*2*(2*s + 1)
Let p = 30 - 30. Let a(v) be the second derivative of 1/3*v**3 + v - 1/12*v**4 + p + 0*v**2. Let a(j) = 0. Calculate j.
0, 2
Let j be (-37)/(-20) - (-2)/5. Factor 0 + j*k**4 + 7/4*k**2 + 15/4*k**3 + 1/4*k.
k*(k + 1)*(3*k + 1)**2/4
Let a(h) be the third derivative of 2*h**7/525 - h**6/75 - h**5/75 + h**4/15 + 20*h**2. Find n such that a(n) = 0.
-1, 0, 1, 2
Let c(m) = 5*m - 100. Let f be c(20). Solve 4/3*k**4 + 4/3*k**3 - 8/3*k**2 + 0*k + f = 0 for k.
-2, 0, 1
Let m(a) = -2*a**3 + 3*a - 3. Let g = -3 - 0. Let d(l) = -2*l**3 + 4*l - 4. Let h(t) = g*d(t) + 4*m(t). Factor h(k).
-2*k**3
Let k(o) = -o + 6. Let t = -6 - -12. Let g be k(t). Factor 0*q + g - 2/7*q**2.
-2*q**2/7
Let r(l) be the third derivative of -l**5/20 + l**4/4 + l**2. Let r(m) = 0. Calculate m.
0, 2
Let h(k) = 4*k**2 + 3*k - 4. Let l(i) = -5*i**2 - 4*i + 5. Let f(x) = -4*h(x) - 3*l(x). Factor f(a).
-(a - 1)*(a + 1)
Suppose -6*m = -8*m + 2. Factor -m - 16 - 1 + 30*g + 2*g**3 - 14*g**2.
2*(g - 3)**2*(g - 1)
Suppose -m = -2 + 4. Let o be 0 - m - (2 + -4). Factor s**o + 4*s**3 - 4*s + 2*s + 6*s**2 + 6*s + 1.
(s + 1)**4
Let u = -20413/9 - -2311. Let z = u - 2630/63. Factor 2*c - 4/7 - 8/7*c**3 - z*c**2.
-2*(c + 2)*(2*c - 1)**2/7
Let y(p) be the third derivative of p**8/8 - 19*p**7/210 - p**6/3 + 19*p**5/60 - p**4/12 + 27*p**2. Solve y(m) = 0.
-1, 0, 1/6, 2/7, 1
Let a be 12/9*60/40. Factor -9/2*d**a - 3*d**3 + 3/2*d**4 + 6*d + 6.
3*(d - 2)**2*(d + 1)**2/2
Let x(m) be the second derivative of -9*m**5/35 + m**4/7 + m**3/14 - 21*m. Solve x(o) = 0.
-1/6, 0, 1/2
Let g(i) be the second derivative of -i**4/24 - i**3/6 - i**2/4 - i. Determine k so that g(k) = 0.
-1
Find n, given that 3/2*n**4 + 0 + 0*n + 0*n**3 + 1/2*n**5 + 0*n**2 = 0.
-3, 0
Let d(a) be the second derivative of 1/18*a**4 + 0 + 4/3*a**2 - 5*a + 4/9*a**3. Factor d(b).
2*(b + 2)**2/3
Let p(d) be the third derivative of d**8/30240 - d**7/2520 + d**6/540 - d**5/30 - 3*d**2. Let s(f) be the third derivative of p(f). Let s(q) = 0. What is q?
1, 2
Let o(u) be the third derivative of -u**6/80 - u**5/20 + u**4/16 + u**3/2 - 20*u**2. Factor o(h).
-3*(h - 1)*(h + 1)*(h + 2)/2
Let h(a) = 2*a**4 + 2*a**2 + 2*a - 2. Let j(x) = -x**2 - 3*x + 1. Let g be j(-3). Let b(q) = q**2 + q - 1. Let z(r) = g*h(r) - 2*b(r). Factor z(p).
2*p**4
Let m be 7*(56/(-294))/((-2)/3). Factor m*u + 4/7*u**2 - 4/7 - 2*u**3.
-2*(u - 1)*(u + 1)*(7*u - 2)/7
Suppose 324 = -3*y - 60. Let w = y - -642/5. Suppose -w*i**3 + 0 + 2/5*i + 0*i**2 = 0. Calculate i.
-1, 0, 1
Let j(t) be the third derivative of 1/336*t**8 + 3/8*t**4 + 0*t - 4/15*t**5 - 1/3*t**3 - 1/35*t**7 + 7/60*t**6 + 4*t**2 + 0. Factor j(q).
(q - 2)*(q - 1)**4
Let n = -310 - -316. What is c in 4*c - n - 2/3*c**2 = 0?
