**5 - 15*k**4 + 20*k**2 = 0?
-2, 0, 1
Let s(c) be the second derivative of c**4/12 - c**3/3 + 2*c**2 + 2*c. Let f = 7 + -1. Let d(a) = -1. Let t(x) = f*d(x) + 2*s(x). Factor t(u).
2*(u - 1)**2
Let s(o) be the third derivative of 0*o - 1/180*o**5 - o**2 - 1/72*o**4 + 0 + 0*o**3. Factor s(c).
-c*(c + 1)/3
Let o(y) be the second derivative of -y**5/80 + 3*y**4/16 - 9*y**3/8 + 27*y**2/8 + 25*y. Determine a, given that o(a) = 0.
3
Let f(l) be the third derivative of l**5/300 - l**4/120 - 35*l**2. Let f(c) = 0. What is c?
0, 1
Let v(s) = s**3 + 1. Let a(c) = c**4 + c**3 - c**2 + 1. Let z(k) = -2*a(k) + 2*v(k). Solve z(h) = 0.
-1, 0, 1
Let s(g) be the second derivative of 1/40*g**5 + 0*g**2 + 0 - 1/48*g**4 + 2*g - 1/24*g**3. Factor s(o).
o*(o - 1)*(2*o + 1)/4
Let l(c) be the third derivative of c**6/1440 + c**5/240 + c**4/96 - c**3/2 - 2*c**2. Let g(u) be the first derivative of l(u). Let g(x) = 0. Calculate x.
-1
Let y = -5 + 8. Factor 0*k**5 + k**4 - 4*k**3 + 1 + 2*k**y - 2*k**2 + k**5 + k.
(k - 1)**2*(k + 1)**3
Let w be (-2)/7 + (-6)/(84/(-53)). Let -w*k**5 + 9/2*k**3 + 0 + 5/2*k**2 - 5/2*k**4 - k = 0. Calculate k.
-1, 0, 2/7, 1
Let w(x) = -14*x**3 - 7*x**2 + 12*x. Let y(i) = -57*i**3 - 27*i**2 + 48*i. Let z(b) = -21*w(b) + 5*y(b). Find l such that z(l) = 0.
-2, 0, 2/3
Suppose -3 = -4*g + 2*o - 13, 2*g + 2*o - 10 = 0. Let q = 1 - -1. What is i in g + 0*i**q - 1/3*i + 1/3*i**3 = 0?
-1, 0, 1
Let x(q) = -q**2 + 8*q - 7. Let a be x(7). Determine i so that -3*i + 4*i - 2*i**3 - 1 + a*i**3 + i**2 + i**3 = 0.
-1, 1
Let h(x) = -x**3 - 4*x**2 + 5*x + 3. Let v be h(-5). Let y(z) = -z**2 + 3*z + 1. Let b be y(v). Factor -2*o + b + 1 - o + o**2 + 0*o.
(o - 2)*(o - 1)
Let k(o) = -8*o. Let t(w) = -w**2 + 8*w. Let i(y) = 3*k(y) + 4*t(y). Factor i(h).
-4*h*(h - 2)
Let m = -48/7 - -446/63. Solve 2/3*w**2 + 2/3*w + m + 2/9*w**3 = 0 for w.
-1
Suppose 4*n - 20 = 0, -t + 3*n - 23 = -2*n. Let m be t - 0 - 0/(-2). Factor m*u**4 + 6*u**5 - 5*u**4 + 2*u**2 + 10*u**3 + 17*u**4.
2*u**2*(u + 1)**2*(3*u + 1)
Let t(i) = 40*i**3 + 40*i**2 + 5*i - 5. Let x(s) = -s**3 - s**2 - s - 1. Let m(b) = t(b) - 5*x(b). Factor m(n).
5*n*(3*n + 1)*(3*n + 2)
Let l(c) be the third derivative of c**8/1120 + c**7/280 + c**6/240 + 5*c**3/6 - 4*c**2. Let x(u) be the first derivative of l(u). Factor x(k).
3*k**2*(k + 1)**2/2
Factor 4/7 + 2/7*m - 4/7*m**2 - 2/7*m**3.
-2*(m - 1)*(m + 1)*(m + 2)/7
Let n(o) be the third derivative of 1/12*o**4 - 1/12*o**5 - 1/210*o**7 + 1/30*o**6 + 0 + 0*o + 0*o**3 - 4*o**2. Solve n(t) = 0.
0, 1, 2
Suppose -2*f = -4*f. Let o(p) be the second derivative of -2*p + f*p**3 + 0*p**2 - 1/54*p**4 + 0. Solve o(l) = 0 for l.
