 = 0.
-2/5, 1
Let c(u) be the second derivative of -u**6/60 + u**5/12 - u**4/6 - u**3/3 + 3*u. Let l(m) be the second derivative of c(m). Factor l(h).
-2*(h - 1)*(3*h - 2)
Determine r, given that 2/3*r**2 + 2*r - 8/3 = 0.
-4, 1
Let r(w) be the first derivative of -w**6/420 - w**5/210 + w**2 - 3. Let t(k) be the second derivative of r(k). Determine b, given that t(b) = 0.
-1, 0
Let p(u) = u - 8. Let y be p(10). Suppose j + f = y, -2*f - 3*f = -5*j + 30. Let 0*r**3 - 2*r**5 + 3*r**3 + 3*r**j - r**5 + r**2 + 4*r**5 = 0. What is r?
-1, 0
Let f(t) be the third derivative of t**6/2340 + t**5/195 + t**4/39 + t**3/3 - 5*t**2. Let l(s) be the first derivative of f(s). Let l(g) = 0. What is g?
-2
Let r(m) be the first derivative of m**6/4 + 12*m**5/5 + 33*m**4/4 + 12*m**3 + 27*m**2/4 + 22. Factor r(t).
3*t*(t + 1)**2*(t + 3)**2/2
Let u(v) be the first derivative of -v**4/4 - 2*v**3/3 - v**2/2 + 2. What is c in u(c) = 0?
-1, 0
Let y(j) be the third derivative of -5*j**8/1344 + 17*j**7/840 - j**6/30 + j**5/60 + j**2 - 2. Determine h, given that y(h) = 0.
0, 2/5, 1, 2
Solve 0*n**2 - 2/7*n**3 + 0*n + 2/7*n**4 + 0 = 0.
0, 1
Let k(w) = 2 - 2 - w - 1. Let z(h) = -2*h**3 - 2*h**2 + 10*h + 10. Let b be (-1 + 1)/1 + -8. Let v(l) = b*k(l) - z(l). Factor v(x).
2*(x - 1)*(x + 1)**2
Let y = -30 - -224. Factor 3*r**2 + y - 194.
3*r**2
Let x(s) be the third derivative of -s**7/210 + s**6/120 + s**5/20 - s**4/24 - s**3/3 - 3*s**2 + 18. What is i in x(i) = 0?
-1, 1, 2
Determine d, given that -1/4*d**5 + 0 - 1/2*d - 9/4*d**3 + 5/4*d**4 + 7/4*d**2 = 0.
0, 1, 2
Factor 0 - 1/4*z**2 + 0*z - 1/4*z**3.
-z**2*(z + 1)/4
Let g(v) be the second derivative of -v**6/10 - 21*v**5/20 - 15*v**4/4 - 13*v**3/2 - 6*v**2 + 26*v. Solve g(z) = 0.
-4, -1
Let y(b) be the third derivative of 0*b + 0 - b**3 - b**2 - 1/90*b**5 - 1/6*b**4. Suppose y(w) = 0. Calculate w.
-3
Let z(u) be the second derivative of 1/20*u**5 + 4/3*u**3 - u - 5/12*u**4 + 0 - 2*u**2. Factor z(q).
(q - 2)**2*(q - 1)
Let x(l) be the second derivative of -4*l**2 - 1/3*l**4 - 8*l + 0 + 2*l**3. What is m in x(m) = 0?
1, 2
Let g be ((-105)/63)/(10/(-8)). Find z, given that -8/3*z - 4/3*z**2 - g = 0.
-1
Let b(k) = 2*k. Let l be b(4). Suppose 0*a - l = -2*a. Factor m**2 + a*m + 0*m**2 + 0*m + 4.
(m + 2)**2
Let p(d) be the first derivative of d**4/24 + d**3/12 + 5*d + 6. Let u(m) be the first derivative of p(m). Factor u(x).
x*(x + 1)/2
Factor 0 + 2/5*b - 1/5*b**2.
-b*(b - 2)/5
Let z(s) be the second derivative of 0 - 1/6*s**3 + 9*s + 1/6*s**4 + 0*s**2 - 1/20*s**5. Factor z(y).
-y*(y - 1)**2
Suppose -4*b = -b - 6. Let y(i) be the first derivative of 0*i**b + 0*i + 0*i**4 + 2 - 1/2*i**3 + 3/10*i**5. Solve y(c) = 0.
-1, 0, 1
Let i be (-2)/(-8) + 9/108. Factor 1/3*r + i*r**2 + 0.
r*(r + 1)/3
Let q(g) = -3*g - 7. Let u be q(-3). Factor r**3 + r**4 - u*r**4 + 2*r**3 - 2*r**4.