3
Let t = -3 - 2. Let v(b) = -b**2 + b. Let h(c) = -6*c**2 + 9*c - 4. Let q(z) = t*v(z) + h(z). Factor q(x).
-(x - 2)**2
Let j(r) be the first derivative of 1/9*r**3 + r**2 - 1/90*r**5 + 0*r + 0*r**4 - 1. Let a(u) be the second derivative of j(u). Let a(k) = 0. Calculate k.
-1, 1
Suppose -3*f + 0*t = -t - 3, -f + 9 = -3*t. Let r(o) be the second derivative of f + 1/20*o**5 + 0*o**2 - 1/12*o**4 + o + 0*o**3. Let r(j) = 0. Calculate j.
0, 1
Let l(d) be the second derivative of d**10/37800 + d**9/18900 - d**8/4200 + 2*d**4/3 + 6*d. Let y(z) be the third derivative of l(z). Factor y(u).
4*u**3*(u - 1)*(u + 2)/5
Let j be (231/75 + -3)*1*10. Factor -2/5 + j*c**2 + 0*c - 2/5*c**4 + 0*c**3.
-2*(c - 1)**2*(c + 1)**2/5
Let l(q) = -q**3 - q**2 - q + 2. Let k be l(0). Let u(n) be the second derivative of n**3 + 1/6*n**4 - n + 2*n**k + 0. Factor u(m).
2*(m + 1)*(m + 2)
Let w(u) = 20*u**4 - 60*u**3 + 28*u**2 - 12*u - 12. Let t(g) = g**3 - g**2 + g + 1. Let b(n) = 12*t(n) + w(n). Factor b(h).
4*h**2*(h - 2)*(5*h - 2)
Let q be 4 + -3 + 2/1. Suppose 0 = -q*o + l + 13, 5*o - 3*l - 13 - 14 = 0. Factor v**2 + v**3 - 2*v**o + 2 - 3 + v.
-(v - 1)**2*(v + 1)
Suppose -5*r = c + 5, -3*r = -6*r + 3*c + 15. Factor 0 - 6/5*b**3 - 2/5*b**2 + r*b - 4/5*b**4.
-2*b**2*(b + 1)*(2*b + 1)/5
Let f(m) be the second derivative of -m**7/1260 - m**6/180 - m**5/60 - m**4/36 - m**3/36 + 2*m**2 - 3*m. Let y(i) be the first derivative of f(i). Factor y(u).
-(u + 1)**4/6
Suppose 3*v = -2*c + 2*v + 5, -3*c + 5 = 2*v. Suppose -z + 5*u + 0 = -1, 2*u = 5*z - c. What is k in -3*k**4 + 6*k**4 + 11*k**2 + 6*k + z + 10*k**3 + k**2 = 0?
-1, -1/3
Factor 6912*i + i**4 - 1910*i**2 + 47*i**3 - 5*i**4 + 97*i**3 + 182*i**2.
-4*i*(i - 12)**3
Let 0 - 2/15*j**3 - 2/15*j + 4/15*j**2 = 0. Calculate j.
0, 1
Let q(s) = s**3 - s + 1. Let c(f) = f**4 + 9*f**3 + 6*f**2 - f + 6. Let m(k) = -c(k) + 5*q(k). Find u such that m(u) = 0.
-1
Let j(q) = -16*q + 1. Let v be j(-2). Suppose -33 + v - r**3 - r**4 + r + r**2 = 0. Calculate r.
-1, 0, 1
Let w(o) = o**3 + 15*o**2 + o + 5. Let k be w(-15). Let p be ((-3)/45)/(3/k). Factor 2/9*a**3 - 2/9*a**2 - 2/9*a + p.
2*(a - 1)**2*(a + 1)/9
Let n(r) be the third derivative of 0*r + 1/120*r**5 + 0*r**4 - 1/12*r**3 + 0 - 2*r**2. Suppose n(c) = 0. What is c?
-1, 1
Let v(d) be the first derivative of 3/4*d**4 + 0*d + 6*d**2 - 3 + 4*d**3. Factor v(k).
3*k*(k + 2)**2
Factor -7 - 7*h - 3*h**3 - 2*h + 4 + 0*h**3 - 9*h**2.
-3*(h + 1)**3
Let i be (-7 - -7)/(6/3). Factor 0*k + i - 2/5*k**2 - 2/5*k**3.
-2*k**2*(k + 1)/5
Solve 0*g**2 - 1/5*g**3 + 0*g + 0 = 0.
0
Let h be (-6)/15 - (-12)/5. Factor -9 + c**h + 9.
c**2
Let f(h) = -2*h**3 - 12*h**2 - 6*h + 20. Let s(m) = m - 1. Let k(z) = f(z) + 8*s(z). Factor k(u).
