4*l - 3/4*l**3.
-3*(l - 1)**3/4
Suppose 19 = 9*m + 1. Let q(l) be the third derivative of 3*l**m + 1/120*l**6 - 1/12*l**4 + 0*l + 0*l**3 - 1/60*l**5 + 0. Determine k, given that q(k) = 0.
-1, 0, 2
Let y be (2 - -4)*(-4 + -2). Let g be -3 - -5 - y/(-21). Suppose 2/7 - g*w**3 - 2/7*w**2 + 2/7*w = 0. Calculate w.
-1, 1
Let u(p) be the third derivative of 3/8*p**4 + 3/20*p**5 + 0 + 0*p + p**2 + 1/40*p**6 + 1/2*p**3. What is w in u(w) = 0?
-1
Let n(g) be the first derivative of g**4/4 + g**3/3 - g**2/2 - g - 8. Find t, given that n(t) = 0.
-1, 1
Let q = 38 - 38. Let m(t) be the third derivative of 0 + 0*t + t**2 - 1/6*t**5 + 7/60*t**6 - 1/6*t**4 + q*t**3. Let m(x) = 0. Calculate x.
-2/7, 0, 1
Let l be (-3 - (1 + -3)) + 7. Let f(d) be the second derivative of 0*d**3 + 0*d**2 - 1/105*d**7 + 0*d**5 + 0 - 2*d + 0*d**4 - 1/75*d**l. Factor f(i).
-2*i**4*(i + 1)/5
Factor -6/25*i + 4/25 - 14/25*i**3 - 24/25*i**2.
-2*(i + 1)**2*(7*i - 2)/25
Let d(p) be the first derivative of -3*p**5/5 - 3*p**4/2 - p**3 + 8. What is w in d(w) = 0?
-1, 0
Let l = 7339/11 - 667. Factor 0*r - 2/11 + l*r**2.
2*(r - 1)*(r + 1)/11
Let d(o) = -2*o**3 + 2*o**2 - 1. Let n be d(-1). Let v be (-81)/(-18)*2/3. Determine i, given that 2*i**2 + i**v + 3*i**n + i - 3*i**3 = 0.
-1, 0
Let b(x) be the third derivative of x**8/10080 - x**7/2520 + x**5/20 - 5*x**2. Let m(r) be the third derivative of b(r). Factor m(u).
2*u*(u - 1)
Let n = 129 + -60. Factor 5 - 6 + 60*r**3 + n*r**2 - 5 + 3*r.
3*(r + 1)*(4*r - 1)*(5*r + 2)
Let w(v) be the second derivative of -v**6/60 - v**5/30 + 3*v**2 - 3*v. Let c(b) be the first derivative of w(b). Factor c(u).
-2*u**2*(u + 1)
Let k(y) be the third derivative of -y**7/1120 + y**5/160 - y**3/3 - 4*y**2. Let h(r) be the first derivative of k(r). Solve h(s) = 0 for s.
-1, 0, 1
What is z in 0*z - 1/5*z**2 + 1/5 = 0?
-1, 1
Let d(h) be the second derivative of 0*h**3 + 1/36*h**4 - 1/6*h**2 - 2*h + 0. Factor d(u).
(u - 1)*(u + 1)/3
Let i(h) be the first derivative of -2*h**3/9 + h**2/3 + 4*h/3 - 7. Solve i(r) = 0 for r.
-1, 2
Let i(b) = b**3 + 36*b**2 - 135*b + 154. Let d(k) = -k**3 - 1. Let m(x) = -4*d(x) - i(x). Factor m(a).
3*(a - 5)**2*(a - 2)
Factor -51*p**3 - p**2 + 2*p**4 - p**2 + 53*p**3 - 2*p.
2*p*(p - 1)*(p + 1)**2
Factor 0 - 1/2*u**3 + 1/4*u**2 + 0*u + 1/4*u**4.
u**2*(u - 1)**2/4
Suppose 5 = 5*o + 3*b - 10, -5*b = 5*o - 25. Factor 3/2*j**3 + 0 + o*j - 3*j**2.
3*j**2*(j - 2)/2
Let j(o) be the first derivative of -o**9/9072 + o**8/1680 - o**7/840 + o**6/1080 + 2*o**3/3 + 3. Let w(l) be the third derivative of j(l). Factor w(r).
-r**2*(r - 1)**3/3
Suppose 0 + 1/3*n**2 + 1/3*n = 0. Calculate n.
-1, 0
Let r(w) = w**3 - 7*w**2 - 7*w + 4. Let v be r(8). Suppose 4*b + 14 = 2*h, -3 = h - 3*b - v. Factor 0 + 4/3*t - 10/3*t**h + 2*t**2.
