2*k.
-k*(k + 1)**2/2
Let f be (-596)/6*(-4)/32. Let a = 74/3 - f. Factor 5*s**2 - a*s**5 - 35/2*s**4 + 0 + 3/4*s**3 - s.
-s*(s + 1)**2*(7*s - 2)**2/4
Let h(c) be the first derivative of 0*c**4 - 1/12*c**6 + 0*c**2 + 0*c - 1 + 0*c**3 + 1/10*c**5. Find w, given that h(w) = 0.
0, 1
Let h be ((-6)/14)/((-5)/35). Factor 7 - 9 + h*c**2 - 1.
3*(c - 1)*(c + 1)
Let r(t) be the second derivative of t**5/10 + t**4/12 - t**3/3 - t**2/2 - 9*t. Suppose r(d) = 0. Calculate d.
-1, -1/2, 1
Let u(k) be the second derivative of -5*k**4/12 + 5*k**2/2 + 15*k. Factor u(m).
-5*(m - 1)*(m + 1)
Suppose -r + 0*r**2 - 12*r**2 + 22*r**2 + 6*r + 20*r**4 - 35*r**3 = 0. Calculate r.
-1/4, 0, 1
Let d(u) be the first derivative of 1/3*u**2 + 1/3*u**6 - 1 + 1/15*u**5 - 1/9*u**3 + 0*u - 2/3*u**4. Solve d(f) = 0 for f.
-1, -2/3, 0, 1/2, 1
Let r = 41 + -286/7. Let x = 9/14 - r. Solve -1/2 - c - x*c**2 = 0.
-1
Let a(t) = 2*t**4 + 2*t**3 - 4*t**2 - 6*t - 6. Let d(o) = -2*o**4 - 2*o**3 + 4*o**2 + 5*o + 5. Let z(r) = -5*a(r) - 6*d(r). Factor z(x).
2*x**2*(x - 1)*(x + 2)
Suppose 9 = -4*t - 0*t + 5*p, 0 = 3*t - 4*p + 8. Solve -1/3*h**t + 0 + 0*h**3 + 0*h + 0*h**2 = 0.
0
Let o(d) be the second derivative of 5/18*d**3 + 0 + 1/60*d**5 + 1/3*d**2 + 5*d + 1/9*d**4. Factor o(l).
(l + 1)**2*(l + 2)/3
Let x(t) be the third derivative of t**8/4200 - t**7/1050 + t**6/900 - t**3/3 - 3*t**2. Let o(m) be the first derivative of x(m). Factor o(n).
2*n**2*(n - 1)**2/5
Let k(y) = 3*y**2 - 11*y + 1. Let c be 1/2*2/(-1). Let i(v) = v**2 - v - 1. Let f(d) = c*i(d) - k(d). Solve f(z) = 0.
0, 3
Find o such that -16*o - 4/3*o**3 - 32/3 - 8*o**2 = 0.
-2
Let d(p) be the third derivative of p**6/420 - p**4/21 + 11*p**2. Factor d(i).
2*i*(i - 2)*(i + 2)/7
Let d be (25/15)/(-4 - -9). Factor -2/3*x**2 + 0 + 1/3*x**3 + d*x.
x*(x - 1)**2/3
Let i(b) be the third derivative of -3*b**2 + 1/6*b**3 - 1/120*b**6 + 0 + 0*b + 1/30*b**5 + 1/6*b**4. Let t(r) be the first derivative of i(r). Solve t(c) = 0.
-2/3, 2
Let d(u) be the second derivative of 49*u**4/12 + 14*u**3/3 + 2*u**2 - u. Let d(s) = 0. Calculate s.
-2/7
Let n(o) be the first derivative of -o**6/360 + o**4/24 + o**3 - 1. Let c(b) be the third derivative of n(b). Factor c(g).
-(g - 1)*(g + 1)
Suppose 1 = i - 4. Let h(d) = 4*d - 4. Let m(v) = -v**2 + 5*v - 5. Let u(c) = i*h(c) - 4*m(c). Suppose u(j) = 0. Calculate j.
0
Let m(x) be the second derivative of -x**7/350 - x**6/200 + x**5/100 + x**4/40 + x**2/2 - 4*x. Let j(t) be the first derivative of m(t). Factor j(z).
-3*z*(z - 1)*(z + 1)**2/5
Let o be (-1)/7*91/(-468). Let k(i) be the second derivative of o*i**4 + 1/18*i**3 - i + 0 - 1/3*i**2. Let k(l) = 0. Calculate l.
-2, 1
Suppose 14 = 3*d + 8*c - 4*c, -2 = d - 2*c. Suppose 5*o + 5*b - 275 = 0, b - 2*b = -o + 45. Find j, given that o*j**d - 10*j - 250/3*j**3 + 2/3 = 0.