-2*(u - 1)*(u + 1)*(u + 6)
Suppose -11*k + 10*k + 6 = -g, 0 = -4*k - 2*g. Factor n**k + 1/2*n + 1/2*n**3 + 0.
n*(n + 1)**2/2
Let c(l) = l + 2. Let k be c(2). Let b(f) = -17*f**4 + f**3 - 3*f**2. Let n(y) = 9*y**4 - y**3 + 2*y**2. Let h(j) = k*b(j) + 7*n(j). Factor h(p).
-p**2*(p + 1)*(5*p - 2)
Let c = -87 + 89. Solve 2/3*j - 4/3 + 2/3*j**c = 0 for j.
-2, 1
Let -50/3*p**2 - 15*p - 5/3*p**3 + 0 = 0. Calculate p.
-9, -1, 0
Let y(a) = 59*a - 56. Let s be y(1). Solve 22/13*z + 4/13 + 14/13*z**s + 32/13*z**2 = 0 for z.
-1, -2/7
Let a be (-1)/(-2) + (-9)/(-6). Factor 0 + n**a + n**3 - 1 + 15*n - 16*n.
(n - 1)*(n + 1)**2
Suppose 2 = 5*r + 17. Let i(a) = -a**3 + 11*a**2 + 25*a + 13. Let l(v) = -v**3 + 5*v**2 + 13*v + 7. Let q(h) = r*i(h) + 5*l(h). Factor q(j).
-2*(j + 1)**2*(j + 2)
Let n(k) be the second derivative of -k**8/6720 + k**7/840 - k**6/360 + k**4/12 + 3*k. Let w(h) be the third derivative of n(h). Solve w(d) = 0.
0, 1, 2
Let s(z) be the third derivative of -z**8/840 + z**6/60 + z**5/30 - z**3/2 + 2*z**2. Let i(j) be the first derivative of s(j). Factor i(l).
-2*l*(l - 2)*(l + 1)**2
Suppose -2*o + 72 = 66. Find r such that 0 + 1/2*r**o - 1/2*r + 0*r**2 = 0.
-1, 0, 1
Find w such that 11/4*w**2 - 1/2*w + 0 - 19/4*w**3 - 3/4*w**5 + 13/4*w**4 = 0.
0, 1/3, 1, 2
Suppose 6*f**5 - 2*f**4 - 112/3*f + 8 - 106/3*f**3 + 182/3*f**2 = 0. What is f?
-3, 2/3, 1
Solve 0 + 1/4*v**3 - 1/4*v**2 - 1/2*v = 0 for v.
-1, 0, 2
Let w = -146 - -146. Determine l so that 0 - 1/3*l**2 + w*l = 0.
0
Let f(u) be the second derivative of u**6/120 + u**5/80 + 3*u. Let f(p) = 0. Calculate p.
-1, 0
Let v(h) be the third derivative of h**6/60 - h**4/12 + 8*h**2. Factor v(k).
2*k*(k - 1)*(k + 1)
Let w be -6*((-2)/3 - -2). Let v = w + 11. Let 1/4*r**4 - 1/4*r**v - 1/4*r**2 + 1/4*r + 0 = 0. What is r?
-1, 0, 1
Let o(f) be the third derivative of 0*f**4 + 5*f**2 + 0*f**5 + 0 + 0*f + 0*f**7 + 1/60*f**6 + 0*f**3 - 1/168*f**8. Find x such that o(x) = 0.
-1, 0, 1
Suppose 5 - 1 = 2*d. Let a(o) be the second derivative of o**d + 1/6*o**4 + 2*o - 2/3*o**3 + 0. Factor a(g).
2*(g - 1)**2
Suppose -1 - 27/2*f**2 - 29/2*f = 0. Calculate f.
-1, -2/27
Let m(r) be the second derivative of r**6/2700 + 2*r**5/225 + 4*r**4/45 - r**3/2 - 4*r. Let y(v) be the second derivative of m(v). Factor y(l).
2*(l + 4)**2/15
Suppose 5*w + 27 = 4*i, 2*w - 42 = i - 6*i. Let a = 13 - i. Find f such that -7*f + 6*f**3 + a*f - 3*f**5 + 3*f - 4*f**4 + 4*f**5 - 4*f**2 = 0.
0, 1
Let w = -107/4 - -27. Suppose 1/2*f**4 + 0 - 1/2*f**2 - w*f**5 + 1/4*f + 0*f**3 = 0. Calculate f.
-1, 0, 1
Determine g, given that 4*g + 0*g + 3*g**3 - 7*g - 6 - 6*g = 0.
-1, 2
Let w = 463/3 + -151. Factor -4/3 - 2*x**2 + w*x.
-2*(x - 1)*(3*x - 2)/3
Suppose 5*m = 2*j, -3*m = m + 2*j - 18. Factor 4*r + 5*r**4 + m*r + 3*r**3 - 