*7 - 1/12*y**6 + 2*y - 1/10*y**5. Factor l(a).
-a**2*(a + 1)**2*(2*a + 1)/2
Let m be (-13)/(-3) - 2/(-3). Suppose -35 = -m*s + 4*a, s = -s + a + 11. Let -2*b**3 + b**3 - b**2 - b**s - b**4 = 0. Calculate b.
-1, 0
Let s(q) = -q**2 + q. Suppose 5*h = h - 12. Let g(k) = -k - 1. Let r(o) = -46*o**2 + 22*o - 7. Let j(n) = 3*g(n) - r(n). Let v(m) = h*s(m) + j(m). Factor v(u).
(7*u - 2)**2
Let f(u) be the second derivative of -5*u**4/12 - 3*u**3/2 + u**2 - 2*u. Determine r, given that f(r) = 0.
-2, 1/5
Let i(c) be the third derivative of c**7/840 - c**6/60 - 3*c**4/8 + 4*c**2. Let m(d) be the second derivative of i(d). Determine f, given that m(f) = 0.
0, 4
Let x(j) be the first derivative of 2/3*j**3 + 0*j + 0*j**2 + 2 + j**4 + 2/5*j**5. Factor x(d).
2*d**2*(d + 1)**2
Let v(k) be the third derivative of 1/72*k**4 + 0 - 1/360*k**6 + 0*k + 1/18*k**3 + 5*k**2 - 1/180*k**5. What is q in v(q) = 0?
-1, 1
Let t(c) be the first derivative of 0*c - 1/5*c**2 - 3/10*c**4 - 2/5*c**3 - 2/25*c**5 - 1. Suppose t(h) = 0. What is h?
-1, 0
Let o(q) = 7*q**3 - 29*q**2. Let z(u) = -6*u**3 + 28*u**2. Let m(y) = -4*o(y) - 5*z(y). Factor m(n).
2*n**2*(n - 12)
Let v(r) be the third derivative of -r**8/630 + r**7/140 - r**6/90 + r**5/180 + 5*r**3/6 + 9*r**2. Let q(c) be the first derivative of v(c). Factor q(u).
-2*u*(u - 1)**2*(4*u - 1)/3
Let g(d) be the first derivative of 1/3*d**2 + 0*d + 3 - 2/9*d**3. What is b in g(b) = 0?
0, 1
Suppose 8*l = 14*l. Let b be (-1*1*2)/(-3). Factor l*y**2 + 2/3*y**3 + 0 - b*y.
2*y*(y - 1)*(y + 1)/3
Let n(f) be the first derivative of 3*f**4/32 - 39*f**3/8 + 1521*f**2/16 - 6591*f/8 - 11. Factor n(a).
3*(a - 13)**3/8
Let p(z) be the third derivative of 0 - 1/120*z**6 - 1/8*z**4 + 0*z + 1/6*z**3 - 2*z**2 + 1/20*z**5. Suppose p(r) = 0. Calculate r.
1
Let w(i) be the third derivative of i**8/336 + i**7/105 + i**6/120 + 7*i**2. Factor w(b).
b**3*(b + 1)**2
Let x(l) = -5*l**4 + 5*l**2 - 2*l - 2. Let y(n) = -5*n**4 + 5*n**2 - 3*n - 3. Let m(o) = 3*x(o) - 2*y(o). Factor m(u).
-5*u**2*(u - 1)*(u + 1)
Determine l, given that 2/3*l - l**2 + 1/3*l**3 + 0 = 0.
0, 1, 2
Let m be (-3 - -2) + 7/((-28)/(-16)). Let t(h) be the second derivative of 0 - 2/15*h**m - 1/5*h**2 - 1/30*h**4 + 3*h. Find r such that t(r) = 0.
-1
Suppose 17 - 1 = -q - 4*y, 33 = 2*q - 5*y. Suppose -2*f + q = -f. Suppose -h**2 + 10*h**3 - 14*h**3 - 2*h**f - h**2 = 0. Calculate h.
-1, 0
Let t be 6/9*(-12)/(-14). Let -2/7 - 6/7*o - t*o**2 = 0. Calculate o.
-1, -1/2
Let a = -5 + 8. Suppose -2*t - a*t + 8 = -2*n, -4*t = 3*n - 11. Find v such that -1/4*v**3 + 0*v + 0 + 0*v**t = 0.
0
Let l(h) be the second derivative of 1/30*h**6 + 1/2*h**2 + 0 - 1/6*h**4 + 0*h**5 + 9*h + 0*h**3. Factor l(g).
(g - 1)**2*(g + 1)**2
Let f(k) be the second derivative of 1/48*k**4 - 2*k + 1/12*k**3 + 0 + 1/8*k**2. Factor f(a).
