/3
Let b(w) be the third derivative of 0 + 0*w**3 + 1/30*w**6 + 0*w - 5*w**2 + 1/15*w**5 + 0*w**4. Factor b(n).
4*n**2*(n + 1)
Let n(x) = -5*x**2 - 20*x + 19. Let p(z) = -11*z**2 - 41*z + 37. Let s(w) = 5*n(w) - 2*p(w). Find m, given that s(m) = 0.
-7, 1
What is z in 1 + 1/2*z**2 + 3/2*z = 0?
-2, -1
Factor 1/3*z**3 + 2*z**2 + 8/3 + 4*z.
(z + 2)**3/3
Let r = -8 - -13. Factor r - v**3 - 2*v**3 + 3*v - 5.
-3*v*(v - 1)*(v + 1)
Let s be 2 + (58/3)/(-2). Let n = s + 167/21. Suppose n*d**2 + 2/7 - 4/7*d = 0. Calculate d.
1
Let l(b) = -3*b**2 + 38*b - 52. Let a be l(11). Suppose 3*h**2 - 3/2*h - 3/2*h**a + 0 = 0. What is h?
0, 1
Let s(j) be the first derivative of -j**4/14 + 4*j**3/21 - j**2/7 - 8. Factor s(n).
-2*n*(n - 1)**2/7
Let j(x) be the second derivative of x**10/30240 - x**9/15120 - x**8/6720 + x**7/2520 + x**4/6 + x. Let z(h) be the third derivative of j(h). Factor z(d).
d**2*(d - 1)**2*(d + 1)
Let o be (-15)/(-20)*4 - (2 + -2). Find t such that 0 - 2/3*t**4 - 2/3*t**2 - 4/3*t**o + 0*t = 0.
-1, 0
Solve -38*k**3 + 14*k**4 + 117*k**2 - 2*k**5 + 3 + 5 - 32*k - 50*k**2 - 17*k**2 = 0.
1, 2
Suppose 197 = 3*o + 191. Factor 0*p**o + 0*p + 0 - 2/7*p**3.
-2*p**3/7
Let p(m) be the third derivative of -m**6/40 + 3*m**5/20 - 3*m**4/8 + m**3/2 + m**2. Suppose p(a) = 0. Calculate a.
1
Factor 2*s**3 + 8*s**3 - 5*s**2 - 5*s + 10*s**2 + 0*s**3.
5*s*(s + 1)*(2*s - 1)
Let l = -15 - -15. Suppose -8/7*q**3 - 2/7*q**4 - 4/7*q - 10/7*q**2 + l = 0. Calculate q.
-2, -1, 0
Suppose -28 - 192 = 5*r. Let x be r/(-15) - (-4)/10. Factor 20/3*u**3 + 20/3*u**2 + 2/3 + 10/3*u**4 + x*u + 2/3*u**5.
2*(u + 1)**5/3
Let n(d) be the first derivative of -d**6 + 27*d**5/5 - 12*d**4 + 14*d**3 - 9*d**2 + 3*d - 3. Factor n(u).
-3*(u - 1)**4*(2*u - 1)
Solve 2/13*d**4 + 0*d + 2/13 + 0*d**3 - 4/13*d**2 = 0 for d.
-1, 1
Suppose -3*s = s - 8. Let d = 0 + s. Find k such that -6*k**d - k**3 - 4*k**4 + 2*k + 0*k**3 - 9*k**3 + 2 = 0.
-1, 1/2
Let n(f) be the third derivative of -f**5/20 - f**4/2 - 2*f**3 - 16*f**2. Factor n(t).
-3*(t + 2)**2
Suppose -5*k - 6 - 3 = 3*c, -15 = -2*k + 5*c. Find q, given that -4/9*q**4 + 4/9*q**2 + 2/9*q + k*q**3 - 2/9*q**5 + 0 = 0.
-1, 0, 1
Factor 0*w**4 + 2/11*w**5 + 0 + 0*w**2 + 0*w - 2/11*w**3.
2*w**3*(w - 1)*(w + 1)/11
Let x(m) be the second derivative of 1/48*m**4 + 0*m**2 - 1/24*m**3 - 3*m + 0. Factor x(f).
f*(f - 1)/4
Let j(z) = 4*z**3 - 10*z**2 - 20*z - 10. Let v(h) = 21*h**3 - 51*h**2 - 99*h - 49. Let p(b) = -22*j(b) + 4*v(b). Factor p(f).
-4*(f - 6)*(f + 1)**2
Suppose 2*r = -5*r. Let t(l) be the second derivative of -2/15*l**3 + 3*l + 0 - 1/75*l**6 + 1/10*l**4 + 0*l**2 + r*l**5. Factor t(j).
