. Factor f*n**3 + 0 + 2/3*n**2 + 4/9*n.
2*n*(n + 1)*(n + 2)/9
Let m(h) be the third derivative of -h**5/210 - h**4/84 + 2*h**3/21 + 7*h**2. Solve m(u) = 0 for u.
-2, 1
Factor -2/3*i**2 + 1/3*i + 0 + 1/3*i**3.
i*(i - 1)**2/3
Let o(j) = 21*j**4 - 15*j**3 - 31*j**2 + 11*j + 2. Let v(f) be the first derivative of f**3/3 + f**2/2 + f + 1. Let n(h) = o(h) + 4*v(h). Solve n(a) = 0 for a.
-1, -2/7, 1
Let o = -18 - 0. Let w = 20 + o. Let -1/3*r**4 + 0 - 1/3*r - r**3 - r**w = 0. What is r?
-1, 0
Let h(a) = 7*a - 3. Let t be h(1). Let m(b) be the third derivative of -27/40*b**6 + 0*b + 3/5*b**5 + 0 - 1/6*b**t - 2*b**2 + 0*b**3. Let m(y) = 0. What is y?
0, 2/9
Let x(r) = -9*r**4 + 72*r**3 + 165*r**2 + 99*r + 36. Let c(q) = 2*q**4 - 18*q**3 - 41*q**2 - 25*q - 9. Let w(i) = 21*c(i) + 5*x(i). Factor w(b).
-3*(b + 1)**3*(b + 3)
Suppose 3*y = 7*y. Let i(k) be the third derivative of 0 + 0*k + y*k**3 + 3*k**2 + 1/54*k**4 + 1/270*k**5. Factor i(l).
2*l*(l + 2)/9
Let b = -6361/9 + 707. Suppose 2/9*r + 2/9 - b*r**3 - 2/9*r**2 = 0. Calculate r.
-1, 1
Let n(d) be the second derivative of 1/14*d**4 - 4/7*d**2 + 4*d + 0 + 0*d**3 - 1/70*d**5. What is c in n(c) = 0?
-1, 2
Let s(z) = 4*z**3 + 33*z**2 + 108*z + 111. Let h(u) = -8*u**3 - 65*u**2 - 216*u - 223. Let g(x) = -3*h(x) - 7*s(x). Factor g(k).
-4*(k + 3)**3
Let l be (0 + 3 + 1)/(2 + 4). Let x(v) be the first derivative of 0*v**2 - 3 - 2/9*v**3 + l*v. Determine k so that x(k) = 0.
-1, 1
Let y(r) = -8*r**4 - 10*r**2 + 9*r + 9. Suppose -4*q - 2 = -10. Let x(z) = -z**4 - z**2 + z + 1. Let j(f) = q*y(f) - 18*x(f). Factor j(s).
2*s**2*(s - 1)*(s + 1)
Let h be 12*-4*(-8)/512. Let 0*d**3 + h*d**4 - 9/4*d**2 + 0 + 3/2*d = 0. What is d?
-2, 0, 1
Let r = 19 + -17. Let p(u) be the third derivative of 0 - 1/315*u**7 + 1/54*u**4 + 0*u - 1/135*u**6 + 1/54*u**5 + r*u**2 + 0*u**3. Find z such that p(z) = 0.
-2, -1/3, 0, 1
Let r(q) = q**5 + 7*q**4 - 6*q**3 + 3*q**2 - 5*q. Let s(o) = -o**5 - 8*o**4 + 7*o**3 - 4*o**2 + 6*o. Let u(a) = 6*r(a) + 5*s(a). Factor u(v).
v**2*(v - 1)*(v + 1)*(v + 2)
Let z be 0 - -3 - (3 + -2). Let x(a) be the second derivative of -1/5*a**z + 2/15*a**3 - 1/30*a**4 + 0 + 2*a. Solve x(g) = 0 for g.
1
Let -2*q + 8 + 6*q**3 + 6*q**3 - 10*q - 4*q**4 + 2*q**2 - 6*q**2 = 0. Calculate q.
-1, 1, 2
Let u(c) be the second derivative of c**7/168 + c**6/120 - c**5/80 - c**4/48 - 22*c. Suppose u(h) = 0. Calculate h.
-1, 0, 1
Let a be (-6)/(-18)*6/112. Let g = 197/56 - a. Solve 23/2*x**4 + g*x**5 + x + 13/2*x**2 + 27/2*x**3 + 0 = 0 for x.
-1, -2/7, 0
Let w(r) be the second derivative of -r**5/60 - 9*r. Factor w(i).
-i**3/3
Let k(b) be the first derivative of -b**6/6 + b**5 - 5*b**4/2 + 10*b**3/3 - 5*b**2/2 + b - 6. Factor k(n).
