et r be o(8). Suppose 6*k - 2*h + 2 = k, -4*h = r*k - 4. Solve -2/7*t**3 + k + 2/7*t + 0*t**2 = 0 for t.
-1, 0, 1
Let t(a) = -8*a**4 + a**3 - 7*a**2 - 7*a. Let u(d) = -d**4 - d**2 - d. Let p(w) = 4*t(w) - 28*u(w). Factor p(z).
-4*z**3*(z - 1)
Suppose -4*w = -0*w + 72. Let c be 3 + w/10 + -1. Factor 1/5*o**2 - 1/5*o**3 + c*o - 1/5.
-(o - 1)**2*(o + 1)/5
Factor -i**4 - 6597 + 8*i + 6591 + 11*i + 9*i**3 - 21*i**2.
-(i - 6)*(i - 1)**3
Suppose b = 3*f + 3*b - 19, 9 = 3*f - 3*b. Suppose 5*w - 10 = f. Factor -2/3*o**w - 2/3*o**2 + 2/3*o + 2/3.
-2*(o - 1)*(o + 1)**2/3
Factor r**2 - 21*r**2 - 15*r - 5*r**3 + 0*r**2.
-5*r*(r + 1)*(r + 3)
Let v = 353 - 2463/7. Let t(r) be the first derivative of 40/7*r**2 - 3 - v*r - 78/7*r**3 + 81/14*r**4. Solve t(h) = 0 for h.
2/9, 1
Suppose -d = 3*d - 48. Suppose 3 = -3*a, -g + 5*g = 4*a + d. Determine n so that -g*n**3 + 4*n - 2*n + 0*n = 0.
-1, 0, 1
Factor -5*d - 3*d**3 - 12*d**2 - 5*d + 8*d - 10*d.
-3*d*(d + 2)**2
Let t(b) be the first derivative of 2*b**2 + 1/80*b**5 - 3 + 0*b**3 + 1/48*b**4 + 0*b + 1/480*b**6. Let p(z) be the second derivative of t(z). Factor p(o).
o*(o + 1)*(o + 2)/4
Let y(w) = -w**3 - w**2 + w. Let v be y(-2). Let k = -24/17 - -113/68. Determine z, given that 1/2*z**v + k*z + 0 + 1/4*z**3 = 0.
-1, 0
Let o(s) = -5*s**3 - s**2 + s + 1. Let b be o(-1). Suppose b*k = -0*k. Let 2/9*a + k - 4/9*a**2 + 2/9*a**3 = 0. Calculate a.
0, 1
Let z(g) be the first derivative of 0*g**2 - 2/3*g**3 + 0*g + 1/2*g**4 - 1/10*g**5 + 7. Suppose z(w) = 0. What is w?
0, 2
Suppose 0 + 2 = a. Let h(s) be the second derivative of -1/25*s**5 + 0 + 0*s**3 + 1/30*s**4 + 0*s**a + s - 1/75*s**6 + 2/105*s**7. Suppose h(i) = 0. What is i?
-1, 0, 1/2, 1
Let x = 10 + -9. Let p be (-3 - -1)*x/(-5). Find f such that p*f**2 + 2/5*f + 0 = 0.
-1, 0
Let q(g) = 4*g**3 + 1 - 2*g + g**4 + 2*g**3 + 4*g**2 - 4*g. Let s(r) = 2*r**4 + 13*r**3 + 9*r**2 - 13*r + 2. Let u(b) = -13*q(b) + 6*s(b). Factor u(o).
-(o - 1)**2*(o + 1)**2
Let p(u) = u**3 - 8*u**2 + 7*u + 3. Let m(f) = f**3 - f + 1. Let i(a) = -6*m(a) + 2*p(a). Find w, given that i(w) = 0.
-5, 0, 1
Let m(i) = -43*i**3 + 2*i**2 - i. Let o be m(1). Let w = o - -213/5. Let 1/5 + 4/5*l + w*l**2 = 0. What is l?
-1, -1/3
Let l(o) be the third derivative of 1/360*o**5 + 0 + 0*o**3 + 1/144*o**4 - 2*o**2 + 0*o. Determine a, given that l(a) = 0.
-1, 0
Let q(y) be the second derivative of 0 + 0*y**3 + 0*y**2 - 3/80*y**5 - y - 1/48*y**4 - 1/168*y**7 - 1/40*y**6. Factor q(d).
-d**2*(d + 1)**3/4
Let g = 704 + -236543/336. Let n(l) be the third derivative of 0*l**4 + 1/70*l**7 + 0*l**3 + 2*l**2 + 0*l + 1/60*l**5 + 1/40*l**6 + g*l**8 + 0. Factor n(y).
y**2*(y + 1)**3
Let 1/7*n**3 + 0 - 1/7*n**4 + 0*n**2 + 0*n = 0. Calculate n.
