, 0, 2/5
Let p(g) be the third derivative of 0*g**3 + 4/51*g**4 + 0*g - 4*g**2 + 0 + 1/1020*g**6 - 4/255*g**5. Determine q so that p(q) = 0.
0, 4
Let k(h) be the first derivative of 0*h**2 - 2 + 0*h**3 - 1/9*h**4 + h + 1/30*h**5. Let x(r) be the first derivative of k(r). Factor x(a).
2*a**2*(a - 2)/3
Let s(b) be the first derivative of b**6/7 - 2*b**5/35 - 5*b**4/14 + 2*b**3/21 + 2*b**2/7 - 17. Solve s(m) = 0.
-1, -2/3, 0, 1
Factor 0 - 3/2*n**3 + 1/2*n**4 + n + 1/2*n**5 - 1/2*n**2.
n*(n - 1)**2*(n + 1)*(n + 2)/2
Factor -3*d**4 + 2 - 10*d**2 + 15*d**4 - 7*d**4 + 3.
5*(d - 1)**2*(d + 1)**2
Let y be ((-15)/40)/(81/(-12)). Let i(w) be the second derivative of 0*w**2 + 1/45*w**6 + 0*w**5 - y*w**4 + 3*w + 1/18*w**3 + 0 - 1/126*w**7. Factor i(h).
-h*(h - 1)**3*(h + 1)/3
Let a(q) = -5. Let f(u) = u - 16. Let z(n) = -15*a(n) + 5*f(n). Let s be z(2). Suppose 0*y - 1/2*y**3 + 0 - y**4 + 0*y**2 - 1/2*y**s = 0. What is y?
-1, 0
Let h(a) be the first derivative of a**5/70 + a**4/14 + a**3/7 + a**2/7 - 5*a - 6. Let p(x) be the first derivative of h(x). Factor p(s).
2*(s + 1)**3/7
Find q such that 8/9*q**5 + 14/9*q**4 + 0 + 0*q**2 - 4/9*q**3 + 0*q = 0.
-2, 0, 1/4
Let a(u) be the first derivative of -2*u**5/5 + 2*u**3/3 + 1. Factor a(v).
-2*v**2*(v - 1)*(v + 1)
Let a(v) = -15*v**4 - 207*v**3 - 417*v**2 - 225*v. Let u(r) = -r**4 - 13*r**3 - 26*r**2 - 14*r. Let i(z) = 2*a(z) - 33*u(z). Find t, given that i(t) = 0.
-2, -1, 0
Let h(j) be the second derivative of -j**6/180 - j**5/60 + 5*j**4/72 + j**3/6 + 25*j. Solve h(y) = 0.
-3, -1, 0, 2
Factor 2/11*w**2 + 24/11*w + 72/11.
2*(w + 6)**2/11
Let w(u) be the third derivative of u**6/540 - u**5/90 + 4*u**3/3 - 8*u**2. Let s(t) be the first derivative of w(t). Determine a so that s(a) = 0.
0, 2
Let q = -11/2 + 6. Let a(r) be the first derivative of 1/3*r**6 - 4/5*r**5 + q*r**4 + 0*r**3 + 0*r**2 - 2 + 0*r. Find h such that a(h) = 0.
0, 1
Let b = 6 + 3. Let u(p) = -p**3 + 10*p**2 - 10*p + 12. Let a be u(b). Factor -a*i - 4*i**3 - 6*i**4 + 7*i**3 + 3*i**2 + 3*i**4.
-3*i*(i - 1)**2*(i + 1)
Let m = 46 + -46. Factor m + 1/6*n**2 - 1/3*n**3 + 0*n + 1/6*n**4.
n**2*(n - 1)**2/6
Let t(f) = -20*f + 2. Let r be t(0). Factor 1/2*g + 1/2*g**r + 0 - 1/2*g**4 - 1/2*g**3.
-g*(g - 1)*(g + 1)**2/2
Let w(x) be the second derivative of -x**5/50 + x**3/15 - 6*x. Factor w(z).
-2*z*(z - 1)*(z + 1)/5
Let z(d) be the third derivative of -d**10/113400 + d**9/60480 + d**8/60480 + d**5/15 - 3*d**2. Let h(f) be the third derivative of z(f). Factor h(w).
-w**2*(w - 1)*(4*w + 1)/3
Suppose -3*k - 15 = -5*a, a + 23 = 4*a + k. Suppose 4 = 5*j - a. Factor 2*f**5 + 2*f**4 + 0*f**3 + 2*f**3 + j*f**4.
2*f**3*(f + 1)**2
Let k(f) be the second derivative of f**5/150 - f**4/90 - 2*f**3/45 - 34*f. Find z, given that k(z) = 0.