-2*j*(j - 1)**2*(j + 2)/5
Let r(t) = 21*t**3 - 9*t**2 + 27*t + 3. Let f(d) = d**3 - d**2 + d. Suppose -5*h + 3*v - 75 = 0, 0*v + 74 = -3*h - 4*v. Let q(z) = h*f(z) + r(z). Factor q(a).
3*(a + 1)**3
Suppose -5*j - 3*f + 8*f = 20, 0 = -2*f + 10. Let g = 4 - j. Factor -4/5 - 2*s - 8/5*s**2 - 2/5*s**g.
-2*(s + 1)**2*(s + 2)/5
Let f(l) be the second derivative of -l**5/18 - 7*l**4/36 - 2*l**3/9 - 3*l**2/2 + l. Let z(r) be the first derivative of f(r). Factor z(h).
-2*(h + 1)*(5*h + 2)/3
Let n(p) be the first derivative of -4*p**7/63 + p**6/27 + p**5/15 + p**4/54 - p + 5. Let s(f) be the first derivative of n(f). Suppose s(v) = 0. What is v?
-1/3, -1/4, 0, 1
Factor 6*z + z - 2*z**3 - 3*z - 2*z.
-2*z*(z - 1)*(z + 1)
Let w(h) = -16*h**3 + 199*h**2 - 2951*h + 13709. Let g(p) = 3*p**3 - 40*p**2 + 590*p - 2742. Let i(x) = 11*g(x) + 2*w(x). Find q, given that i(q) = 0.
14
Suppose -7*k + 12*k = 20. Let p(w) be the second derivative of 0 - 1/48*w**k + 0*w**3 + 0*w**2 - 2*w. Factor p(x).
-x**2/4
Let s(g) = g**2 + 6*g + 2. Let m be s(-5). Let v = m - -5. Factor -6*p - 2 - 6*p**2 + 0*p**v - 2*p**3 + 0*p.
-2*(p + 1)**3
Let g(x) be the third derivative of -3*x**2 + 0*x**4 - 1/150*x**5 - 1/840*x**8 + 1/300*x**6 + 0*x + 0*x**3 + 0 + 1/525*x**7. Factor g(n).
-2*n**2*(n - 1)**2*(n + 1)/5
Let p be -2 - (-5)/(10/16). Let d be p/(-27) + 4/18. Factor 0*z + 0*z**2 + 0 + 4/3*z**4 + 10/3*z**5 + d*z**3.
2*z**4*(5*z + 2)/3
Let r be 7/(693/282)*-3. Let o = r + 746/77. Factor 8/7*f**2 + 2/7 + o*f.
2*(2*f + 1)**2/7
Suppose 0 = -6*h - 111 - 153. Let u be (-33)/h*(-16)/(-66). Suppose -4/11*x + 6/11*x**2 + 8/11*x**3 - 8/11*x**4 - u = 0. What is x?
-1/2, 1
Let -5*j**2 - 6 + 9*j**2 + 2*j**2 - 16*j = 0. What is j?
-1/3, 3
Let w be (-12)/(-10)*(-10)/(-4). Let g(f) be the first derivative of -1 + 0*f**2 - 1/2*f + 1/6*f**w. Suppose g(r) = 0. Calculate r.
-1, 1
Let z(o) = 15*o**5 + 15*o**4 + 5*o**3 - 5*o**2 + 5. Let n(y) = -16*y**5 - 15*y**4 - 5*y**3 + 6*y**2 - 6. Let q(r) = -5*n(r) - 6*z(r). Factor q(b).
-5*b**3*(b + 1)*(2*b + 1)
Let n(m) be the second derivative of m**4/42 - m**3/21 - 13*m. What is q in n(q) = 0?
0, 1
Let 0 - 26/5*v**2 + 8/5*v**3 + 6/5*v = 0. What is v?
0, 1/4, 3
Solve 4*h**2 + 6*h - h**3 - 22*h - 16 + 5*h**3 = 0 for h.
-2, -1, 2
Suppose -4*y + 11 = -17. Let p**2 - y*p**3 + 2*p**3 - 3*p**2 + 3*p**3 = 0. Calculate p.
-1, 0
Solve 2/5 + 4/5*p + 2/5*p**2 = 0.
-1
Suppose 1 = b - 2. Let u(r) be the second derivative of 0 - 1/15*r**4 + 0*r**b + 0*r**5 + r + 1/75*r**6 + 1/5*r**2. Factor u(t).
2*(t - 1)**2*(t + 1)**2/5
Suppose -5*k - 8 = -23. Suppose 0 = -5*z + f - 5, 0*z + k*z - 5*f = -25. Find u, given that -2/3*u**2 + 0*u**3 + 2/3*u**4 + z - 1/3*u + 1/3*u**5 = 0.
-1, 0, 1
Let 0 - 4*o**2 - 2*o - 3/2*o**3 = 0. What is o?