0
Let d be ((-12)/(-8) - 1)/12. Let m(f) be the second derivative of 0 - 1/40*f**5 + 1/168*f**7 + f + 0*f**4 + 0*f**2 + d*f**3 + 0*f**6. Factor m(u).
u*(u - 1)**2*(u + 1)**2/4
Let p(v) be the second derivative of -1/6*v**5 - 3*v - 1/2*v**2 - 2/3*v**4 + 0 - 4/3*v**3 - 1/60*v**6. Let i(q) be the first derivative of p(q). Factor i(z).
-2*(z + 1)*(z + 2)**2
Suppose 3 + 0 = i. Let 6/7*n - 2/7 + 2/7*n**i - 6/7*n**2 = 0. What is n?
1
Let c(v) be the second derivative of v**9/1008 + v**8/140 + v**7/56 + v**6/60 - v**3/3 - 3*v. Let w(h) be the second derivative of c(h). Factor w(u).
3*u**2*(u + 1)**2*(u + 2)
Let u(a) be the third derivative of a**6/30 + a**5/60 - a**4/6 + a**3/3 + 2*a**2. Let c(n) be the first derivative of u(n). Suppose c(y) = 0. Calculate y.
-2/3, 1/2
Suppose 4*d - 26 = 5*p, -11*p = 2*d - 7*p. Let -2/3*w**d - 4*w**2 + 8/3*w - 2/3 + 8/3*w**3 = 0. What is w?
1
Let v(l) = -l**2 + 2*l + 4. Let w(k) = -2*k**2 + 4*k + 9. Suppose 4*r - 6 = -3*u - 2*u, 0 = -2*r - 2*u + 4. Let q(y) = r*w(y) - 9*v(y). Factor q(g).
g*(g - 2)
Suppose 0 = -9*f + 7*f + 12. Let j(i) be the third derivative of 0*i + 1/80*i**5 + 2*i**2 - 1/480*i**f - 1/32*i**4 + 1/24*i**3 + 0. Factor j(x).
-(x - 1)**3/4
Let a(v) = v**3 + v**2 - v - 1. Let o(g) = 13*g**3 - 18*g - 5. Let y(z) = -3*a(z) + o(z). Let t(f) = -f**3 - 1. Let s(u) = 4*t(u) + y(u). Factor s(c).
3*(c - 2)*(c + 1)*(2*c + 1)
Let x(f) be the third derivative of -f**7/630 + f**6/180 - f**5/180 + 3*f**2. Find c such that x(c) = 0.
0, 1
Suppose -2 - 2 = -y. Factor 0*k**2 - 2*k**3 + k**2 + y*k**3 - k**4 - 2*k.
-k*(k - 2)*(k - 1)*(k + 1)
Let f(o) be the first derivative of 3*o**8/28 + 11*o**7/70 + o**6/20 - o**2/2 - 5. Let b(r) be the second derivative of f(r). Factor b(v).
3*v**3*(3*v + 2)*(4*v + 1)
Let u be (-6)/(-9)*3/2. Let i be -2 - (-3 + -2 + u). Find w, given that i*w + 2/3 - 2*w**3 - 2/3*w**2 = 0.
-1, -1/3, 1
Factor 2 + 3*y**2 + 2*y**3 - 2*y - 10*y**2 + 5*y**2.
2*(y - 1)**2*(y + 1)
Let x be (-39)/(-18) - 12/18. Factor 3*y**2 - x*y**4 + 0 + 0*y + 3/2*y**3.
-3*y**2*(y - 2)*(y + 1)/2
Let u(h) be the third derivative of -h**11/110880 - h**10/12600 - h**9/5040 + h**5/60 - 2*h**2. Let c(v) be the third derivative of u(v). What is x in c(x) = 0?
-2, 0
Let t(i) be the first derivative of i - 4 - 5*i**2 + 25/3*i**3. Factor t(l).
(5*l - 1)**2
Let f(z) = -z - 4. Let t be f(-6). Factor -2*m - 4*m**3 - 4*m**2 + 0*m**2 - m**4 - 4*m**2 + 3*m**t.
-m*(m + 1)**2*(m + 2)
Let p(a) be the third derivative of a**5/360 + a**4/24 + 2*a**3/9 - 28*a**2. Determine t, given that p(t) = 0.
-4, -2
Let h(k) be the third derivative of 0 + 1/108*k**4 + 0*k**3 + 0*k + 1/270*k**5 + 2*k**2. Factor h(i).
2*i*(i + 1)/9
Determine i so that 32*i**3 + 6*i + 9*i**2 - 64*i**3 + 32*i**3 - 3*i**4 = 0.
-1, 0, 2
Let i(l) be the second derivative of l**6/45 - l**5/10 + l**4/18 + l**3/3 - 2*l**2/3 - 13*l. What is h in i(h) = 0?