-1, 0, 2
Let l = 1/9 + 13/45. Let f(c) be the first derivative of -2/5*c - l*c**3 + 3/5*c**2 - 2 + 1/10*c**4. Factor f(k).
2*(k - 1)**3/5
Let p be 2/4*26/16380. Let c(f) be the third derivative of 0*f**4 - 1/2016*f**8 + 0 + 0*f + 0*f**3 + 1/720*f**6 + p*f**7 + f**2 - 1/360*f**5. Factor c(q).
-q**2*(q - 1)**2*(q + 1)/6
Solve -1 - 7/4*i**2 + 4*i = 0 for i.
2/7, 2
Let m(s) be the first derivative of 5*s**6/24 - 2*s**5/5 - s**4/4 + 5*s**3/6 - s**2/8 - s/2 + 3. Find j, given that m(j) = 0.
-1, -2/5, 1
Factor 5/4*x**3 + 20*x - 10*x**2 + 0.
5*x*(x - 4)**2/4
Suppose -2*x + 8 = 0, -15 = -2*z - 2*x - 1. Let -2*y**4 - 2*y**3 - z*y**2 + 0*y**2 + 3*y**2 = 0. What is y?
-1, 0
Let q be ((-10)/(-4))/((-5)/(-12)). Suppose -q*h = -4*h. Suppose 4/13*j**2 + 0*j + h + 6/13*j**3 - 6/13*j**5 - 4/13*j**4 = 0. What is j?
-1, -2/3, 0, 1
Let v = 11/2 + -131/24. Let o(l) be the third derivative of -1/20*l**6 + 0*l**4 + 0 - 2*l**2 - 1/15*l**5 - v*l**8 + 4/35*l**7 + 0*l**3 + 0*l. Factor o(s).
-2*s**2*(s - 1)**2*(7*s + 2)
Let y(h) = -4*h - 34. Let n be y(-9). Let w(s) be the third derivative of -1/210*s**5 + 2*s**n + 0*s + 1/420*s**6 + 0*s**3 + 0*s**4 + 0. Factor w(x).
2*x**2*(x - 1)/7
Let m(x) = 40*x**5 - 105*x**4 + 105*x**2 - 15*x + 25. Let o(n) = -5*n**5 + 13*n**4 - 13*n**2 + 2*n - 3. Let g(c) = 3*m(c) + 25*o(c). Let g(z) = 0. What is z?
-1, 0, 1
Suppose 3*u = 3 + 3. Let z be (2/6)/(11/66). Let -10*r**3 + 2*r**4 - z + 0*r + r**4 + u*r + 6*r**2 + r**4 = 0. Calculate r.
-1/2, 1
Let g(c) be the third derivative of 25*c**8/112 + 2*c**7/7 - 9*c**6/10 - 13*c**5/10 + 11*c**4/8 + 3*c**3 + 12*c**2. What is a in g(a) = 0?
-1, -2/5, 3/5, 1
Let o(q) be the second derivative of 8/27*q**3 - 1/30*q**5 + 0 + 4/9*q**2 + 1/54*q**4 - 2*q. Solve o(z) = 0 for z.
-1, -2/3, 2
Let g(c) = -c + 18. Let v be g(14). Let p(k) be the second derivative of k + 0*k**v + 0 - 1/6*k**3 + 1/20*k**5 + 0*k**2. Factor p(o).
o*(o - 1)*(o + 1)
Let b(s) be the first derivative of -s**4/4 + s**3/3 + s**2/2 - s + 5. Determine o, given that b(o) = 0.
-1, 1
Let t(c) be the second derivative of -289*c**4/42 + 68*c**3/21 - 4*c**2/7 + 3*c. Determine s so that t(s) = 0.
2/17
Factor 122*x**2 - 16*x**4 - 4*x**5 + 34*x**3 + 6*x**2 + 14*x**3 - 402*x + 146*x.
-4*x*(x - 2)**2*(x + 4)**2
Let z(u) be the second derivative of -u**7/3780 + u**6/540 - u**4/27 - u**3 - 8*u. Let g(q) be the second derivative of z(q). Solve g(j) = 0.
-1, 2
Let v(c) be the first derivative of c**3 - 8. Factor v(p).
3*p**2
Let b be (-2 - -2)/(3 + -1). Find f, given that -f**3 - 2*f**3 + b*f**3 = 0.
0
Let w(p) be the third derivative of p**9/241920 + p**8/80640 + p**5/15 - 4*p**2. Let y(f) be the third derivative of w(f). Factor y(s).
s**2*(s + 1)/4
Let l = -3 - -3. Let d be (-4)/(-2) - (l + -1). Suppose 0 + 0*r - 2/5*r**d + 2/5*r**2 = 0. Calculate r.
