Let v(k) = k - 14. Let q be v(12). Let t = 5 + q. What is o in 8/7*o + 2/7*o**5 + 0 - 12/7*o**4 + 26/7*o**t - 24/7*o**2 = 0?
0, 1, 2
Let c(q) be the first derivative of 4*q**3/3 - 5*q**2 + 4*q + 3. Factor c(k).
2*(k - 2)*(2*k - 1)
Let n(f) be the second derivative of f**3 + 0 - 7*f - 1/12*f**4 - 9/2*f**2. Determine a, given that n(a) = 0.
3
Let s(b) be the second derivative of -b**5/70 - b**4/21 + b**3/21 + 2*b**2/7 - 3*b. Factor s(r).
-2*(r - 1)*(r + 1)*(r + 2)/7
Let u(m) be the third derivative of m**9/181440 - m**8/30240 + m**7/15120 - m**5/60 - 4*m**2. Let j(g) be the third derivative of u(g). Factor j(r).
r*(r - 1)**2/3
Let x(j) be the first derivative of j**4/2 + 16*j**3/3 + 16*j**2 - 12. Factor x(d).
2*d*(d + 4)**2
Suppose 3*p = -3*p. Let h be -1 - (44/7)/(-4). Suppose -2/7*s**2 + p + h*s = 0. Calculate s.
0, 2
Solve 8/13 - 24/13*g + 18/13*g**2 = 0 for g.
2/3
Suppose -h + 0 + 2 = 0. Let z = -281 + 284. What is g in -6/7*g - 2/7*g**z + 6/7*g**h + 2/7 = 0?
1
Let v(z) = 4*z**4 - 23*z**3 - 108*z**2 - 111*z - 40. Let h(r) = -2*r**4 + 11*r**3 + 54*r**2 + 55*r + 20. Let c(g) = -5*h(g) - 3*v(g). Factor c(f).
-2*(f - 10)*(f + 1)**3
Let q(x) be the first derivative of -x**7/70 - x**6/40 + x**2/2 - 4. Let f(i) be the second derivative of q(i). Suppose f(u) = 0. What is u?
-1, 0
Let k(u) be the second derivative of -u**7/1260 + u**6/120 - u**5/30 - u**4/12 - 7*u. Let g(b) be the third derivative of k(b). Suppose g(h) = 0. Calculate h.
1, 2
Let b = -27/8 - -159/40. Factor -b*y**3 + 0 - 6/5*y + 9/5*y**2.
-3*y*(y - 2)*(y - 1)/5
Let t(f) be the first derivative of 3*f + 1/4*f**3 + 3 + 3/2*f**2. Let t(g) = 0. Calculate g.
-2
Let q(u) be the second derivative of -u - 1/15*u**3 + 0 + 0*u**2 + 1/60*u**4. Suppose q(x) = 0. What is x?
0, 2
Let i(x) be the second derivative of -x**4/12 - 4*x**3/3 - 7*x**2/2 - 21*x. Solve i(q) = 0.
-7, -1
Let u(z) be the first derivative of 8/11*z + 1/22*z**4 - 5 + 10/33*z**3 + 8/11*z**2. Find h such that u(h) = 0.
-2, -1
Factor 2 + 2/3*y**2 + 8/3*y.
2*(y + 1)*(y + 3)/3
Let d(a) = -1. Let s(h) = 9*h**2 + 13*h. Let n(t) = -5*d(t) - s(t). Let q(v) = 20*v - 13 + 14*v**2 + 7 - 2. Let c(u) = -8*n(u) - 5*q(u). Factor c(w).
2*w*(w + 2)
Suppose 2*w - 3*s + 4 = s, 3*w = -2*s - 6. Let h be (1/(-15))/(w/18). Find p, given that 1/5*p**2 + 2/5 - h*p = 0.
1, 2
Let v(m) = -m + 1. Let w be v(0). Suppose -2*b + w = -13. Suppose -8*x**3 - 4*x - 2*x**3 - 4*x**5 - 11*x**4 + 18*x**5 + 18*x**2 - b*x**4 = 0. What is x?
-1, 0, 2/7, 1
Let z be (-26)/(-65)*10/18. Factor -2/3*m**3 + 2/9*m**2 + 0 + 0*m + 2/3*m**4 - z*m**5.
-2*m**2*(m - 1)**3/9
Let t be (-135)/100 + 35/20. Factor -t*x**3 + 2/5*x**2 + 2/5*x - 2/5.
-2*(x - 1)**2*(x + 1)/5
Solve -19*o + 21*o + 2*o**2 - 3*o**4 - 2*o**3 + o**4 = 0.
-1, 0, 1
Let i(q) be the second derivative of -3*q + 0*q**2 - 1/3*q**3 + 0 - 1/6*q**4. Factor i(j).