-(n - 1)**5
Let k be (-2)/1 + 180/81. Let l(a) be the second derivative of 0 + a - k*a**3 - 1/3*a**2 - 1/18*a**4. Factor l(f).
-2*(f + 1)**2/3
Let w(f) be the second derivative of -f**7/63 - 2*f**6/45 + f**5/10 + 2*f**4/9 - 4*f**3/9 - 11*f. Find g such that w(g) = 0.
-2, 0, 1
Let f(n) = 5*n - 48. Let k be f(10). Factor 2/3*z**k + 0*z + 0.
2*z**2/3
Suppose -3*n - 3*z + 5*z + 10 = 0, 6 = -n - 4*z. Find g such that 8 + 5*g**2 - 4*g**2 + 5*g**n - g**3 - 12*g = 0.
2
Suppose -2*p + 1 = -9. Let g(r) = 4*r**2 + 5*r**3 + 1 - 4*r - p - r. Let x(c) = 6*c**3 + 4*c**2 - 5*c - 5. Let b(w) = 7*g(w) - 6*x(w). Factor b(q).
-(q - 2)*(q - 1)**2
Let v be 4/(-14) + 160/70. Let j be (-30)/(-189) - v/(-7). Find g, given that -2/9*g + 2/9*g**3 - j*g**2 + 4/9 = 0.
-1, 1, 2
Determine j so that 2*j**4 - 7*j**4 + 21*j**5 + j**4 - 17*j**5 = 0.
0, 1
Let t(j) be the first derivative of -3*j**5/4 + 7*j**4/4 - j**3 - 5*j - 2. Let k(l) be the first derivative of t(l). Let k(o) = 0. What is o?
0, 2/5, 1
Let v be ((5 - 0)*1)/(40/16). Factor 3/2*d**v + 0 + 0*d.
3*d**2/2
Let u(w) be the second derivative of -1/4*w**4 - 3/20*w**5 - 1/6*w**3 - 1/30*w**6 - w + 0 + 0*w**2. Find p such that u(p) = 0.
-1, 0
Let a = 31/120 + 3/40. Factor -1/3*o**2 - a*o + 0.
-o*(o + 1)/3
Let z(c) = c**2 - c - 5. Let s be z(-4). Let k = -16 + 31. Factor -k*b**2 + 46*b**3 + 4*b - s*b**2 + 10*b**3.
2*b*(4*b - 1)*(7*b - 2)
Let q(l) be the second derivative of -l**7/420 + l**5/60 - l**3/12 - 2*l**2 - 5*l. Let s(j) be the first derivative of q(j). Factor s(z).
-(z - 1)**2*(z + 1)**2/2
Let o = -94 + 96. Suppose -4/7 - 8/7*r**o + 18/7*r = 0. What is r?
1/4, 2
Let w = -4 + 13. Let o = 11 - w. Factor -12*p**3 + p**4 + 2*p + 9*p**o - 4*p + 4*p**4.
p*(p - 1)**2*(5*p - 2)
Factor -2/3 - l - 1/3*l**2.
-(l + 1)*(l + 2)/3
Suppose 4 = 2*q - 2. Let m(f) be the third derivative of -1/3*f**q + 0*f**4 - 3*f**2 + 1/30*f**5 + 0 + 0*f. Factor m(p).
2*(p - 1)*(p + 1)
Let s = 11881/60 - 198. Let d(o) be the second derivative of 0*o**2 + 0 - 1/10*o**5 - 4*o - 5/24*o**4 - s*o**6 - 1/6*o**3. Factor d(p).
-p*(p + 1)**2*(p + 2)/2
Let x(z) be the first derivative of z**5/20 - z**4/6 + z**3/6 - 3*z + 8. Let y(v) be the first derivative of x(v). Suppose y(d) = 0. What is d?
0, 1
Let t be 6/21 - 60/(-35). What is y in -y - 6 - 2*y - 2*y**2 - 2*y**t + 7*y**2 = 0?
-1, 2
Let b(f) be the first derivative of f**4/4 + 8*f**3/3 + 13*f**2/2 + 6*f + 18. Let b(j) = 0. What is j?
-6, -1
Solve -10/3*p**4 - 40/3*p + 16/3 + 34/3*p**3 - 4*p**2 = 0 for p.
-1, 2/5, 2
Solve 11*y**2 + 2*y**2 - 9*y**2 + 8*y - 4*y**3 = 0.
-1, 0, 2
Solve 3/2 - 15/4*a - 81/4*a**2 - 33/4*a**4 - 93/4*a**3 = 0 for a.
-1, 2/11
Let m(y) = y**3 + 6*y**2 - 6*y + 9. Let i be (28/(-8))/(2/4). Let w be m(i). Factor k**2 + 0 - 2 + k**w.