0, 1
Let t be (-1)/(10/(-32)) - (-2)/(-10). Factor 0 + 0*v**2 - 1/3*v**t + 1/3*v.
-v*(v - 1)*(v + 1)/3
Let a = -11 + 17. Factor -3*j**2 + 2*j**2 - 3*j + a - j**2 - j**2.
-3*(j - 1)*(j + 2)
Let c(i) = -i**3 - 3*i - 3. Let w be c(-2). Let m = w + -7. Factor 0*a**3 + 2*a**m - a**3 + 3*a**3.
2*a**3*(a + 1)
Let o(t) be the third derivative of t**6/60 + t**5/30 - t**4/12 - t**3/3 - 34*t**2. Factor o(x).
2*(x - 1)*(x + 1)**2
Suppose 0*u**3 + 2/7*u**4 + 1/7*u**5 - 1/7*u - 2/7*u**2 + 0 = 0. What is u?
-1, 0, 1
Suppose -47*y - 26 = -60*y. Suppose 18/5*t**3 + 2/5*t**5 + 0 + y*t**4 + 4/5*t + 14/5*t**2 = 0. What is t?
-2, -1, 0
Factor -2/3*k + 2/3*k**2 - 2/9*k**3 + 2/9.
-2*(k - 1)**3/9
Suppose -5*k - 7*y + 5*y + 5 = 0, -5*y - 25 = 0. Suppose -1/2*f**k - 1 + 3/2*f**2 - 1/2*f**4 + 1/2*f = 0. What is f?
-2, -1, 1
What is y in 1/5*y**3 - 3/5*y**2 + 3/5*y - 1/5 = 0?
1
Let o be (-44)/9*172/(-964). Let t = o - -4/241. Solve -2/9*f**2 + t*f - 8/9 = 0 for f.
2
Let d(z) = -3*z + 42. Let s be d(14). Let b(w) be the second derivative of -1/105*w**6 - 3*w - 1/21*w**3 + 1/42*w**4 + 0 + 1/70*w**5 + s*w**2. Factor b(v).
-2*v*(v - 1)**2*(v + 1)/7
Let z(h) be the second derivative of -3*h + 1/165*h**6 + 0*h**2 + 0*h**3 - 1/55*h**5 + 1/66*h**4 + 0. Factor z(g).
2*g**2*(g - 1)**2/11
Let x(c) be the first derivative of c**4/14 + 2*c**3/7 + 2*c**2/7 + 34. Factor x(f).
2*f*(f + 1)*(f + 2)/7
Let o(s) be the second derivative of s**8/3360 + s**7/672 - s**5/96 - s**4/48 - 5*s**3/6 - s. Let a(c) be the second derivative of o(c). Solve a(q) = 0.
-2, -1, -1/2, 1
Let r be (-1)/(14/(-6) + 2). Determine j, given that -3/4*j + 3/4*j**2 + 3/4*j**r - 3/4 = 0.
-1, 1
Let x be (21/(-4))/(-3) - 1. Suppose -5*i + 15 = 5. Suppose 0*u + 0 + 1/4*u**i - 1/4*u**5 + x*u**4 - 3/4*u**3 = 0. What is u?
0, 1
Let c = 20 + -12. Determine k, given that -c*k**4 - 42*k**2 - 9*k**4 - 50*k**3 + 6*k**4 - 7*k**4 - 6*k + 4 = 0.
-1, 2/9
Let b(h) be the second derivative of h**6/165 - h**5/110 - 6*h. Let b(t) = 0. Calculate t.
0, 1
Let i = -2/141 + 100/423. Suppose 2*s - 5*o + 6 = -11, 10 = 2*o. Factor i*b**2 + 2/3*b**3 - 2/3*b - 4/9 + 2/9*b**s.
2*(b - 1)*(b + 1)**2*(b + 2)/9
Let q(l) be the first derivative of l**4/20 - 2*l**3/15 + 4. Let q(c) = 0. What is c?
0, 2
Let g(w) be the second derivative of -1/90*w**5 + 0 + 0*w**2 + w - 2/27*w**3 + 1/18*w**4. Factor g(f).
-2*f*(f - 2)*(f - 1)/9
Let q(a) = -a**3 + 11*a**2 + 16*a - 48. Let g be q(12). Let 0*f + 2/13*f**2 - 2/13*f**5 + 6/13*f**4 - 6/13*f**3 + g = 0. What is f?
0, 1
Suppose -2*h - 45 = -5*h. Let v = -11 + h. Factor 0*g**2 - 3 - v*g + 1 - 2*g**2.
-2*(g + 1)**2
Factor -3*r**2 - 2 + 3*r**3 - r**2 - 5*r - 4*r**3.
-(r + 1)**2*(r + 2)
Let g(i) be the second derivative of i**5/100 - 3*i**4/40 + i**3/5 - 3*i**2/2 - 3*i. Let c(q) be the first derivative of g(q). Find t such that c(t) = 0.