(a + 1)**2/4
Let q be (-10 - -2)/2 + 4. Find v, given that 0 - 2/3*v**4 + q*v**2 + 4/3*v**3 + 0*v = 0.
0, 2
Let m(w) be the second derivative of -w**7/168 + w**6/120 + 3*w**5/80 - 5*w**4/48 + w**3/12 - 6*w. Factor m(h).
-h*(h - 1)**3*(h + 2)/4
Solve 25 - 25 + 2*y**3 = 0 for y.
0
Let a(x) be the third derivative of 1/180*x**5 + 0 - 1/1008*x**8 + 2*x**2 + 1/360*x**6 + 0*x**3 + 0*x**4 - 1/630*x**7 + 0*x. Solve a(z) = 0 for z.
-1, 0, 1
Let a(n) be the first derivative of 2*n**5/5 + n**4/2 - 4*n**3/3 - 16. Factor a(y).
2*y**2*(y - 1)*(y + 2)
Let r(c) be the third derivative of c**7/126 - 17*c**6/180 + c**5/5 + 7*c**4/24 - 2*c**2. Let h(z) be the second derivative of r(z). Factor h(s).
4*(s - 3)*(5*s - 2)
Let x(n) = n**3 + 4*n**2 - 4*n + 5. Let h be x(-5). Let z be (-9)/4 + (h - -3). Factor 0 + 0*l - 3/4*l**2 + z*l**3.
3*l**2*(l - 1)/4
Suppose 10 - 10 = -u. Let g be 2*2/6 - 0. Suppose -g*f + 2/3*f**2 + u = 0. Calculate f.
0, 1
Let f(w) be the first derivative of -1/3*w**2 + 1/9*w**3 + 0*w - 6. Factor f(h).
h*(h - 2)/3
Let q(u) = -u**2 - 1. Let h(n) = -5*n**2 + n - 4. Let a(f) = h(f) - 4*q(f). Find g such that a(g) = 0.
0, 1
Factor 65*h**2 + 3*h**3 - 18*h + 22*h**3 - 12*h.
5*h*(h + 3)*(5*h - 2)
Let r(f) be the first derivative of 5*f**2 - 2*f + 216/5*f**5 + 6*f**3 - 1 - 81/2*f**4. Let r(i) = 0. What is i?
-1/4, 1/3
Let i = -26 + 26. Let r(b) be the second derivative of -b + 0*b**2 + 0 + i*b**4 + 1/20*b**5 - 1/6*b**3. Factor r(c).
c*(c - 1)*(c + 1)
Suppose -w = w + 16. Let y be -2 - 2 - (2 + w). Factor 0 - 3/2*l**3 + 0*l + 0*l**y.
-3*l**3/2
Let r(u) be the first derivative of -u**3/24 + u**2/8 - 8. Factor r(v).
-v*(v - 2)/8
Let d = 268/3 + -89. Let a(i) be the third derivative of d*i**3 + 3*i**2 + 1/30*i**5 + 0*i + 0 - 1/6*i**4. Solve a(m) = 0.
1
Let t be (-54)/36 - 14/(-4). Let s be 2/(-4)*(-2)/t. Factor -1/2*p**5 + 0*p**4 + 0*p**2 + s*p**3 + 0*p + 0.
-p**3*(p - 1)*(p + 1)/2
Let 2/3*r**3 - 2/3*r**4 + 0*r**2 + 0*r + 0 = 0. What is r?
0, 1
Let j be (6/7)/(1/(-7)). Let i be 15/10 + 1/j. Determine g so that -10/3*g**4 + 10/3*g**2 - i*g - 2/3*g**3 + 2*g**5 + 0 = 0.
-1, 0, 2/3, 1
Let u be 3/(-18)*(-16)/20. Let m(t) be the first derivative of -2/9*t**3 + 0*t**2 + 0*t + u*t**5 - 1/9*t**6 + 1/6*t**4 + 2. Find a such that m(a) = 0.
-1, 0, 1
Suppose -4*z + 2*s + 30 = 0, 0 = z - 4*s - 22 + 4. Solve 2*u**3 - 2 - u - 6*u**2 + u + z*u = 0 for u.
1
Let b(f) be the third derivative of -f**8/252 + 4*f**7/315 + f**6/45 - 4*f**5/45 - f**4/18 + 4*f**3/9 - 2*f**2. What is n in b(n) = 0?
-1, 1, 2
Let t(n) = 9*n**4 - 9*n**3 - 13*n**2 + 13*n + 13. Let i(u) = 4*u**4 - 4*u**3 - 6*u**2 + 6*u + 6. Let b(w) = 13*i(w) - 6*t(w). Factor b(a).