2*(k - 1)*(k + 1)
Let d(k) = 7*k**2 - 5. Suppose 3*u + 4 = 5*u. Suppose 5 = s - u*s. Let t(x) = 3*x**2 - 2. Let n(y) = s*t(y) + 2*d(y). Let n(q) = 0. Calculate q.
0
Let k(b) be the third derivative of b**11/166320 - b**10/37800 + b**9/30240 - b**5/15 - 2*b**2. Let v(f) be the third derivative of k(f). Factor v(j).
2*j**3*(j - 1)**2
Factor 130*j**3 - 3*j**4 + j**5 - 130*j**3 - 4*j**5.
-3*j**4*(j + 1)
Let 2/19*v**5 - 4/19*v**2 + 0 + 4/19*v**4 - 2/19*v + 0*v**3 = 0. What is v?
-1, 0, 1
Let k(j) be the second derivative of j**4/30 - j**3/5 - 8*j. Factor k(v).
2*v*(v - 3)/5
Suppose 1 - 2*c**2 - 2*c**2 - 3 + 8*c - 2 = 0. What is c?
1
Let x(g) = g**4 + g**3 - g**2. Let d(u) = -2*u**4 - u**3 - 3*u + 2. Let t(k) = 5*d(k) + 20*x(k). Determine b so that t(b) = 0.
-2, -1, 1/2, 1
Let y(b) be the first derivative of -b**8/3360 - b**7/1680 + b**6/240 + b**5/48 + b**4/24 + 2*b**3/3 + 3. Let t(a) be the third derivative of y(a). Factor t(s).
-(s - 2)*(s + 1)**3/2
Let k be (12/27)/(24/108). Let w be 20/35 + (-2)/7. Find y, given that 2/7 + 0*y - w*y**k = 0.
-1, 1
Let r(s) be the second derivative of -2*s**7/21 - 8*s**6/15 - 4*s**5/5 - 9*s. Solve r(n) = 0.
-2, 0
Let s(r) be the second derivative of 1/120*r**5 + 0*r**2 + 0*r**3 + 0*r**4 + 0 - 1/180*r**6 - 4*r. Factor s(d).
-d**3*(d - 1)/6
Let u(r) = -24*r**4 - 33*r**3 - 9*r**2 - 33*r. Let z(j) = -3*j**4 - 4*j**3 - j**2 - 4*j. Let h(p) = -4*u(p) + 33*z(p). Let h(i) = 0. What is i?
-1, 0, 1
Let t = -9 + 8. Let a be t + -1 + 5 + -1. Factor 10/9*r + 2/9*r**3 - 8/9*r**a - 4/9.
2*(r - 2)*(r - 1)**2/9
Let r(t) be the second derivative of 2*t**7/21 - 4*t**6/15 + 2*t**4/3 - 2*t**3/3 + 2*t. Factor r(a).
4*a*(a - 1)**3*(a + 1)
Suppose 13 = 5*d + 4*x - 9, -d - 13 = -5*x. Let m(z) = -7*z**2 + 14*z - 2. Let c(i) = -7*i**2 + 13*i - 1. Let w(j) = d*c(j) - 3*m(j). Find p such that w(p) = 0.
2/7, 2
Suppose 0 + 4/9*i - 2*i**2 - 10/9*i**4 + 8/3*i**3 = 0. Calculate i.
0, 2/5, 1
Let z(t) be the second derivative of t**6/10 + 3*t**5/5 + 3*t**4/4 - 2*t**3 - 6*t**2 + t + 12. Factor z(s).
3*(s - 1)*(s + 1)*(s + 2)**2
Let l(j) = 103*j**4 - 17*j**3 - 67*j**2 - 13*j. Let n(f) = -514*f**4 + 86*f**3 + 334*f**2 + 66*f. Let p(k) = 14*l(k) + 3*n(k). What is d in p(d) = 0?
-2/5, 0, 1
Suppose 0 = 5*k + s - 8, 4*k - 9*k - 5*s = 0. Factor 3/2*t**k - 1/2 - t.
(t - 1)*(3*t + 1)/2
Let p(l) be the third derivative of l**5/180 - l**4/9 + 8*l**3/9 - 8*l**2. Find m, given that p(m) = 0.
4
Let a(b) be the third derivative of 0*b**4 - b**2 + 0 - 1/90*b**5 + 0*b + 1/180*b**6 + 0*b**3 + 1/315*b**7 - 1/504*b**8. Factor a(h).
-2*h**2*(h - 1)**2*(h + 1)/3
Let s be 3/(-4) - 23/(-4). Let p(g) = 12*g**2 - 26*g - 8. Let u(m) = -23*m**2 + 53*m + 16. Let k(z) = s*p(z) + 2*u(z). Suppose k(q) = 0. Calculate q.
-2/7, 2
Let o = 37 + -35. S