-3*r**3*(r - 1)
Let s(g) = -g**2 - 7*g - 7. Let f be s(-5). Factor -5/3*h**2 + 1/3*h**f - 4/3 + 8/3*h.
(h - 2)**2*(h - 1)/3
Let o(l) be the third derivative of 0*l**3 + 1/300*l**6 + 0 + 4*l**2 + 0*l**5 + 0*l - 1/60*l**4. Factor o(c).
2*c*(c - 1)*(c + 1)/5
Suppose 2234 = 6*d - 928. Let p = d - 3677/7. Factor -8/7*v**4 - 2/7*v**5 - 8/7*v**2 - p*v**3 - 2/7*v + 0.
-2*v*(v + 1)**4/7
Let g(i) be the second derivative of i**6/45 + i**5/15 - i**4/6 + 12*i. Determine n so that g(n) = 0.
-3, 0, 1
Let v be (-216)/35 + (-2)/(-1). Let z = 32/7 + v. Let z*q**3 - 2/5*q**2 - 2/5*q + 2/5 = 0. Calculate q.
-1, 1
Let b = 14 + -12. Let c be ((-27)/(-21) - 1)*1. Let -c*k + 2/7*k**b + 0 = 0. What is k?
0, 1
Let c(p) = -2*p. Suppose 3*z + n + 7 = -0*z, 0 = -5*z + 5*n - 5. Let h be c(z). Let 2/3*w**3 - 1/3*w**h + 0 - 1/3*w**2 + 0*w = 0. Calculate w.
0, 1
Suppose -3*i + 2 = -7. Let x(h) be the second derivative of -2*h + 1/63*h**7 + 0*h**4 + 0*h**2 + 0*h**6 - 1/30*h**5 + 0*h**i + 0. Factor x(q).
2*q**3*(q - 1)*(q + 1)/3
Let b(a) be the third derivative of -a**6/360 + a**5/60 - 2*a**3/9 - 47*a**2. Determine i so that b(i) = 0.
-1, 2
Let g(h) be the third derivative of 5*h**5/12 - 35*h**4/24 - 5*h**3 + 33*h**2. Factor g(n).
5*(n - 2)*(5*n + 3)
Let b = 2 + 1. Factor -w**3 + 3*w**3 + 0*w**b - 4*w**2.
2*w**2*(w - 2)
Let -2*c - 8*c**2 - 3*c**2 + 4 + 9*c**2 = 0. What is c?
-2, 1
Let m = 66341/5 + -13378. Let i = -109 - m. Factor -2/5 - i*a**2 - a - 1/5*a**3.
-(a + 1)**2*(a + 2)/5
Factor -4/3 + 14/3*d + 8*d**2 - 30*d**3.
-2*(3*d - 1)**2*(5*d + 2)/3
Let c(o) = o**2 + 2 + 3*o + 0 + o. Let v be c(-4). Find i such that -4*i**5 + i**3 + 0*i**3 + 4*i**v + i + 2*i**3 - 4*i**4 = 0.
-1, -1/2, 0, 1
Let q(b) be the second derivative of 4*b**6/15 - 3*b**5/5 + 2*b**3/3 + 16*b + 1. Factor q(i).
4*i*(i - 1)**2*(2*i + 1)
Suppose j**2 + 4*j - 3*j**2 - 4*j + 2*j**4 = 0. What is j?
-1, 0, 1
Let w(y) be the first derivative of 1/6*y**3 + 1 - 1/4*y**2 + 0*y. Factor w(g).
g*(g - 1)/2
Let d(v) be the second derivative of -v**10/50400 + v**9/18900 + v**8/33600 - v**7/6300 + v**4/12 + 4*v. Let j(w) be the third derivative of d(w). Factor j(p).
-p**2*(p - 1)**2*(3*p + 2)/5
Let a = 78 + -388/5. Suppose -10 = k - 6*k. Factor -a*t**k - 2/5*t + 0.
-2*t*(t + 1)/5
Let a(q) be the second derivative of -q**6/1800 + q**5/600 + q**3/6 + 7*q. Let u(n) be the second derivative of a(n). Suppose u(c) = 0. Calculate c.
0, 1
Suppose 23*s - 7*s = 32. Let 8/9 - 2/9*b**3 + 10/9*b**s - 16/9*b = 0. What is b?
1, 2
Let k(j) be the second derivative of 3*j - 1/50*j**5 + 2/75*j**6 + 0*j**2 + 0*j**4 - 1/105*j**7 + 0*j**3 + 0. Factor k(f).
-2*f**3*(f - 1)**2/5
Solve 109 - 4*v**2 + 16*v + 6*v**2 - 11 + 12*v = 0 for v.