0, 1
Let v be 2/(-2) + 4 + -1. Let o be v/(-10) + 213/15. Solve -3*k**2 + 24*k + 0 - o - 13 - 6*k = 0 for k.
3
Let z be (3 - (1 + -4)) + -4. Suppose 23*u**3 - 17*u - 7*u**3 + 25*u - 36*u**z = 0. What is u?
0, 1/4, 2
Let z(r) = r**2 + 3*r - 1. Let k be z(-4). Factor -4*d**k + 0*d + 5*d**3 + 0*d.
d**3
Let p = 7 + 5. Let r be 4/p - (-10)/6. Suppose -10/7*m**r + 0 + 2/7*m - 2*m**4 + 4/7*m**5 + 18/7*m**3 = 0. What is m?
0, 1/2, 1
Let -6*p**2 - 9*p**2 - 8*p**4 + 12 + 11*p**4 = 0. Calculate p.
-2, -1, 1, 2
Let j(m) be the second derivative of m**7/420 - m**6/90 + m**5/60 + 2*m**3/3 + 5*m. Let t(q) be the second derivative of j(q). Let t(f) = 0. Calculate f.
0, 1
Let o(c) be the first derivative of -1/2*c**4 + 16/5*c - 4/5*c**3 - 5 - 2/25*c**5 + 4/5*c**2. Find k, given that o(k) = 0.
-2, 1
Factor -5*h**3 - 107*h + 135 + 22*h**2 + 23*h**2 - 28*h.
-5*(h - 3)**3
Solve 8*p**2 - 3*p**2 + 2 + 4*p - 3*p**2 = 0.
-1
Let y(s) = 2*s - 5. Let q = 2 + 2. Let z be y(q). Factor 0*k**2 - 3*k - 3*k**4 + 2*k**2 - k**5 + 2*k**5 + 1 + 2*k**z.
(k - 1)**4*(k + 1)
Let w(n) = n**2 + 8*n + 15. Let c be w(-6). Factor 2/5 + 7/5*x - 13/5*x**2 - 18/5*x**c.
-(x + 1)*(2*x - 1)*(9*x + 2)/5
Let d = -2 + 2. Let a = 4 + d. Factor 1 + 3*f**3 - 5*f**a + 8*f**2 - 1 - 4*f**4 - 4*f.
-f*(f + 1)*(3*f - 2)**2
Let o(z) be the first derivative of -z**4/4 - z**3/3 + z**2/2 + z + 4. Suppose o(s) = 0. What is s?
-1, 1
Let l(c) = -c**2 - 8*c + 3. Let j be l(-9). Let f(i) = -i - 4. Let b be f(j). What is o in -2/5*o + 4/5*o**3 + 4/5*o**b - 2/5*o**4 - 2/5*o**5 - 2/5 = 0?
-1, 1
Let i(x) = -51*x**3 + 2*x**2 + 8*x + 8. Let v(s) = 34*s**3 - s**2 - 5*s - 5. Let c(d) = 5*i(d) + 8*v(d). Determine j so that c(j) = 0.
-2/17, 0
Let 3*b**3 - 15*b**2 + 50*b - 1 + 1 - 38*b = 0. Calculate b.
0, 1, 4
Let b be 20*15/80*(-2)/(-5). Find p such that -3/2*p**5 - b*p + 0*p**2 + 0 + 0*p**4 + 3*p**3 = 0.
-1, 0, 1
Suppose 12*w**2 - 2*w**2 - 6*w**2 - 3*w**2 - 3*w = 0. What is w?
0, 3
Let d(m) be the first derivative of 5*m**4/12 - 7*m**3/9 - 4*m**2/3 + 4*m/3 - 15. Suppose d(n) = 0. Calculate n.
-1, 2/5, 2
Let t be 72/99 - (-1 + 1). Let 2/11*u**2 - t*u + 6/11 = 0. What is u?
1, 3
Factor 0 + 2/17*q**3 + 2/17*q - 4/17*q**2.
2*q*(q - 1)**2/17
Let a(l) = -2*l**2 + 43*l - 19. Let i be a(21). Factor 0 + 1/4*v**i - 1/2*v.
v*(v - 2)/4
Suppose 5*u - 2*h = 15, 12 = 4*u - 0*u - 2*h. Solve -1 - 2*o**u + 2*o + 0*o**4 + 0*o**3 + o**4 + 0*o**4 = 0 for o.
-1, 1
Let x(c) = 3*c**2 - 15*c - 32. Let j(g) = 4*g**2 - 23*g - 48. Let i(t) = 5*j(t) - 7*x(t). Let k be i(-8). Let -3/4*r**2 + k + 3/4*r = 0. What is r?
0, 1
Let q(a) be the second derivative of -a**7/189 + a**6/27 - a**5/9 + 5*a**4/27 - 5*a**3/