 + 6*q**2 = 0 for q.
-2, -1
Let z(a) = -100*a. Let l be z(-1). Let r be 2 - (l/36 - 1). Suppose 0 - 8/9*p + 8/9*p**2 - r*p**3 = 0. What is p?
0, 2
Let d = 3 - -1. Solve 3 - m**3 - m**2 + m**5 + 1 - 4 + m**d = 0 for m.
-1, 0, 1
Suppose -4*o + 4 = -k, -4*k = 4*o - 6 + 2. Factor -1 + k*w - w - w**3 - 3*w**2 - 2*w.
-(w + 1)**3
Suppose -o - 117 = 5*u, -3*u - 53 - 26 = 5*o. Let r = -9 - u. Factor -8 - 24*w - 2*w**2 + r*w**2 + 2*w**2.
2*(w - 2)*(7*w + 2)
Let f = -44 + 84. Let v = f - 438/11. Suppose 4/11*t - v*t**2 + 0 = 0. Calculate t.
0, 2
Let d(z) be the third derivative of -1/84*z**4 + 0*z + 0*z**7 + 1/210*z**6 + 0 + 6*z**2 - 1/1176*z**8 + 0*z**5 + 0*z**3. Solve d(l) = 0 for l.
-1, 0, 1
Let i be 2/5 - 26/(-10). Suppose -6*q = -4*q - 8. Find j, given that -i*j**2 - 2*j**2 + q + 9*j - j = 0.
-2/5, 2
Let b(j) be the first derivative of j**4/36 + 4*j**3/9 + 8*j**2/3 + 8*j - 10. Let p(o) be the first derivative of b(o). Suppose p(g) = 0. Calculate g.
-4
Suppose -5*w + 6 + 4 = 0. Factor 5*o**3 - 2*o**2 + 2*o - 4*o**3 + w*o**4 - 3*o**3.
2*o*(o - 1)**2*(o + 1)
Let d(r) be the third derivative of -r**5/15 + r**4/6 + 4*r**3/3 - 15*r**2. Factor d(n).
-4*(n - 2)*(n + 1)
Factor 5*a**4 - 3 + 0*a - 6*a**3 + 6*a - 2*a**4.
3*(a - 1)**3*(a + 1)
Let j = 44357 + -309965/7. Let c = j + -76. Suppose c + 4/7*i**3 - 2/7*i**5 - 2/7*i - 4/7*i**2 + 2/7*i**4 = 0. What is i?
-1, 1
Let q(i) = -i**2 + 3*i + 4. Let d be q(-1). Let v(n) be the first derivative of -n**2 + d*n + 1 - 2/3*n**3. Find f, given that v(f) = 0.
-1, 0
Let u = -140 + 144. Let g(k) be the second derivative of -1/3*k**2 - u*k + 0 - 2/9*k**3 - 1/18*k**4. Let g(c) = 0. Calculate c.
-1
Let o be (-39)/15 - (-6)/(1 + 1). Suppose 0 + 0*f + o*f**2 = 0. What is f?
0
Solve -4*s**2 - 2*s - 5/2*s**3 - 1/2*s**4 + 0 = 0.
-2, -1, 0
Let d = -422 - -425. Let n = 391/5 - 78. Factor 0 + 0*b**4 + 0*b**2 + 0*b + n*b**d - 1/5*b**5.
-b**3*(b - 1)*(b + 1)/5
Let b be (-2 - 1)*4/(-8). Let u = b - 1. Solve 0 - u*f - 1/2*f**2 = 0.
-1, 0
Let 3/7*w**5 + 0*w**3 + 0*w + 6/7*w**4 + 0*w**2 + 0 = 0. What is w?
-2, 0
Let t(w) be the first derivative of -1/300*w**5 + 0*w**3 - 3 + 1/60*w**4 + 0*w + 1/2*w**2. Let f(u) be the second derivative of t(u). Factor f(i).
-i*(i - 2)/5
Let k = -38 - -38. Let q(a) be the first derivative of -2*a - 3/2*a**2 + 1/4*a**4 + k*a**3 + 3. Find v, given that q(v) = 0.
-1, 2
Let t be 4/(-10)*(-2)/2. Determine p, given that -2/5*p**2 + 4/5*p - t = 0.
1
Let a be 18/6 - (-1999)/5. Let g = 406 - a. Factor -6/5*c**5 + g*c**4 + 0 + 0*c + 4/5*c**2 - 14/5*c**3.
-2*c**2*(c - 1)**2*(3*c - 2)/5
Let p(v) = v**2 - v - 1. Let l be 3 + -5 + 5 + 0. Let k be 2 + (2 - 2) - -1. Let u(z) = -z**3 + z**2 + 1. Let t(q) = k*u(q) + l*p(q). Factor t(b).