-2, -2/3, 0
Let l be ((-3)/(-2))/(-3)*-2*2. Find g, given that 2/3*g**5 + 2/3*g**3 - 4/3*g - 2*g**2 + 0 + l*g**4 = 0.
-2, -1, 0, 1
Let o(a) = -2*a**2 - 6*a + 6. Let i(q) = 3*q**2 + 6*q - 5. Let h(j) = 3*i(j) + 4*o(j). What is k in h(k) = 0?
3
Let d(i) be the first derivative of 3*i**7/14 + 4*i**6/5 + 9*i**5/10 - i**3/2 - i + 5. Let z(b) be the first derivative of d(b). Factor z(v).
3*v*(v + 1)**3*(3*v - 1)
Let c = -10 + 10. Let t(s) be the third derivative of 0*s + 1/210*s**5 - 1/1176*s**8 - 1/735*s**7 + c - 2*s**2 + 1/420*s**6 + 0*s**3 + 0*s**4. Solve t(y) = 0.
-1, 0, 1
Suppose 20*q = 23*q. Let m(g) be the third derivative of -1/10*g**5 - 2*g**2 + 0*g - 4/3*g**3 + q + 2/3*g**4. Solve m(n) = 0 for n.
2/3, 2
Let u(g) be the third derivative of -g**8/10080 - g**7/1260 - g**6/540 + g**4/12 - 2*g**2. Let j(w) be the second derivative of u(w). Find i such that j(i) = 0.
-2, -1, 0
Let x(f) be the first derivative of 98*f**5/15 + 35*f**4/3 - 2*f**3/3 - 20*f**2/3 + 8*f/3 - 7. Factor x(q).
2*(q + 1)**2*(7*q - 2)**2/3
Let c(z) be the third derivative of -z**6/1980 - z**5/110 - 3*z**4/44 - z**3/2 - z**2. Let q(b) be the first derivative of c(b). Factor q(w).
-2*(w + 3)**2/11
Let c(p) be the second derivative of -p**5/60 + p**3/18 - 11*p. Find u such that c(u) = 0.
-1, 0, 1
Let k(v) be the third derivative of 1/60*v**4 + 0*v**3 + 0*v - 1/150*v**5 + 0 + v**2. Let k(x) = 0. Calculate x.
0, 1
Let k(x) be the third derivative of 4*x**7/945 - 7*x**6/540 + x**5/135 + x**4/108 - 2*x**2. Factor k(j).
2*j*(j - 1)**2*(4*j + 1)/9
Let x(d) = -12*d + 11*d - 4 - 1. Let v be x(-7). Solve -5*h**4 - v*h**3 + h + h + 3*h**4 + 2*h**2 = 0 for h.
-1, 0, 1
Let 0 + 1/2*d**5 - d**3 + 1/2*d + 0*d**4 + 0*d**2 = 0. Calculate d.
-1, 0, 1
Let p(a) be the first derivative of a**5/4 + a**4/6 - 5*a**3/6 - a**2 + 3*a + 1. Let i(l) be the first derivative of p(l). Suppose i(o) = 0. Calculate o.
-1, -2/5, 1
Let a be (-103)/(-7) + 6/21. Let w(h) = -h**2 + 16*h - 13. Let g be w(a). Let -1/5*t**3 + 0 - 1/5*t + 2/5*t**g = 0. What is t?
0, 1
Let j(o) = -18*o**2 + 19*o**2 - o**3 - 1 + 3*o - 2*o. Let q be j(-1). Factor q - n**3 + 4/3*n**2 - 1/3*n.
-n*(n - 1)*(3*n - 1)/3
Let c(w) = 6*w - 32. Let b be c(6). Let l(a) be the first derivative of 4/9*a**3 + 4/15*a**5 + 1/18*a**6 - 4 + 1/6*a**2 + 1/2*a**b + 0*a. Factor l(d).
d*(d + 1)**4/3
Let n(j) be the third derivative of 0*j**5 + 0*j**7 + 0*j**3 - 6*j**2 - 1/1512*j**8 + 0*j + 0*j**4 + 0 + 0*j**6. Factor n(v).
-2*v**5/9
Let n(y) be the second derivative of 2*y**7/63 - 4*y**6/45 + 2*y**4/9 - 2*y**3/9 - 24*y. Suppose n(u) = 0. Calculate u.
-1, 0, 1
Factor -449*n - 2*n**4 + 449*n - 6*n**3.
-2*n**3*(n + 3)
Let r(f) = -6*f**3 - f**2 - f + 6. Let c(j) = -7*j**3 - j**2 - j + 7. Let u(b) = 5*c(b) - 6*r(b). Let x be u(1). Factor 1/2*m**2 + x*m + 2.
(m + 2)**2/2
Let c(v) = -v - 1. Let r(g) = -5*g*