1/5
Solve -2/7*v + 4/7*v**3 + 0*v**4 + 0*v**2 - 2/7*v**5 + 0 = 0 for v.
-1, 0, 1
Let l be (1/2)/(60/24). Suppose 0*c + 0*c**2 + 0 + 1/5*c**4 - l*c**3 = 0. Calculate c.
0, 1
Let b(k) = -2*k**2 - 11*k + 13. Let i(u) = u**2 + 6*u - 7. Let x(q) = -6*b(q) - 11*i(q). Find l, given that x(l) = 0.
-1, 1
Let a(n) = 4*n**3 - 5*n**2 + 9*n - 3. Let y(x) = x**3 + x + 1. Let p(b) = a(b) - 5*y(b). Let o be p(-6). Solve q**3 + q**3 - 4*q + 6*q + o*q**2 = 0 for q.
-1, 0
Suppose -12 = -7*h + h. Find a such that 7/5*a + 2/5 + a**h = 0.
-1, -2/5
Suppose -5*h + 2*h = 0. Suppose 4*u**4 - 2*u**4 + h*u**4 - u + u**3 - 3*u**4 + u**2 = 0. What is u?
-1, 0, 1
Let z(i) be the first derivative of 12*i**5/35 - 8*i**4/7 + 4*i**3/3 - 4*i**2/7 + 5. Factor z(g).
4*g*(g - 1)**2*(3*g - 2)/7
Let z(u) be the third derivative of -1/10*u**6 + 2/15*u**5 + 0 + u**2 + 0*u + 0*u**3 + 0*u**4 + 2/105*u**7. Factor z(g).
4*g**2*(g - 2)*(g - 1)
Suppose -5*n = -8*n + 9. Solve 20*j**3 - 2*j**2 + 3*j - 17*j**n + 8*j**2 = 0.
-1, 0
Let m(t) = t + 8. Let l be m(0). Let r = -8 + l. Determine n so that n**3 + 0 + r*n - 2/3*n**2 + 2/3*n**4 = 0.
-2, 0, 1/2
Let l(j) be the second derivative of -j**6/6 + j**5/2 + 5*j**4/4 - 10*j**3/3 - 10*j**2 + 2*j. Factor l(k).
-5*(k - 2)**2*(k + 1)**2
Let b = -334 - -5012/15. Let y(z) be the first derivative of -2/5*z**2 - 1 - b*z**3 + 0*z. Determine k so that y(k) = 0.
-2, 0
Solve 4/5*p**2 + 0 + 4/5*p = 0.
-1, 0
Let j(p) = p**3 + p**2 + p + 2. Let o be j(0). Let q(x) be the first derivative of -2 - 1/8*x**4 - 4*x - 3*x**o - x**3. Suppose q(d) = 0. Calculate d.
-2
Let m(b) be the second derivative of -3*b**5/20 + 3*b**4/4 - b**3 + 5*b. Determine i so that m(i) = 0.
0, 1, 2
Let t(a) be the first derivative of -a**5/6 + a**4/9 - 2*a - 2. Let y(w) be the first derivative of t(w). Factor y(d).
-2*d**2*(5*d - 2)/3
Let w(u) be the second derivative of -u**5/2 - 5*u**4/4 - 5*u**3/6 + 10*u. Factor w(s).
-5*s*(s + 1)*(2*s + 1)
Suppose 3/4*j**2 + 3/8*j**3 - 3/8*j - 3/4 = 0. Calculate j.
-2, -1, 1
Let n(g) be the third derivative of -1/6*g**4 - 1/6*g**3 - 1/60*g**6 - 1/12*g**5 - 2*g**2 + 0*g + 0. Solve n(k) = 0.
-1, -1/2
Determine d, given that -2/5*d**2 - 72/5*d - 648/5 = 0.
-18
Let x(z) be the second derivative of z**6/90 - z**5/20 + 2*z**3/9 - 13*z. Determine n, given that x(n) = 0.
-1, 0, 2
Let s(r) be the third derivative of -2*r**7/315 - r**6/60 - r**5/90 - 43*r**2. Suppose s(m) = 0. What is m?
-1, -1/2, 0
Determine t, given that 15/2*t + 5/2 + 15/2*t**2 + 5/2*t**3 = 0.
-1
Let f(i) = i**2 + i - 2. Let c be f(1). Let h(d) be the second derivative of 1/15*d**6 + d**2 + 2*d + 0 + c*d**5 + 0*d**3 - 1/3*d**4. Find k such that h(k) = 0.
-1, 1
Suppose -o - 4*o = -20. Let v be o/(0 + 1) - 2. Factor -6*s + s + v*s + s - 2*s**2.
-2*s*(s + 1)
Solve 1/2*k**3 + k + 0 - 3/2*k**2 = 0.