-2*j*(j + 1)
Let j = -29 - -35. Let f(m) be the third derivative of 0*m - 1/210*m**7 + 0 + 1/60*m**5 + 0*m**3 + m**2 - 1/120*m**j + 1/24*m**4. Factor f(z).
-z*(z - 1)*(z + 1)**2
Suppose -1 - 5 = -3*l. Let s(f) = -2*f**2 + 15*f - 16. Let u be s(6). Factor u*y + 2/9*y**3 + 0 + 4/3*y**l.
2*y*(y + 3)**2/9
Suppose -i**2 + 0 - 1/2*i - 1/2*i**3 = 0. What is i?
-1, 0
Let f(q) be the first derivative of 3 - 1/4*q**4 + 0*q + 0*q**2 - 1/3*q**3. What is d in f(d) = 0?
-1, 0
Let q(d) be the third derivative of -d**6/120 + d**5/30 + d**4/6 - d**3/6 - d**2. Let n be q(3). Suppose 0 + 2/7*u + 2/7*u**3 + 4/7*u**n = 0. Calculate u.
-1, 0
Suppose -225*o = -215*o. Factor o - 9/8*u - 1/8*u**3 - 3/4*u**2.
-u*(u + 3)**2/8
Let x(k) be the first derivative of -16*k**4/5 + 32*k**3/15 - 2*k**2/5 + 5. Factor x(i).
-4*i*(4*i - 1)**2/5
Let z(a) be the first derivative of 5*a**3/6 - 8*a**2 + 6*a - 10. Determine d so that z(d) = 0.
2/5, 6
Let b = 2180/3 - 726. Suppose -1/3*s + 1/3*s**2 - b = 0. What is s?
-1, 2
Let q be (-1)/((-15)/7) - (-20)/100. Let n(f) be the first derivative of -1/2*f + 7/8*f**2 - q*f**3 + 3/16*f**4 - 2. Factor n(h).
(h - 1)**2*(3*h - 2)/4
Let r(a) = 71*a + 1. Let k be r(-1). Let l be (0 + -5)*k/25. Factor -m - l*m**2 + 2*m**5 + 5*m - 8*m**4 + 18*m**3 - 2*m**4.
2*m*(m - 2)*(m - 1)**3
Let y = -9 + 12. Let l(p) be the third derivative of -7/60*p**6 - 2/3*p**y + 1/15*p**5 + 0*p + 0 + 7/12*p**4 - 2*p**2. Find q, given that l(q) = 0.
-1, 2/7, 1
Let o(v) = -5*v**3 + 5*v**2 - v - 8. Let r(s) = 6*s**3 - 4*s**2 + 2*s + 8. Let n(z) = -4*o(z) - 3*r(z). Determine c so that n(c) = 0.
-1, 1, 4
Let b(z) = z - 12. Let d be b(8). Let l be (-4 - -1)*d/6. Factor 5*i**l - 6*i - i**3 + 7*i**2 - 6*i - 2*i**3.
-3*i*(i - 2)**2
Let d = 253/21 + -82/7. Let b(x) be the first derivative of 0*x - x**4 + d*x**6 + 0*x**5 + 0*x**3 + 4 + x**2. Factor b(j).
2*j*(j - 1)**2*(j + 1)**2
What is l in l**3 + 8*l - 2*l**2 - 4*l + 6*l**2 + 0*l = 0?
-2, 0
Determine w, given that -6*w + 3/4*w**2 + 12 = 0.
4
Let t = 14/9 - 1/18. Solve 1 - 6*v**3 - 17/2*v**2 - t*v = 0 for v.
-1, -2/3, 1/4
Let b = -3/118 + 90/59. Factor -b*p - 2*p**2 + 1/2.
-(p + 1)*(4*p - 1)/2
What is y in y**3 + 14*y**5 + 24*y**4 + 21*y**4 + 3*y**2 + 13*y**5 + 20*y**3 = 0?
-1, -1/3, 0
Let p = 3 + -19/7. Let 3/7*s - p - 1/7*s**3 + 0*s**2 = 0. Calculate s.
-2, 1
Let n = 2 - -3. Let k(p) = 6*p**3 - p**2 + 1. Let c be k(1). Let g(f) = 4*f**2 + 2*f + 6. Let m(r) = -3*r**2 - 2*r - 5. Let z(l) = c*m(l) + n*g(l). Factor z(t).
2*t*(t - 1)
Let d(c) be the third derivative of -1/330*c**5 + 3*c**2 + 0*c + 0 - 1/66*c**4 + 0*c**3. Factor d(b).
-2*b*(b + 2)/11
Let y(x) be the first derivative of x**8/112 - x**7/35 + x**6/40 - x**2/2 - 5. Let d(j) be the second derivative of y(j). Determine t so that d(t) = 0.