-1, 1, 2
Let r = -3/125 + 423/2000. Let z = 17/80 + r. Let -2/5*d + z*d**2 + 0 = 0. What is d?
0, 1
Let i(k) be the third derivative of k**6/80 - k**5/80 - k**4/16 + k**3/8 - 25*k**2. Factor i(l).
3*(l - 1)*(l + 1)*(2*l - 1)/4
Let t(f) = -f**2 + 2*f - 7. Let y be t(-6). Let w be (-10)/y - (-62)/22. Factor 4/9*u**w - 4/9*u**2 + 2/9*u**4 - 2/9*u**5 - 2/9*u + 2/9.
-2*(u - 1)**3*(u + 1)**2/9
Let m(v) = -4*v**4 + 6*v**3 + 2*v**2 - 6*v. Let j(h) = 8*h**4 - 13*h**3 - 3*h**2 + 13*h. Let f(u) = 2*j(u) + 5*m(u). Suppose f(g) = 0. What is g?
-1, 0, 1
Factor -r**4 + 2*r**3 + 4*r**4 - 2*r + 2*r**2 - 2*r**4 - 3*r**2.
r*(r - 1)*(r + 1)*(r + 2)
Let o(d) be the first derivative of -d**7/21 + 4*d**6/15 - d**5/2 + d**4/3 - d + 9. Let t(b) be the first derivative of o(b). Suppose t(h) = 0. What is h?
0, 1, 2
Let z be (-3)/(((-18)/4)/3). Suppose 0*y + 0 + z*y**2 - 2*y - 4 = 0. Calculate y.
-1, 2
Let s(w) be the third derivative of 0 + 0*w**3 + 1/40*w**6 - 1/70*w**7 + 0*w**4 + 0*w + 4*w**2 + 1/20*w**5 - 1/112*w**8. Factor s(u).
-3*u**2*(u - 1)*(u + 1)**2
Let y(u) be the first derivative of -4*u**3 + 21*u**2/2 - 9*u - 1. Solve y(f) = 0.
3/4, 1
Let b = -4 - -1. Let u(h) = h + 3. Let a be u(b). Factor a*t**5 - 2*t**5 + 0*t - t**4 - 3*t**4 + 2*t + 4*t**2.
-2*t*(t - 1)*(t + 1)**3
Let z(f) be the first derivative of -2 + 1/240*f**5 + 1/24*f**3 + 0*f + 1/48*f**4 + 1/2*f**2. Let c(t) be the second derivative of z(t). Factor c(g).
(g + 1)**2/4
Let x be 4/22 - 42/(-11). Suppose 7*k = x*k. Determine f, given that -2/3*f**3 + k - 2/3*f + 4/3*f**2 = 0.
0, 1
Suppose -10 = 4*x - 38. Factor -o + o**3 + 2 - x + 5.
o*(o - 1)*(o + 1)
Let t(y) be the first derivative of 1/2*y**2 + 4/3*y**3 - 1/4*y**4 + 4 - 4/5*y**5 + 0*y. Factor t(a).
-a*(a - 1)*(a + 1)*(4*a + 1)
Let p(b) = -b**3 - 18*b**2 + b + 21. Let s be p(-18). Factor 0 - 8/9*t**2 - 2/9*t - 2/9*t**5 - 4/3*t**s - 8/9*t**4.
-2*t*(t + 1)**4/9
Let y(c) be the second derivative of c**6/120 - c**5/10 + c**4/2 - 4*c**3/3 + 3*c**2/2 - 3*c. Let q(n) be the first derivative of y(n). Factor q(i).
(i - 2)**3
Let i(l) = -3*l**2 + 10*l + 1. Let p(x) = -7*x**2 + 21*x + 1. Let a(c) = 9*i(c) - 4*p(c). Let a(w) = 0. Calculate w.
-5, -1
Factor 0*x**2 + 3/4*x**3 + 3/4*x**5 - 3/2*x**4 + 0 + 0*x.
3*x**3*(x - 1)**2/4
Let c be 5*3*(-12)/(-45). Factor -4*t**2 - 3*t**3 + 2*t**2 - 3*t**c - 4*t**2 + 12*t**3.
-3*t**2*(t - 2)*(t - 1)
Let h be -9*20/(-45)*-3. Let y be (6/(-1))/(60/h). Solve y*g**2 - 4/5*g - 2/5 = 0.
-1/3, 1
Let i(n) be the first derivative of -3 + 0*n**5 - 1/42*n**4 + 2*n + 0*n**2 + 0*n**3 + 1/105*n**6. Let g(u) be the first derivative of i(u). Factor g(b).
2*b**2*(b - 1)*(b + 1)/7
Let k = -6 - -8. Suppose -2*q**3 + 0*q**2 + q**2 - 4 + 2*q + 3*