 14*n**3 + 8 - 8*n = 0. What is n?
-1, 2/3, 1, 2
Let f(k) be the second derivative of k**6/900 + k**5/150 - k**4/20 + 5*k**3/6 + 9*k. Let z(j) be the second derivative of f(j). Factor z(h).
2*(h - 1)*(h + 3)/5
Let o(n) = 9*n**3 - 4*n**2 + 11*n + 8. Let u(b) = -20*b**3 + 8*b**2 - 24*b - 18. Let h(g) = -9*o(g) - 4*u(g). Find r such that h(r) = 0.
0, 1, 3
Let n = 1/18115 - -289833/126805. Factor 2/7*x**3 + 0 + n*x**2 + 0*x.
2*x**2*(x + 8)/7
Suppose -10 = -7*l + 2*l. Suppose -l*f + 21 - 17 = 0. Factor 0 + 2/15*s**3 - 2/5*s**f + 4/15*s.
2*s*(s - 2)*(s - 1)/15
Let q be (-338)/396 + 1 - 11/121. Let x(k) be the first derivative of -2/27*k**3 + q*k**2 + 1/36*k**4 + 0*k + 2. Factor x(v).
v*(v - 1)**2/9
Let k(s) be the first derivative of -s**3/18 + 7*s**2/12 - s + 18. Let k(l) = 0. What is l?
1, 6
Let m(v) be the first derivative of 2*v**3 + 3*v + 27/4*v**2 + 1. Suppose m(t) = 0. Calculate t.
-2, -1/4
Let p(x) = -x**3 - 16*x**2 + 2*x + 36. Let w be p(-16). Factor 15*k**3 + 28*k**4 - 12*k**3 - 24*k**w + k**5.
k**3*(k + 1)*(k + 3)
Let n(o) = -3*o - 9. Let z be n(-6). Suppose -4*l + a = -z, -3*a - 10 = -l - 5. Factor l*j**4 + 0*j**4 + 6*j**2 - 8*j**3 + 4*j**2 - 18*j + 14*j.
2*j*(j - 2)*(j - 1)**2
Suppose 2*r = -2*n - 6, 4*n - 3*r + 5*r = -2. Factor 7*o**n - 2*o - 10*o**2 + 0*o**2 + 5*o**2.
2*o*(o - 1)
Let p = 2417/2550 - 16/17. Let k(b) be the third derivative of -3*b**2 - 1/600*b**6 + 0*b + 0 + 0*b**4 + 1/1050*b**7 + 0*b**3 - p*b**5. Factor k(d).
d**2*(d - 2)*(d + 1)/5
Let f(a) be the first derivative of a**7/3780 + 8*a**3/3 - 23. Let q(u) be the third derivative of f(u). Suppose q(t) = 0. Calculate t.
0
Let g(m) be the second derivative of -m**8/1680 + m**7/315 + m**6/180 - m**5/15 + 13*m**4/12 + 6*m. Let q(h) be the third derivative of g(h). Factor q(w).
-4*(w - 2)*(w - 1)*(w + 1)
Let t(c) be the second derivative of -3*c**6/20 + 33*c**5/80 + 3*c**4/8 - 9*c**3/8 + 3*c**2/4 - 2*c - 175. Let t(p) = 0. Calculate p.
-1, 1/3, 1/2, 2
Let t(v) be the third derivative of 61*v**5/30 + 59*v**4/12 - 2*v**3/3 + v**2 + 10*v. Factor t(w).
2*(w + 1)*(61*w - 2)
Let b(y) be the second derivative of -1/40*y**5 + 0 - 1/24*y**4 + y + 1/12*y**3 + 1/4*y**2. Factor b(k).
-(k - 1)*(k + 1)**2/2
Suppose -8/7*u**2 + 32/7 + 2/7*u**3 - 8/7*u = 0. What is u?
-2, 2, 4
What is m in 3*m - 4 + 4*m**2 + 3/4*m**3 = 0?
-4, -2, 2/3
Solve 90/17*i**4 + 0 - 2*i**3 - 48/17*i**2 - 8/17*i = 0 for i.
-2/5, -2/9, 0, 1
Determine q, given that -4/13*q + 18/13*q**2 + 0 - 14/13*q**3 = 0.
0, 2/7, 1
Let a be (-1023)/372 + (-46)/(-8). Determine g, given that -2*g**2 - 2*g + 0 + 1/2*g**4 + 1/2*g**a = 0.
-2, -1, 0, 2
Let o(v) be the third derivative of 21*v**2 + 1/30*v**5 + 0*v**4 + 0*v - 1/105*v**7 + 0 + 1/60*v**6 - 1/168*v**8 + 0*v**3. Let o(d) = 0. Calculate d.