-2*t*(t - 1)*(5*t + 2)/3
Let d be (-145)/(-25) - 2/(-10). Let z = d + -3. Factor -y**5 + 12*y**3 - 9*y**z - 6*y**4 + 4*y**5.
3*y**3*(y - 1)**2
Let n(j) be the first derivative of 2*j**2 + 3 + 10/3*j**3 + 0*j + 3/2*j**4. Factor n(i).
2*i*(i + 1)*(3*i + 2)
Let v = -8 + 2. Let t = -3 - v. Find j such that 243*j**4 + 0 + 57*j**t + 27*j + 2 + 135*j**2 + 240*j**3 = 0.
-1/3, -2/9
Let l(y) be the third derivative of y**10/60480 - y**8/13440 - 5*y**4/24 + 2*y**2. Let k(r) be the second derivative of l(r). Solve k(q) = 0.
-1, 0, 1
Solve -2/13*c**4 + 0*c + 0*c**2 + 0 + 2/13*c**3 = 0.
0, 1
Suppose 2/11*n**2 - 14/11*n + 20/11 = 0. What is n?
2, 5
Let v(c) = c**3 - 9*c**2 + 8*c + 2. Let z be v(8). Let -2/7*u**z + 2/7 + 2/7*u**3 - 2/7*u = 0. What is u?
-1, 1
Let m(w) be the second derivative of w**5/50 + w**4/5 + 4*w**3/5 + 8*w**2/5 + 2*w. Suppose m(x) = 0. What is x?
-2
Find u such that -4/9*u**5 + 40/9*u + 0 - 4*u**3 + 28/9*u**4 - 28/9*u**2 = 0.
-1, 0, 1, 2, 5
Let q = 7 + -1. Let f = q + -2. Factor -2*k**2 + 10 + k - k**5 - 10 + 2*k**f.
-k*(k - 1)**3*(k + 1)
Suppose 11 = 3*t + 11. Let p(y) be the second derivative of -1/24*y**3 - 2*y - 1/48*y**4 + t + 1/4*y**2. Factor p(b).
-(b - 1)*(b + 2)/4
Let c(y) be the third derivative of 1/30*y**4 + 0*y + 4/15*y**3 - 7*y**2 - 1/150*y**6 + 0 - 2/75*y**5. Let c(m) = 0. What is m?
-2, -1, 1
Let k = -325 - -326. Let k - 1/2*a**2 + 1/2*a = 0. Calculate a.
-1, 2
Factor 0*l**2 + 0 + 1/2*l**3 + 1/4*l**4 + 0*l.
l**3*(l + 2)/4
Let a(o) be the second derivative of -o**5/90 - 7*o**4/54 - 2*o**3/9 - 13*o. Determine d, given that a(d) = 0.
-6, -1, 0
Factor 780/7*n**3 - 554/7*n**2 + 120/7*n - 338/7*n**4 - 8/7.
-2*(n - 1)**2*(13*n - 2)**2/7
Let u(a) = -a**3 - a - 1. Let q(c) = 4*c**4 - 17*c**3 + 15*c**2 - 11*c - 3. Let l(t) = q(t) - 4*u(t). Factor l(d).
(d - 1)**3*(4*d - 1)
Let d be 64/8 - 6 - (-4)/(-5). Let u(y) be the first derivative of d*y + 1/5*y**3 + 9/10*y**2 + 2. Suppose u(b) = 0. What is b?
-2, -1
Let b(m) be the second derivative of m**8/504 - m**6/60 + m**5/45 + 2*m**2 - 2*m. Let j(f) be the first derivative of b(f). Factor j(o).
2*o**2*(o - 1)**2*(o + 2)/3
Let c(i) = 0 + 4*i + 2 - 4. Let j be c(2). Factor -4*r**2 - 4*r**3 - 10*r**2 - j*r**4 - 4*r - 12*r**3.
-2*r*(r + 1)**2*(3*r + 2)
Let z(u) be the third derivative of 0 - 1/15*u**6 - 1/3*u**3 - 1/5*u**5 + 0*u - 1/105*u**7 - 3*u**2 - 1/3*u**4. Let z(y) = 0. Calculate y.
-1
Factor 3*c - 2419*c**2 - 3*c + 2417*c**2.
-2*c**2
Let t(a) be the third derivative of a**7/280 + 3*a**6/160 + 3*a**5/80 + a**4/32 - 18*a**2. Find v such that t(v) = 0.
-1, 0
Let v = -6 - -13/2. Let a(b) = -b + 5. Let g be a(4). Factor 3/2*f - g - v*f**2.
-(f - 2)*(f - 1)/2
Suppose 0*n - 3*z = 4*n - 20, 5*n = 5*z - 10. Factor 2/3*y - 1/3*y**n - 1/3.
