7/210 - n**6/30 - n**5/12 - n**4/12 - 22*n**2. Factor b(u).
-u*(u + 1)**2*(u + 2)
Let d be -1 + 1 - (8 + -10). Factor -z**2 - 6 + 2*z**d + 6.
z**2
Suppose -26 = -5*g - 2*q - 2*q, 0 = 3*q - 12. Suppose -k = g*k. Suppose 2*r**3 + 0 - 2*r + k = 0. Calculate r.
-1, 0, 1
Let o(b) = -b**2 + 3*b. Let t(n) = -n**2 + 5*n. Let q = -3 - -6. Let f(d) = q*t(d) - 5*o(d). Solve f(i) = 0.
0
Let v(k) be the third derivative of k**6/480 - k**5/80 + 2*k**3/3 + 2*k**2. Let g(s) be the first derivative of v(s). Let g(r) = 0. Calculate r.
0, 2
Let b = -1 - -16. Suppose 2*c + 3*c = b. Factor -2 + 0*a**2 - 3*a**2 + 8*a - c*a**2.
-2*(a - 1)*(3*a - 1)
Let a(v) = v**3 + 3*v**2 - 2*v - 4. Let d be a(-3). Let k be (3 + -4)*2 - (-7)/3. Suppose 1/3*c**d - k*c + 0 = 0. What is c?
0, 1
Suppose 28 = 5*u + 9*u. Suppose 0 + 1/4*v + 0*v**u - 1/4*v**3 = 0. Calculate v.
-1, 0, 1
Let a = 12 - 7. Suppose 6 = a*u - 14. Factor 0*o**3 + 0*o + 1/4*o**u - 1/2*o**2 + 1/4.
(o - 1)**2*(o + 1)**2/4
Let k(t) = 2*t**2 + 6. Let m(x) = 8*x**2 + 5*x + 6. Let b(v) = -9*v**2 - 6*v - 5. Let j(n) = 5*b(n) + 6*m(n). Let s(g) = -4*j(g) + 7*k(g). Factor s(z).
2*(z - 1)*(z + 1)
Suppose 7 = f - 2*u, 10 = 3*f + u + 4*u. Suppose d + 4*d + 20 = f*i, 4*i - 16 = 5*d. Solve 2/5*w**4 + 0*w**3 + 0*w + d - 2/5*w**2 = 0 for w.
-1, 0, 1
Suppose p - 3 = 1. Suppose -4*v = 4*w + p, -3*w - 23 = -0*v - 2*v. Solve -g**v - g**4 - 2*g**5 - g**5 = 0 for g.
-2/3, 0
Suppose -3*r + 10 = -5, 5 = -3*i + r. Let t(u) be the first derivative of 0*u**2 + i*u + 2/35*u**5 - 2 + 0*u**3 - 1/14*u**4. Solve t(b) = 0 for b.
0, 1
Let g(a) = -10*a**2 + 100*a - 500. Let p(v) = 11*v**2 - 100*v + 500. Let m(w) = 6*g(w) + 5*p(w). Find y, given that m(y) = 0.
10
Let r = 82 - 82. Let g(z) be the second derivative of -2*z + 0*z**2 + r - 1/48*z**4 + 1/120*z**6 - 1/80*z**5 + 1/24*z**3. Suppose g(j) = 0. Calculate j.
-1, 0, 1
Let b(g) be the first derivative of -5*g**4/4 + 20*g**3/3 + 2. Let b(z) = 0. What is z?
0, 4
Let a be (-26)/4 - (-2)/4. Let q(z) = -z**2 - 6*z + 2. Let x be q(a). Factor -x*i**2 + 3 - 1 + 2 + 2*i.
-2*(i - 2)*(i + 1)
Let k(b) be the third derivative of -b**5/15 - b**4/3 + 2*b**3 - 13*b**2. Factor k(u).
-4*(u - 1)*(u + 3)
Let w = -58/2399 + 2977565/16793. Let d = w + -177. Factor 0 - d*r**2 - 2/7*r.
-2*r*(r + 1)/7
Factor 0*y**3 - 2/5*y**4 + 0 - 4/5*y + 6/5*y**2.
-2*y*(y - 1)**2*(y + 2)/5
Let l(h) = h**2. Let z(q) = q**3 - 2*q**2 - 2*q. Let b(k) = -3*l(k) - 3*z(k). Factor b(t).
-3*t*(t - 2)*(t + 1)
Let y(r) = 2*r**2 - 3*r + 3. Let p be y(2). Suppose p*w + 12 = j, j - w - 4 = -0*j. Factor -4 - t**j + 3*t - 5*t + 0 + 3*t**2.
2*(t - 2)*(t + 1)
Let i be -3 + (1 + 0)*6. Let a(q) be the third derivative of 0 + 1/24*q**4 + 1/60*q**5 + 0*q**3 - i*q**2 + 0*q. Find g such that a(g) = 0.