-1, 0, 1
Suppose 21 = -2*h + 9*h. Suppose -2*g - 6 = -5*g + h*l, 0 = 4*l. Determine a, given that -a**3 - 5/2*a**4 + 3/2*a**5 - 1/2*a - 1/2 + 3*a**g = 0.
-1, -1/3, 1
Factor 10/7 + 1/7*n**3 - 1/7*n - 10/7*n**2.
(n - 10)*(n - 1)*(n + 1)/7
Let w(t) be the second derivative of t**5/10 + 7*t**4/6 + 10*t**3/3 + 494*t. Solve w(r) = 0.
-5, -2, 0
Let n(l) be the third derivative of -2*l**6/3 + 2*l**5 + 225*l**4/8 - 405*l**3/2 + 4*l**2 + 29*l. Factor n(o).
-5*(o + 3)*(4*o - 9)**2
Let i(a) be the third derivative of -a**6/120 + 3*a**5/20 - 13*a**4/12 + 4*a**3 - a**2 - 138. Find y such that i(y) = 0.
2, 3, 4
Factor 8*a**2 + 30*a**3 - a + 3*a + 31*a**3 - 55*a**3.
2*a*(a + 1)*(3*a + 1)
Let d(y) = -9*y**3 - 3*y**2 - y - 7. Let u(b) = 7*b**3 + 3*b**2 + b + 5. Let k(f) = -4*d(f) - 5*u(f). Factor k(h).
(h - 3)*(h - 1)*(h + 1)
Let t be 52/(-7) + (16 - (-80)/(-10)). Factor 2/7*b**5 + 4/7*b**2 + 0 - 2/7*b + 0*b**3 - t*b**4.
2*b*(b - 1)**3*(b + 1)/7
Let s(x) be the third derivative of x**6/300 + x**5/10 + 7*x**4/30 - 3*x**2 - 8. Factor s(c).
2*c*(c + 1)*(c + 14)/5
What is y in -6 - 11/2*y + 1/2*y**2 = 0?
-1, 12
Let v be ((-3)/2)/(1/(-2)). Suppose 12 = -v*b + 6*b. Factor 4*h + 2 + 9*h**2 + h**b - 5*h**3 + 0 - 11*h.
(h - 2)*(h - 1)**3
Let q(u) be the first derivative of -7*u**4/4 - 29*u**3/12 + u**2/8 + u/2 - 74. Factor q(g).
-(g + 1)*(4*g - 1)*(7*g + 2)/4
Suppose 10 = 5*x, -2*x = 4*n - 4*x - 40. Let z(g) = g**3 - 12*g**2 + 12*g - 9. Let f be z(n). Factor -3*p - p**2 - 2*p**f + 3*p.
-3*p**2
Suppose -375*l + 350*l + 100 = 0. Factor -5/3*m**l - 5/3*m**2 + 0*m + 0 - 10/3*m**3.
-5*m**2*(m + 1)**2/3
Let q = 32 + -32. Let u be (q + 1)*5*(-4)/(-24). Factor -1/6 + 2/3*y + u*y**2.
(y + 1)*(5*y - 1)/6
Let u = 4425/4 - 1106. Let -u*p**5 + 1/4*p**2 + 3/4*p**4 + 0 + 0*p - 3/4*p**3 = 0. Calculate p.
0, 1
Let x(k) be the second derivative of k**9/6804 - k**8/3780 - k**7/1890 + k**6/810 - k**3/3 - 13*k. Let m(b) be the second derivative of x(b). Factor m(z).
4*z**2*(z - 1)**2*(z + 1)/9
Let r be (35/(-3) + 9)*(-2)/20. Find f, given that 2/15 + 2/15*f**4 - r*f**2 + 0*f + 0*f**3 = 0.
-1, 1
Let a be (20 - 11)*1/6. Let i(y) be the second derivative of 0 + a*y**2 - 1/12*y**4 + 1/3*y**3 - 6*y. Factor i(n).
-(n - 3)*(n + 1)
Let j = -57 + 27. Let g(d) = d**3 - d**2 + 1. Let t(c) = -25*c**3 + 25*c**2 - 30. Let k(h) = j*g(h) - t(h). Let k(y) = 0. What is y?
0, 1
Let p = 401 + -4811/12. Let g(w) be the second derivative of 0*w**2 + 1/72*w**4 - 4*w - p*w**3 + 0. Factor g(z).
z*(z - 3)/6
Let j(h) be the second derivative of -h**8/3150 + h**7/900 - h**6/1350 - h**5/900 - 2*h**3/3 - 2*h. Let l(u) be the second derivative of j(u). Factor l(d).
-2*d*(d - 1)**2*(4*d + 1)/15
Let z be (-3)/5 - 102/(-20). Suppose 0 = 10*g + 320 - 340. What is l in -z - 1/2*l**g + 3*l = 0?