-7
Suppose 0*t**2 - 18*t**3 + 48*t**4 - 32*t**5 + t**2 + t**2 = 0. Calculate t.
0, 1/4, 1
Factor 10/3 - 5/3*v - 5/3*v**2.
-5*(v - 1)*(v + 2)/3
Let z(y) be the third derivative of 0 + 0*y**3 + 2/35*y**7 - 7/40*y**6 + 0*y + 1/8*y**4 - 4*y**2 + 1/10*y**5. Determine g so that z(g) = 0.
-1/4, 0, 1
Let n(p) be the second derivative of -1/80*p**5 + 6*p - 1/12*p**3 + 0*p**2 + 0 + 1/16*p**4. Factor n(g).
-g*(g - 2)*(g - 1)/4
Let j be 7/(-12)*(-16)/6. Let r = j - 19/18. Factor -r - 2*q - q**3 - 5/2*q**2.
-(q + 1)**2*(2*q + 1)/2
Let u be (-32)/(-36)*(-12)/(-16). Let t(y) be the second derivative of 2/3*y**4 - y + 0 + u*y**2 + 1/6*y**5 + y**3. Find n such that t(n) = 0.
-1, -2/5
Let -4*i**5 + 2*i**3 - 4*i**3 - 6*i**3 + 4*i**3 - 8*i**4 = 0. What is i?
-1, 0
Solve -a**3 - 4*a + 10*a**2 - 3*a**3 - 2*a**3 - 2*a**3 + 2*a**4 = 0.
0, 1, 2
Let c(b) be the third derivative of -1/6*b**3 + 0*b - b**2 + 0 - 1/720*b**6 - 1/12*b**4 + 1/60*b**5. Let x(q) be the first derivative of c(q). Factor x(w).
-(w - 2)**2/2
Let v(x) = -3*x**4 - 4*x + 3. Let z(c) = -16*c**4 - c**3 - 21*c + 16. Let b(q) = -33*v(q) + 6*z(q). Suppose b(n) = 0. Calculate n.
-1, 1
Let j(v) = v**3 - 3*v + 1. Let m be j(2). Let f(c) be the second derivative of 1/5*c**2 + 1/30*c**4 + 0 + 2/15*c**m + c. Solve f(r) = 0.
-1
Factor -16 - 35*q - 28*q**2 - 16*q + 4 + 11*q.
-4*(q + 1)*(7*q + 3)
Factor -1/4*k**2 + 4*k**5 - 6*k**4 + 0*k + 0 + 9/4*k**3.
k**2*(k - 1)*(4*k - 1)**2/4
Let g(d) = 6*d**4 + 2*d**3 - 4*d + 4. Let y be -3 + 1 - (-14 - -3). Let w(o) = 13*o**4 + 5*o**3 - 9*o + 9. Let n(b) = y*g(b) - 4*w(b). Factor n(l).
2*l**3*(l - 1)
Let l(r) be the second derivative of 0*r**3 + 1/6*r**4 - 2*r + 0*r**2 + 0. Factor l(n).
2*n**2
Let z(j) be the first derivative of -j**6/2340 - j**5/195 - j**4/39 + 2*j**3/3 + 2. Let p(w) be the third derivative of z(w). Determine i, given that p(i) = 0.
-2
Let g(y) be the third derivative of 0*y - 1/240*y**5 - y**2 + 0 - 1/24*y**3 - 1/48*y**4. Determine t so that g(t) = 0.
-1
Factor 5*s**2 - 4*s**2 - 3*s**3 + 5*s**3 - 3*s**3.
-s**2*(s - 1)
Let p(g) = g**3 + 4*g**2. Let b be p(-4). Let x be (b + 3)/(1 - 0). Find q such that q + 1/4*q**4 + 3/2*q**2 + 1/4 + q**x = 0.
-1
Let 49/6*c**4 - 2/3 - 14/3*c**3 - 15/2*c**2 + 14/3*c = 0. What is c?
-1, 2/7, 1
Solve -8*x**2 + 7*x**2 + 5*x**3 + 5*x**4 + 15*x - 13*x**2 - 11*x**2 = 0.
-3, 0, 1
Suppose 4*s = 5*j + 6 + 19, -3*j + 2 = s. Suppose -a - 1 = -5, 3*k - s*a = -20. Factor k + 1/2*l - 1/2*l**2.
-l*(l - 1)/2
Suppose 1 = a - 2. Suppose 4 = -2*d + 10. Suppose 2*p**3 + p**a - p**2 - 2*p**d = 0. What is p?
0, 1
Let a be (-2)/(2*(-2)/8). Suppose 0 = -3*p + 8 + 1. Factor -2*d**4 + 2*d**p + 2*d + 6*d**2 - a*d - 3 - 1.
-2*(d - 2)*(d - 1