-1, 0
Let s = -4 + 8. Let h = s - -10. Let f(d) = 2*d**2 + 5*d + 3. Let o(g) = -6*g**2 - 14*g - 8. Let w(b) = h*f(b) + 5*o(b). Solve w(i) = 0 for i.
-1, 1
Let g be (-3)/(0 + -3) + 4/(-8). Find k, given that 1/2*k**2 - g*k - 1/2 + 1/2*k**3 = 0.
-1, 1
Let u(w) be the second derivative of 1/12*w**6 + 0*w**2 + 0*w**3 - 2*w + 7/40*w**5 + 1/12*w**4 + 0. Factor u(y).
y**2*(y + 1)*(5*y + 2)/2
Let j(d) be the first derivative of -d**6/18 - 2*d**5/5 - 13*d**4/12 - 4*d**3/3 - 2*d**2/3 + 5. Let j(w) = 0. What is w?
-2, -1, 0
Let f(u) be the third derivative of u**8/1008 - u**7/315 + u**5/90 - u**4/72 + 6*u**2. What is t in f(t) = 0?
-1, 0, 1
Let r = -3 + 10. Let s = r + -4. Solve 3*n**2 - n**3 + 2 + n**2 + 2*n**s + 5*n = 0.
-2, -1
Suppose 0*u + 2/15*u**3 + 0 + 2/15*u**2 = 0. What is u?
-1, 0
Suppose -h = 3*h + 64. Let l be (-10)/(-36) - h/72. Suppose -1/2*s - 1/3*s**2 + 1/3*s**3 + l*s**4 + 1/6*s**5 - 1/6 = 0. What is s?
-1, 1
Suppose l + 3*l = 36. Suppose 3*o = -3 + l. Factor 0 + 0*c**o + 0*c**4 - 1/2*c**5 - 1/2*c + c**3.
-c*(c - 1)**2*(c + 1)**2/2
Let b(a) be the second derivative of 1/30*a**3 + 1/60*a**4 + 0 - 6*a + 0*a**2. Solve b(v) = 0 for v.
-1, 0
Let c = -67/21 + 27/7. Suppose -2/3*m**2 + 4/3*m - c = 0. Calculate m.
1
Let i(t) be the second derivative of -t**4/60 - t**3/10 + 14*t - 3. Factor i(h).
-h*(h + 3)/5
Let i = 29 - 115/4. Let l be 3/(-1) - (-2 - 1). Suppose 0*r**2 + l - i*r + 1/4*r**3 = 0. What is r?
-1, 0, 1
Factor 51/5*j**2 - 48/5*j - 12/5*j**3 + 9/5.
-3*(j - 3)*(j - 1)*(4*j - 1)/5
Let i(s) be the first derivative of 1/2*s**4 + 3 + 0*s**3 - 3*s**2 - 4*s. Factor i(k).
2*(k - 2)*(k + 1)**2
Let o be (-15270)/(-18216) + 2/8. Let t = o - -2/759. Solve t*k**5 + 0 + 4/11*k + 38/11*k**4 + 4*k**3 + 2*k**2 = 0 for k.
-1, -2/3, -1/2, 0
Let b = -1106/5 - -222. Let i(w) be the first derivative of -2 - 2/5*w - 2/3*w**3 - b*w**2 - 1/5*w**4. Factor i(v).
-2*(v + 1)**2*(2*v + 1)/5
Let s(h) = 4*h**3 + 9*h**2 + 12*h + 1. Let m(q) = 4*q**3 + 10*q**2 + 12*q + 2. Let o(b) = -3*m(b) + 2*s(b). Find u such that o(u) = 0.
-1
Let n(l) be the first derivative of -3/4*l**4 - 9 + 0*l**2 - 2/3*l**3 + 0*l + 0*l**5 + 1/6*l**6. Let n(g) = 0. What is g?
-1, 0, 2
Let a(r) be the third derivative of -r**11/554400 - r**10/252000 + r**5/10 + 4*r**2. Let n(c) be the third derivative of a(c). Factor n(y).
-3*y**4*(y + 1)/5
Let w be 66/9*15/10. Suppose -5*j + w = 1. Suppose 0*y**4 + 0*y + 1/5*y**3 - 1/5*y**5 + 0 + 0*y**j = 0. Calculate y.
-1, 0, 1
Let a = 1 - -1. Suppose 2*i - 12 = -a*i. Factor 0*d**2 - i*d**2 - d + 2*d**2.
-d*(d + 1)
Let d(u) = -u**2 + u - 3. Let z(x) = x**2 - x + 4. Suppose 5*s + 3 + 12 = 0. Let a(o) = s*z(o) - 4*d(o). Let a(l) = 0. What is l?
0, 1
Let c be (-346)/14 + (-20)/70. Let u be 0 - 5/(c/15). Determine s, given that -1/4*s**u + 1/4*s - 1/4 + 1/4*s**2 = 0.