-2*a**3*(a - 1)
Suppose 16*y**3 + 4*y**4 + 1 + 15*y**2 + 9*y**2 + 3 - 10*y + 26*y = 0. Calculate y.
-1
Let a(w) = w**2 - 1. Let l be a(-2). Let n be 0*-2*l/(-6). Suppose k**5 - 2*k**3 + k**5 + n*k**5 = 0. Calculate k.
-1, 0, 1
Let o(z) be the first derivative of z**6/8 - 11*z**5/20 + 15*z**4/16 - 3*z**3/4 + z**2/4 - 18. Solve o(p) = 0.
0, 2/3, 1
Let f = 333 - 333. Find n, given that 1/5*n**4 + 3/5*n**5 + f*n + 0 - 1/5*n**2 - 3/5*n**3 = 0.
-1, -1/3, 0, 1
Suppose -3 = -4*q - w, -2*q = w + 1 - 0. Let -7/4*f + 1/4*f**5 - 1/2*f**4 + 1/2 + 2*f**q - 1/2*f**3 = 0. What is f?
-2, 1
Let h(y) = y**2 + 4*y + 9. Let q be h(-3). Let q*z + 3/2*z**2 + 9/2 = 0. What is z?
-3, -1
Factor 2/9*h**2 + 4/9*h**3 - 16/9*h - 8/9.
2*(h - 2)*(h + 2)*(2*h + 1)/9
What is x in 154/5*x**4 + 0 + 132/5*x**3 + 16/5*x - 104/5*x**2 - 98/5*x**5 = 0?
-1, 0, 2/7, 2
Suppose r + 5*y - 2*y + 15 = 0, -5*y - 26 = 2*r. Let u be (r/(-20))/((-2)/(-48)). Solve -12/5*c**3 + 0*c - 8/5*c**5 + 0 - u*c**4 - 2/5*c**2 = 0 for c.
-1, -1/4, 0
Let q(a) be the second derivative of -a**7/840 - a**6/120 - a**5/40 + a**4/3 + a. Let s(g) be the third derivative of q(g). Factor s(d).
-3*(d + 1)**2
Factor 4*g**2 + 4/3*g**4 + 0 + 4/3*g + 4*g**3.
4*g*(g + 1)**3/3
Let j(f) be the third derivative of f**7/70 - f**6/40 - f**5/20 + f**4/8 + 36*f**2. Let j(u) = 0. Calculate u.
-1, 0, 1
Let v(y) be the first derivative of 1/3*y**2 + 2 + 4/9*y**3 + 0*y. Factor v(h).
2*h*(2*h + 1)/3
Factor 1/4*o**3 + 9/2 - 23/8*o**2 + 15/2*o.
(o - 6)**2*(2*o + 1)/8
Suppose -25 = -3*o + 5*n, 2*o - 4*n = -4 + 24. Suppose -5*x + 2*x = o. Let 2/5*z + 4/5*z**4 - 6/5*z**3 + 0*z**2 + x = 0. What is z?
-1/2, 0, 1
Suppose -2*f + 10 = -2*h, 0*h - 2*h + 5*f - 7 = 0. Let u = h + 6. Find d, given that d**2 + 1 - 1 + u = 0.
0
Factor -39/4*a + 9 + 3/4*a**2.
3*(a - 12)*(a - 1)/4
Suppose -3*n**3 - 11*n + n**3 + 15*n - 2*n**3 = 0. Calculate n.
-1, 0, 1
Solve -15*f**2 + 88*f - 34*f + 5*f**4 - 44*f = 0.
-2, 0, 1
Let v(p) be the third derivative of p**5/270 - 4*p**3/27 + 14*p**2. Suppose v(w) = 0. Calculate w.
-2, 2
Let k(l) = -4*l**4 + 5*l**3 + 5*l**2 + 5*l + 5. Let j(z) = -z**4 + z**3 + z**2 + z + 1. Let u(d) = -5*j(d) + k(d). Factor u(a).
a**4
Let r(j) be the third derivative of j**8/2240 + j**7/1680 - j**3/2 - j**2. Let b(x) be the first derivative of r(x). Factor b(d).
d**3*(3*d + 2)/4
Let g(n) be the third derivative of n**2 + 0*n + 0 + 1/30*n**5 + 1/12*n**4 + 0*n**3. Factor g(f).
2*f*(f + 1)
Let c(d) be the second derivative of 4*d**7/105 - d**6/10 + d**4/6 - 3*d**2 + 2*d. Let w(m) be the first derivative of c(m). Factor w(g).
4*g*(g - 1)**2*(2*g + 1)
Factor -27*q**2 - 16 + 36*q + 27/4*q**3.
(3*q - 4)**3/4
Suppose 4*n - 3*h = 27, 4*n - 4*h = -16 + 44. Suppose l + 2*l = n. Determine i so that 