0, 1
Let f = -31/12 + 2177/852. Let z = 81/355 + f. Factor 0 + 3/5*w**2 - z*w - 2/5*w**3.
-w*(w - 1)*(2*w - 1)/5
Let b be 2/(-12) - (-550)/420. Let z(i) be the first derivative of -2 - 2/21*i**3 - 4/7*i**2 - b*i. Find j such that z(j) = 0.
-2
Let i be 5/10 - (-278)/(-4). Let f be (-9)/12 - i/60. Factor -f + 3/5*q**3 - 8/5*q**2 + 7/5*q.
(q - 1)**2*(3*q - 2)/5
Let v(h) = 11*h**5 - 5*h**4 - 15*h**3 - 8*h**2 - h - 9. Let b(a) = -5*a**5 + 2*a**4 + 7*a**3 + 4*a**2 + 4. Let q(y) = -9*b(y) - 4*v(y). Factor q(u).
u*(u - 1)**2*(u + 2)**2
Determine l so that 1/4 - 1/2*l**2 + 1/4*l = 0.
-1/2, 1
Find k such that 2/7*k**5 - 8/7*k + 6/7*k**3 - 10/7*k**4 + 0 + 10/7*k**2 = 0.
-1, 0, 1, 4
Factor 3/5*t**2 + 9/5*t + 6/5.
3*(t + 1)*(t + 2)/5
Suppose k - 4*r = -0*k + 22, -5*r = 5*k + 15. Factor 2*p**2 - 2*p**5 + 2*p**k + 4*p**5 + 0*p**3 + 10*p**3 + 8*p**4.
2*p**2*(p + 1)**2*(p + 2)
Let s(k) = 5*k - 1. Let y be s(1). Let -1 - 1 + 1 + f**5 + f + y*f**2 - f**4 - 2*f**3 - 2*f**2 = 0. What is f?
-1, 1
Suppose 3*g = 19 + 2. Suppose -g*w = 3 - 10. Factor m - 1/4*m**2 - w.
-(m - 2)**2/4
Suppose 5*a + 3*h = 5, 11 = -4*h - 9. Let q(l) be the first derivative of -8/45*l**5 - 13/18*l**a - 10/9*l**3 - 1 - 7/9*l**2 - 2/9*l. Factor q(o).
-2*(o + 1)**3*(4*o + 1)/9
Suppose 3*z = z + 2, -4*l = 5*z + 3. Let v(r) = -r**4 + 20*r**3 + 21*r**2. Let c(j) = 4*j**3 + 4*j**2. Let u(n) = l*v(n) + 11*c(n). Factor u(g).
2*g**2*(g + 1)**2
Let a(i) be the second derivative of 0*i**2 + 0*i**3 - 2*i + 1/4*i**4 + 3/20*i**5 + 0. Factor a(w).
3*w**2*(w + 1)
Suppose 0 = x + 32 - 33. Let d(c) be the first derivative of -2/35*c**5 - 8/7*c**2 + 8/7*c + 2/21*c**3 + x - 1/21*c**6 + 5/14*c**4. Factor d(v).
-2*(v - 1)**3*(v + 2)**2/7
Let d(i) be the second derivative of -9/10*i**5 - 1/3*i**3 - 2/21*i**7 + 5/6*i**4 + 7/15*i**6 + 0*i**2 + 0 - 3*i. Factor d(m).
-2*m*(m - 1)**3*(2*m - 1)
Let f(d) be the second derivative of d**5/40 + d**4/24 - 3*d. Factor f(z).
z**2*(z + 1)/2
Let c(g) be the second derivative of g**6/45 - g**5/10 - g**4/9 + 4*g**3/3 - 8*g**2/3 + 32*g. Factor c(s).
2*(s - 2)**2*(s - 1)*(s + 2)/3
Determine k, given that 0 - 4/15*k**2 + 0*k + 0*k**4 - 2/5*k**3 + 2/15*k**5 = 0.
-1, 0, 2
Let g(d) = -8*d**3 + 13*d**2 + 8*d + 13. Let r(f) = -4*f**3 + 6*f**2 + 4*f + 6. Let t(a) = 6*g(a) - 13*r(a). Factor t(z).
4*z*(z - 1)*(z + 1)
Let x(k) = k**2 - 2*k - 3. Let c(y) be the third derivative of y**5/60 - y**4/12 - 2*y**3/3 - y**2. Let b(g) = 4*c(g) - 5*x(g). Factor b(u).
-(u - 1)**2
Factor -1/5*g**3 - 2/5*g**2 + 0*g + 0.
-g**2*(g + 2)/5
Let v(r) = 2*r**3 + 6*r**2 - 8*r - 8. Let u(d) = d**3 + 2*d**2 - 3*d - 3. Let x be 2 + 1