-1, 1
Suppose 2*z = -0*z. Let f(k) be the second derivative of 1/18*k**4 + 2/9*k**3 + z + 2*k + 1/3*k**2. Solve f(q) = 0 for q.
-1
Factor -30*y**3 + 4*y**3 + 40*y + 36 - 4*y**4 - 14*y**3 - 32*y**2.
-4*(y - 1)*(y + 1)**2*(y + 9)
Let y(v) be the third derivative of v**6/300 + v**5/150 - v**4/12 + v**3/5 + 24*v**2. Let y(j) = 0. What is j?
-3, 1
Suppose -4*o + 16 = m + 5, m = 4*o - 21. Suppose 4*v - o = -2*g, v - g - 10 = -v. Factor 0*c**v + 0*c + 1/2*c**2 - 1/4*c**4 - 1/4.
-(c - 1)**2*(c + 1)**2/4
Let g(y) be the second derivative of y**4/24 + 5*y**3/6 + 25*y**2/4 - 6*y. Find m, given that g(m) = 0.
-5
Let w be (-2)/30*9/(-6). Let f(r) be the third derivative of 0 + r**2 + w*r**5 + 0*r - 1/4*r**4 + 1/3*r**3 - 1/60*r**6. Factor f(s).
-2*(s - 1)**3
Let r = -41/2 - -21. Factor r*x**3 + 0*x + 1/2*x**4 - 1/2*x**2 - 1/2*x**5 + 0.
-x**2*(x - 1)**2*(x + 1)/2
Let y be (-158)/8 + 10 + 10. Solve y*h**3 + 3/2*h**2 + 3*h + 2 = 0.
-2
Suppose 3*c - l = 3*l - 20, 3*l - 15 = -3*c. Let h = 3 - 7/3. Let -h*q - 1/3*q**2 + c = 0. Calculate q.
-2, 0
Let u be (-15)/(375/130) + 8. Suppose 7 - 3 = 2*b. Suppose 2/5*q**4 - b*q**3 + 18/5*q**2 + 4/5 - u*q = 0. What is q?
1, 2
Suppose 5*q + 2*o - 4 = 3, -5*q = -4*o - 31. Let h(r) = -r**2 + 5*r - 4. Let d be h(q). Suppose 0*c + 0 + 2/5*c**4 + 0*c**3 - 2/5*c**d = 0. What is c?
-1, 0, 1
Factor 32*m + 3 - 50*m**3 + 10*m**2 + 0 + 5.
-2*(m - 1)*(5*m + 2)**2
Let j(v) be the third derivative of v**2 + 0 + 0*v + 1/12*v**3 + 1/96*v**4 - 1/80*v**5. Factor j(r).
-(r - 1)*(3*r + 2)/4
Let p be ((-1)/3)/(5/(-60)). Let -166*d**3 + 39*d**4 + 180*d**2 + d**p + 3*d - 16 - 11*d = 0. What is d?
-1/4, 2/5, 2
Factor -2*m + 0*m + 2*m + 20*m**2 - 5*m.
5*m*(4*m - 1)
Let t(w) be the third derivative of w**6/600 - 7*w**5/300 - w**4/15 + 27*w**2. Determine s so that t(s) = 0.
-1, 0, 8
Let m = 31 - 30. Let k(a) = 4*a**2 + 2*a - 2. Let w be k(m). Factor 4/5*c**3 - 3/5*c - 1/5*c**5 + 2/5*c**2 - 2/5 + 0*c**w.
-(c - 2)*(c - 1)*(c + 1)**3/5
Let i(t) be the second derivative of 3/20*t**5 + 3*t - 3/40*t**6 + 0*t**2 + 0*t**3 + 0 + 1/4*t**4. Factor i(a).
-3*a**2*(a - 2)*(3*a + 2)/4
Let p = 33 - 32. Let m(c) be the first derivative of -2/5*c**5 + 0*c**2 + 0*c - p + c**4 - 2/3*c**3. Let m(q) = 0. What is q?
0, 1
Let x(u) be the second derivative of -u**5/72 - u**4/36 + u**3/36 + u**2 + 7*u. Let q(f) be the first derivative of x(f). Let q(p) = 0. Calculate p.
-1, 1/5
Factor 1/4*d**2 - 1/4*d + 0.
d*(d - 1)/4
Factor -2/9 - 4/9*k**3 - 2/9*k**5 - 4/9*k**2 + 2/3*k**4 + 2/3*k.
-2*(k - 1)**4*(k + 1)/9
Let o(f) be the second derivative of 7/15*f**6 + 1/2*f**5 - 1/3*f**4 + 0 + 0*f**3 + 0*f**2 + f. Factor o(v).
2*v**2*(v + 1)*(7*v - 2)
Let a(v) be