-(y - 1)**2/3
Let u(r) be the third derivative of -r**6/108 - 2*r**5/45 - r**4/12 - 2*r**3/27 + 6*r**2. Solve u(q) = 0.
-1, -2/5
Let v(o) be the first derivative of o**7/1680 - o**6/240 + o**5/120 + 5*o**3/3 + 8. Let g(t) be the third derivative of v(t). Factor g(j).
j*(j - 2)*(j - 1)/2
Suppose -7*q = -3*q - 52. Let n = 13 - q. Determine b so that 1/3 + n*b - 1/3*b**2 = 0.
-1, 1
Suppose 0*c + 21 = 7*c. Suppose -6/5*i + 2/5*i**5 + 4/5*i**c + 6/5*i**4 - 4/5*i**2 - 2/5 = 0. What is i?
-1, 1
Let j be (12/(-10))/(45/(-24)). Let a = -6/25 + j. Determine r, given that 2/5*r**2 + 4/5*r + a = 0.
-1
Let n = 14 + -9. Suppose 2*j = -3*f - 9, -2*j - 4*f - n = 3*j. Factor -5/3*w + 2/3 + 4/3*w**2 - 1/3*w**j.
-(w - 2)*(w - 1)**2/3
Let s(x) be the second derivative of x**5/20 + x**4/8 - x**3 - x**2 - 5*x. Let l(w) be the first derivative of s(w). Factor l(t).
3*(t - 1)*(t + 2)
Let q(k) be the third derivative of -k**10/1134000 - k**9/453600 + k**5/15 - k**2. Let p(n) be the third derivative of q(n). Suppose p(t) = 0. Calculate t.
-1, 0
Let n(x) be the second derivative of 5*x - 1/120*x**5 + 1/24*x**4 - 1/180*x**6 - 1/6*x**2 + 1/36*x**3 + 0. Factor n(c).
-(c - 1)**2*(c + 1)*(c + 2)/6
Let k = -3490/3 + 1174. Factor -2/3*m**2 - k - 16/3*m.
-2*(m + 4)**2/3
Let p = 23 - 14. Let l = 3 + p. Suppose 0*o - 69*o**2 + 21*o**3 + 0 + 55*o + 5*o - l = 0. Calculate o.
2/7, 1, 2
Suppose w - 6 = -w. Determine m so that 4*m**w + 25*m + 24*m**2 - 15*m + 26*m = 0.
-3, 0
Let x(w) be the second derivative of 4/7*w**4 - 4*w + 2/105*w**6 - 20/21*w**3 + 6/7*w**2 - 6/35*w**5 + 0. Determine t so that x(t) = 0.
1, 3
Let f(m) be the first derivative of -m**4/8 - 11*m**3/6 - 6*m**2 + 18*m - 7. Factor f(l).
-(l - 1)*(l + 6)**2/2
Let i(y) be the first derivative of -y**4/14 - 4*y**3/21 + 3*y**2/7 + 2. Factor i(j).
-2*j*(j - 1)*(j + 3)/7
Let v be 17/(-5)*(-10 - 26). Let d = v - 122. Let -2/5*u**2 - d*u + 4/5 = 0. Calculate u.
-2, 1
Let u(g) = g + 2. Let j be u(1). Let o be 2 + 0 - 5/3. Factor 0 - 1/3*a + o*a**j + 0*a**2.
a*(a - 1)*(a + 1)/3
Factor -5/4*g**2 + 0*g + 5/4.
-5*(g - 1)*(g + 1)/4
Find l such that -3/4*l**4 + 0*l + 1/2*l**3 - 1/2*l**5 + l**2 - 1/4 = 0.
-1, 1/2, 1
Let z(a) be the second derivative of -25*a**7/21 + a**6/3 + 41*a**5/10 - a**4/6 - 16*a**3/3 - 4*a**2 + 7*a. Let z(m) = 0. What is m?
-1, -2/5, 1
Let t(s) = -5*s**2 + s. Let p(f) = -f**2 + 3*f**2 - f**2. Suppose 0 = -i - 3*i + 16. Let u(v) = i*p(v) + t(v). Factor u(b).
-b*(b - 1)
Let v = -201/4 - -211/4. What is m in -1/4 + 1/4*m + 2*m**3 + v*m**2 = 0?
-1, -1/2, 1/4
Let d = -8 + 14. Let a be 6/(-9) - (-8)/d. Factor 2*f**5 + 0 + 2/3*f**2 - 10/3*f**4 + 0*f + a*f**3.
2*f**2*(f - 1)**2*(3*f + 1)/3
Let n be 1/(-2)*0/5. Let u(g) be