3
Factor 1/2*n**2 + 6 + 13/2*n.
(n + 1)*(n + 12)/2
Let i(y) be the second derivative of -5*y**7/42 + 2*y**6/3 - y**5 - 10*y + 5. Factor i(m).
-5*m**3*(m - 2)**2
Suppose -114*v + 5*v = 112*v - 663. Factor 5*k**v + 9/2*k**2 + 1/2*k**4 + 0*k + 0.
k**2*(k + 1)*(k + 9)/2
What is t in -5*t**2 - 69*t**3 + 408852*t - 3*t**5 + 47*t**2 - 408780*t - 42*t**4 = 0?
-12, -2, -1, 0, 1
Let f(b) be the second derivative of -b**7/98 + 9*b**6/70 - 33*b**5/140 - 25*b**4/28 + 12*b**3/7 + 6*b**2 - 96*b. Solve f(d) = 0.
-1, 2, 7
Find c, given that 80/3 - 316/3*c**2 + 4*c**3 + 56/3*c**4 - 64*c = 0.
-2, -1, 2/7, 5/2
Let b(t) = -t**3 - t**2 + 1. Let f(k) = -2*k**3 - k**2 - 3*k + 3. Let c(h) = -3*b(h) + f(h). Factor c(i).
i*(i - 1)*(i + 3)
Let p be 8/(-28) + 575/175. Let v(f) be the first derivative of -3/2*f**2 - 1/2*f**6 - 9/2*f**4 - 8 + 0*f - 12/5*f**5 - 4*f**p. Factor v(b).
-3*b*(b + 1)**4
Factor -32/3 + 4/3*m**4 + 56/3*m - 16/3*m**3 - 4*m**2.
4*(m - 4)*(m - 1)**2*(m + 2)/3
Let p(o) be the first derivative of o**5/50 + 3*o**4/40 - o**3/30 - 3*o**2/20 - 306. Factor p(r).
r*(r - 1)*(r + 1)*(r + 3)/10
Let k(t) be the second derivative of -t**5/110 - 9*t**4/22 - 81*t**3/11 - 729*t**2/11 - 90*t. Suppose k(j) = 0. What is j?
-9
Find s such that 5/3*s**2 + 0 - 2*s + 1/3*s**3 = 0.
-6, 0, 1
Suppose 19 = 4*i - g + 12, 3*g + 1 = 2*i. Factor -1/6 + 0*j + 1/6*j**i.
(j - 1)*(j + 1)/6
Suppose -31*d + 38*d - 112 = 0. Let 3*s**5 - 12*s**3 + 12*s**2 + 5*s**4 + 8*s**3 - d*s**2 = 0. What is s?
-2, -2/3, 0, 1
Let l(z) be the second derivative of 121*z**7/84 - 33*z**6/10 + 37*z**5/40 + 3*z**4/2 + z**3/3 - 17*z + 1. Factor l(b).
b*(b - 1)**2*(11*b + 2)**2/2
Suppose -5*h - 54 = -9. Let k be (21 + h)*(-1)/(-14)*2. Suppose 3/7*m**3 - 12/7*m - 30/7*m**2 + k*m**4 + 24/7 + 3/7*m**5 = 0. What is m?
-2, 1
Let s(j) be the second derivative of j**7/14 + 2*j**6/5 - 9*j**5/5 - 27*j**4/2 + 27*j**3/2 + 243*j**2 + 70*j - 2. Solve s(f) = 0.
-3, 2, 3
Let s = 1164/5 - 231. Let g(n) be the first derivative of -s*n**5 + 1/2*n**6 + 1 + 9/4*n**4 - n**3 + 0*n**2 + 0*n. Suppose g(j) = 0. Calculate j.
0, 1
Suppose -5*w = 12 - 72. Let f be w/(-2)*(-6)/18. Let 13 - 12*d + 8 + 2*d**f - 3 = 0. Calculate d.
3
Let l(w) be the first derivative of w**6/27 - 2*w**5/45 - w**4/18 + 2*w**3/27 - 54. Factor l(k).
2*k**2*(k - 1)**2*(k + 1)/9
Let i(v) be the first derivative of 8*v**4/3 + 140*v**3/9 - 56*v**2/3 - 20*v - 409. Factor i(t).
4*(t - 1)*(t + 5)*(8*t + 3)/3
Let u = 176 + -176. Let b(q) be the first derivative of -1/6*q**3 + u*q - 3 + 1/4*q**2. Factor b(h).
-h*(h - 1)/2
Let f be 4031/(-1276) + 5/4. Let z = -83/55 - f. Find p, given that -z*p + 1/5*p**2 + 0 = 0.
0, 2
Let o(c) = -1. Let s(g) = -1. Let d(p) = -4*o(p