0, 1, 2
Let d(m) be the third derivative of -m**7/210 - 7*m**6/120 + m**5/20 + 55*m**4/24 - 25*m**3/3 + 36*m**2 + m. Factor d(w).
-(w - 2)*(w - 1)*(w + 5)**2
Suppose 22*d - 18 = 16*d. Let o = 1068/5 - 212. Factor -2/5*q**d - 16/5*q - 2*q**2 - o.
-2*(q + 1)*(q + 2)**2/5
Let n = 4771/27188 + 3/971. Let v = n + 4/7. Factor v*z**2 + 0 + 3/4*z.
3*z*(z + 1)/4
Let m(b) be the first derivative of -b**4/4 - 2*b**3 - 3*b**2 - b + 2. Let n be m(-5). Find l such that -5*l + n*l + 2*l**3 - l**4 + 1 - l = 0.
-1, 1
Let c(s) = 3*s**3 + 7*s**2 - 5*s. Suppose 0*z - 25 = 5*z. Let v(p) = p**3 + p**2 - p. Let d be (2 + 10/(-4))*-2. Let o(k) = d*c(k) + z*v(k). Factor o(y).
-2*y**2*(y - 1)
Let m(q) = -3*q**2 - 4. Let o(b) = -5*b**2 - 7. Suppose -5*h - 11 = -4*f, 4*h + 0*h = -5*f + 24. Let x(r) = f*o(r) - 7*m(r). Factor x(i).
i**2
Let w(s) = -s**3 - 21*s**2 - 21*s - 17. Let a be w(-20). Solve 0 - 3/2*c**a + c**2 + 1/2*c**4 + 0*c = 0 for c.
0, 1, 2
Let y = 128 - 3071/24. Let j(t) be the third derivative of 0*t**3 - y*t**4 - 3*t**2 + 0 + 1/30*t**5 - 1/120*t**6 + 0*t. Factor j(u).
-u*(u - 1)**2
Factor 5*d**3 - 5*d - 7*d**4 + 3*d + d**3 + 7*d**2 - 4*d**3.
-d*(d - 1)*(d + 1)*(7*d - 2)
Let v(o) = -132*o**4 + 27*o**3 - 15*o + 15. Let n(k) = 19*k**4 - 4*k**3 + 2*k - 2. Let z(c) = 15*n(c) + 2*v(c). Factor z(b).
3*b**3*(7*b - 2)
Factor -6/5 - 2/15*h**2 - 4/5*h.
-2*(h + 3)**2/15
Solve 3*n**2 + 0*n**2 - n**3 - 10 + 6 = 0.
-1, 2
Suppose 6*y**2 + 78*y - 1 + 2*y**2 - 4*y**3 - 7 - 74*y = 0. What is y?
-1, 1, 2
Let 0 - 2/5*i - 3/5*i**4 + 3/5*i**2 + 1/5*i**3 + 1/5*i**5 = 0. What is i?
-1, 0, 1, 2
Factor 0 + 4/7*g + 2/7*g**2.
2*g*(g + 2)/7
Let u = 104/129 + -6/43. Factor -u - 2/3*n**2 - 4/3*n.
-2*(n + 1)**2/3
Find a such that -10*a**2 + 24*a + 13*a**4 + 9*a**4 - 24*a**3 - 4*a**4 - 8 = 0.
-1, 2/3, 1
Let z(h) be the first derivative of h**3/15 + 3*h**2/10 + 2*h/5 + 63. Factor z(d).
(d + 1)*(d + 2)/5
Suppose 2*s + 2 = 6. Factor 0*n**4 + 21*n - 26*n**2 - 8 - s*n**4 + 3*n + 12*n**3.
-2*(n - 2)**2*(n - 1)**2
Let p = -22014788/305 - -72180. Let t = p + 2/61. Factor 4/5 + 6/5*d + t*d**2.
2*(d + 1)*(d + 2)/5
Let n(z) be the second derivative of 3/20*z**5 + 0 - 5*z - z**3 + 0*z**2 + 1/4*z**4. What is i in n(i) = 0?
-2, 0, 1
Let l = 21 + -18. Solve -2*k**2 + 8*k**4 - 1/3*k**l + 0 - 1/3*k - 16/3*k**5 = 0 for k.
-1/4, 0, 1
Factor -9*a**2 - 3*a**3 + 15 + 0*a**3 - 3.
-3*(a - 1)*(a + 2)**2
Let l be (1/24)/((-25)/(-10)). Let h(y) be the third derivative of 0 + y**2 + 1/6*y**3 - 1/210*y**7 + l*y**6 + 0*y + 0*y**5 - 1/12*y**4. Factor h(n).
-(n - 1)**3*(n + 1)
Let m(c) be the second derivative of -c**7/21 + 2*c**6/1