-3*b*(b - 1)**2
Let p(c) = -10*c**3 - 14*c**2 - c + 3*c - 6*c. Let o(s) = -3*s**3 + 3*s**3 - s**3 - s**2. Let y(z) = -4*o(z) - p(z). Solve y(u) = 0 for u.
-1, -2/7, 0
Let c(g) be the first derivative of g + 5/4*g**2 + 1/8*g**4 - 6 + 2/3*g**3. Determine u so that c(u) = 0.
-2, -1
Let j be (4/(-32))/((-15)/80). Factor -j*x**3 + 0 + 2*x**2 - 4/3*x.
-2*x*(x - 2)*(x - 1)/3
Let r(j) be the second derivative of j**5/80 + j**4/12 - j**3/8 - 9*j**2/4 + 42*j. Suppose r(n) = 0. What is n?
-3, 2
Let p(f) be the first derivative of 0*f - 1/9*f**2 + 2/9*f**3 - 3 + 2/45*f**5 - 1/6*f**4. Find r, given that p(r) = 0.
0, 1
Suppose -5*y + 2*y - 23 = -4*p, 9 = 2*p - y. Let z(j) be the third derivative of 5/12*j**4 + 0 + 0*j - 1/3*j**3 - 3*j**p - 5/24*j**5. Factor z(b).
-(5*b - 2)**2/2
What is a in -4 + 6 + 2*a**2 - 3*a + 7*a = 0?
-1
Let f(n) be the second derivative of -2*n + 0 - 1/2*n**2 + 1/12*n**3 + 1/24*n**4. Factor f(b).
(b - 1)*(b + 2)/2
Determine f so that -6*f**5 + 10*f**4 - 5*f - 10*f**2 - 7*f**5 + 20*f**3 - 2*f**5 = 0.
-1, -1/3, 0, 1
Let h = 0 + 0. Let y = h + 2. Factor v**2 + v - 2*v**2 - y*v**2 + 5*v**3 - 3*v**3.
v*(v - 1)*(2*v - 1)
Factor -2/11*t**2 + 2/11 + 2/11*t**3 - 2/11*t.
2*(t - 1)**2*(t + 1)/11
Suppose 2*s - 4*s = 22*s. Solve 1/8*p**2 + s - 1/4*p = 0 for p.
0, 2
Let m(j) = -31*j**2 - 3*j - 2. Let o be m(-1). Let g be (-7)/(-2) - (-5)/o. Factor 2/3 - 3*u + 4/3*u**3 + 5/3*u**5 - 4*u**4 + g*u**2.
(u - 1)**3*(u + 1)*(5*u - 2)/3
Let q(f) = -f + 1. Let x(w) = -4*w**2 + 18*w - 6. Let c(b) = -6*q(b) - x(b). Factor c(t).
4*t*(t - 3)
Let n(a) be the first derivative of a**3/4 - 15*a**2/8 + 9*a/2 + 1. Factor n(c).
3*(c - 3)*(c - 2)/4
Suppose 0 = 4*h + h - 5*q - 15, q + 3 = 0. Let c be (6/20)/((-11)/(-4) - 2). Find t, given that 6/5*t**3 + 2/5*t**5 - 6/5*t**4 - c*t**2 + 0*t + h = 0.
0, 1
Let r(p) be the first derivative of -3 - 3/8*p**2 + 0*p**5 + 1/4*p**4 + 1/6*p**3 - 1/2*p - 1/24*p**6. Find t such that r(t) = 0.
-1, 1, 2
Let m = 0 - -4. Let u(l) be the third derivative of 1/30*l**5 - l**2 + 0*l + 0*l**m + 0 + 0*l**3. Suppose u(r) = 0. Calculate r.
0
Let p(k) be the second derivative of k**4/18 - 5*k**3/9 + 2*k**2 + 7*k. Factor p(z).
2*(z - 3)*(z - 2)/3
Let b = -19 + 32. Let -b*s**3 - 2*s**5 + 16*s**4 + 15*s**5 - 3*s**5 + 5*s**3 - 2*s + 4 - 20*s**2 = 0. What is s?
-1, 2/5, 1
Let i be 5/20 - 62/(-96). Let u(j) be the second derivative of -21/80*j**5 + 0 + 0*j**3 + i*j**4 - 1/2*j**2 - 3*j. Factor u(m).
-(m - 2)*(3*m - 1)*(7*m + 2)/4
Let h(b) be the second derivative of -3*b + 0 + 3/40*b**5 - 1/8*b**4 + 0*b**2 + 0*b**3. Solve h(x) = 0.