1, 2
Find l such that 1/2*l**4 + 0*l**3 + 1/2 + 0*l - l**2 = 0.
-1, 1
Let g(u) be the third derivative of -u**7/140 - 13*u**6/80 - 9*u**5/8 + 25*u**4/16 + 125*u**3/2 - 13*u**2 + 2*u. Factor g(z).
-3*(z - 2)*(z + 5)**3/2
Let p(x) be the first derivative of 3*x**3/5 + 3*x**2/2 + 6*x/5 - 5. Factor p(g).
3*(g + 1)*(3*g + 2)/5
Solve 243/8 - 27/4*j + 3/8*j**2 = 0 for j.
9
Suppose -3 = 5*m - 13. Factor 0*y**3 + 2*y**3 + 10*y**2 + m + 9*y + 0 + y**3.
(y + 1)*(y + 2)*(3*y + 1)
Let g(d) = d**2 + 10*d + 18. Let c be g(-8). Let z**c + 0 - 1/2*z**3 - 1/2*z = 0. What is z?
0, 1
Suppose 62 = 4*x + 5*c - 31, 0 = -2*c - 6. Let j = x - 25. Let -j*k**2 + 1/2 + 3/2*k = 0. What is k?
-1/4, 1
Let m be (2/(-15))/(-2*3/18). Suppose -4/5 + 6/5*c - m*c**2 = 0. Calculate c.
1, 2
Let a(d) be the first derivative of -2*d**3/3 + 7*d**2 - 12*d - 7. Determine s so that a(s) = 0.
1, 6
Let f(m) be the third derivative of m**7/840 + m**6/180 + m**5/120 + 2*m**3/3 + m**2. Let a(x) be the first derivative of f(x). Suppose a(d) = 0. Calculate d.
-1, 0
Factor -j**2 + 1 + 1/3*j - 1/3*j**3.
-(j - 1)*(j + 1)*(j + 3)/3
Let k(q) be the first derivative of -3*q**4/4 + 3*q**2/2 + 5. Factor k(u).
-3*u*(u - 1)*(u + 1)
Let d(j) be the second derivative of -3*j**5/20 - j**4/4 + 2*j**3 + 6*j**2 - 16*j. Find s such that d(s) = 0.
-2, -1, 2
Let o(t) = 2*t**2 + 12*t + 4. Let m(x) = 4*x - 5*x - 1 + 0 + 2. Let z = 2 - 1. Let u(i) = z*o(i) + 4*m(i). Suppose u(s) = 0. Calculate s.
-2
Factor -2/3*r**3 - 1/3*r**2 + 1/6*r**5 + 1/2*r + 1/3*r**4 + 0.
r*(r - 1)**2*(r + 1)*(r + 3)/6
Let d(h) = h**3 - 5*h**2 - h + 7. Let q be d(5). Suppose -3*s = -7*s + 2*y + 20, 3*s = 2*y + 17. Factor 3/4*v**4 - 1/4*v - 3/4*v**q + 0 + 1/4*v**s.
v*(v - 1)*(v + 1)*(3*v + 1)/4
Let p(x) = 6*x**4 + 6*x**3 - 3*x**2 + 3*x. Let a(k) = 7*k**4 + 7*k**3 - 4*k**2 + 4*k. Let v(l) = 3*a(l) - 4*p(l). Factor v(w).
-3*w**3*(w + 1)
Suppose 5*c - 7 = -12*f + 9*f, 0 = 5*c - 2*f - 12. Let g(o) be the second derivative of 1/27*o**3 - 2/9*o**2 - c*o + 1/54*o**4 + 0. Let g(v) = 0. Calculate v.
-2, 1
Let n(b) be the second derivative of 1/5*b**5 + 0*b**3 + 0*b**2 + 2/3*b**4 + 0 - 5*b - 1/42*b**7 - 1/15*b**6. Determine g, given that n(g) = 0.
-2, 0, 2
Suppose -6 = -4*s + 2. Factor -7*v**2 - v**s + 7*v**2 + v + 2.
-(v - 2)*(v + 1)
Let f = 8 - 5. Suppose -3*s - z + 8 = 0, -f*s + z + z = 7. Factor -4*w**2 + w**4 + 0*w**2 + 2*w**2 + s.
(w - 1)**2*(w + 1)**2
Let i(o) = -o - 16. Let z be i(-18). Solve 2/5 + 2/5*r**5 + 2*r + 4*r**z + 4*r**3 + 2*r**4 = 0.
-1
Let o(s) be the first derivative of -s**4/2 - 6. Factor o(j).
-2*j**3
Let i be (1 - 1)*(-2)/4. Let m be 8/(-6) - (i + -2). Factor 4/3 + m*v**3 - v**2 - 4/3*v + 1/3*v**4.
(v - 1)