0, 1
Suppose 0*c + 6 = 5*g - 4*c, -4*c = 2*g - 8. Factor 2/3*f**g - 2/3*f**3 + 0 - 2/3*f**4 + 2/3*f**5 + 0*f.
2*f**2*(f - 1)**2*(f + 1)/3
Let q(p) = -p**3 - p**2 + 5*p + 3. Let y = -3 - -6. Let s(x) = 2*x**3 + 2*x**2 - 9*x - 5. Let z(u) = y*s(u) + 5*q(u). Factor z(k).
k*(k - 1)*(k + 2)
Let j = -395/161 - -40/23. Let k = -13/28 - j. Factor -k*x - 1/2*x**2 + 1/2 + 1/4*x**3.
(x - 2)*(x - 1)*(x + 1)/4
Let f be (-4)/(-10) - 9/(-15). Let a be (1 - (f - 2)) + 0. Find y such that -y**a + 0 - 2/7*y - 9/7*y**3 - 5/7*y**4 - 1/7*y**5 = 0.
-2, -1, 0
Factor -1/3*n**3 + n**2 + 0 - 2/3*n.
-n*(n - 2)*(n - 1)/3
Factor 3*m + 6*m - 4*m**3 + 4*m**2 - m.
-4*m*(m - 2)*(m + 1)
Let x(o) be the third derivative of 0*o**4 + 0*o**6 - 1/140*o**7 - 1/4*o**3 + 2*o**2 + 0*o + 0 + 1/20*o**5. Determine d, given that x(d) = 0.
-1, 1
Let w(g) be the second derivative of g**4/12 - g**3/3 + 2*g. Suppose w(a) = 0. Calculate a.
0, 2
Suppose 2*n = -2*t + 2, -5*n - 1 = 4. Factor 11 - 2*s - 2*s**3 - 11 + 4*s**t.
-2*s*(s - 1)**2
Let 28 - 57 - t**2 + 29 = 0. Calculate t.
0
Let i = 2745/4 - 685. Factor -3*z**3 + 9/4*z**2 + i*z**4 - 1/2*z + 0.
z*(z - 1)**2*(5*z - 2)/4
Let x = 5 - 1. What is a in -3*a**3 + x*a**3 + a**3 + a - 3*a**3 = 0?
-1, 0, 1
Let i = 6873/4 + -1710. Determine o, given that 3/4 - 21/4*o**2 - 9/4*o + i*o**3 + 9/2*o**4 - 6*o**5 = 0.
-1, -1/2, 1/4, 1
Let u(s) be the second derivative of 5/18*s**3 + 0 - 1/90*s**6 - 1/60*s**5 + 1/12*s**4 + 9*s + 1/3*s**2. Factor u(c).
-(c - 2)*(c + 1)**3/3
Determine w, given that 4/3*w**2 + 10/3*w**3 + 8/3*w**4 + 0 + 0*w + 2/3*w**5 = 0.
-2, -1, 0
Let u be 2/(261/30 + -1). Let k = u + 2/77. Let -4/7*q**4 + 0 - 8/7*q**2 + k*q + 10/7*q**3 = 0. What is q?
0, 1/2, 1
Let y = 24 - 24. Let v(f) be the third derivative of -1/60*f**6 + 0*f + 1/210*f**7 + y + 0*f**4 + 0*f**3 + 1/60*f**5 + 4*f**2. What is l in v(l) = 0?
0, 1
Let o(d) be the third derivative of 2*d**7/105 - d**5/15 - 6*d**2. Factor o(l).
4*l**2*(l - 1)*(l + 1)
Suppose 45*f = 41 + 49. Determine n so that -f*n**2 - 4/7*n + 4/7*n**3 + 0 + 2*n**4 = 0.
-1, -2/7, 0, 1
Let u(x) = 10*x**5 + 15*x**4 - 10*x**3 - 5*x**2 + 5. Let k(s) = -15*s**5 - 22*s**4 + 15*s**3 + 8*s**2 - 7. Let q(i) = 5*k(i) + 7*u(i). Factor q(z).
-5*z**2*(z - 1)*(z + 1)**2
Suppose -3 = 2*i - 11. Factor 56*b**3 - 3*b**i + 13*b**4 + 9*b**2 + 11*b**4 - 20*b**3 - 6*b.
3*b*(b + 1)**2*(7*b - 2)
Let o(u) be the third derivative of -1/52*u**4 + 0 + 0*u + 1/390*u**5 + 2/39*u**3 + 7*u**2. Factor o(y).
2*(y - 2)*(y - 1)/13
Let b(r) be the second derivative of