t x(l) be the second derivative of -l**6/2160 + l**5/720 + l**3/2 + 3*l. Let r(m) be the second derivative of x(m). Solve r(a) = 0.
0, 1
Let c be (-6)/(-4)*(-4 - -6). Let x be (-2)/((-6)/9) - c. Factor x + 2/9*l**2 + 0*l.
2*l**2/9
Let l(w) be the second derivative of w**7/1260 - w**6/135 + w**5/45 - w**3/6 + 4*w. Let a(r) be the second derivative of l(r). Find n such that a(n) = 0.
0, 2
Let b(q) be the first derivative of -q**2 + 1/3*q**3 + 0*q + 2 + 1/6*q**4 - 1/10*q**5. Let m(j) be the second derivative of b(j). Factor m(g).
-2*(g - 1)*(3*g + 1)
Let j(u) be the third derivative of -2*u**7/105 - u**6/15 + u**5/15 + u**4/3 - u**2. Factor j(m).
-4*m*(m - 1)*(m + 1)*(m + 2)
Let s be 3 + (-34)/10 + 2. Let l be (-4)/5*10/(-4). What is j in 12/5*j - s + 1/5*j**3 - 6/5*j**l = 0?
2
Let h(x) be the first derivative of x**5/150 - x**4/60 - 2*x**3/15 + x**2 + 3. Let k(i) be the second derivative of h(i). Suppose k(f) = 0. What is f?
-1, 2
Let w(d) = -4*d**2 + 7*d - 3. Let q(p) = p - 1. Let s(i) = 7*i - 7. Let k(c) = 6*q(c) - s(c). Let v(y) = -2*k(y) - w(y). Suppose v(m) = 0. What is m?
1/4, 1
Let a(k) be the second derivative of -k**8/2240 - k**7/840 + k**6/240 + k**5/40 + k**4/12 + 4*k. Let z(x) be the third derivative of a(x). Factor z(d).
-3*(d - 1)*(d + 1)**2
Let b(r) be the second derivative of -r**5/10 + r**4/6 + r**3/3 - r**2 + 6*r. Let b(c) = 0. Calculate c.
-1, 1
Let o(q) be the second derivative of -q**8/560 + 3*q**7/280 - q**6/40 + q**5/40 + q**3 - 2*q. Let v(j) be the second derivative of o(j). Factor v(t).
-3*t*(t - 1)**3
Suppose 1 = -5*u - c, 5*u = 3*c + 6 - 3. Factor u + 0*f - 1/3*f**4 - 1/3*f**2 + 2/3*f**3.
-f**2*(f - 1)**2/3
Suppose 3*h = -0*h - 30. Let i be ((-8)/h)/((-4)/(-10)). What is z in -4*z**4 + z**4 + i*z**4 = 0?
0
Let k(d) be the third derivative of d**5/180 + d**4/36 + d**3/18 + 3*d**2. Factor k(v).
(v + 1)**2/3
Factor 2*t**2 + 7*t - 8*t - t.
2*t*(t - 1)
Let d(i) be the first derivative of -i**6/10 + 9*i**4/20 - 2*i**3/5 - 13. Factor d(q).
-3*q**2*(q - 1)**2*(q + 2)/5
Suppose 0 = s - 4, 19*p - 18*p + 2*s = 10. Suppose -3/2 - 1/6*b**p + b = 0. What is b?
3
Let f = -11 - -22. Let b = -9 + f. Factor -3/2*x + x**b - 1 + 3/2*x**3.
(x - 1)*(x + 1)*(3*x + 2)/2
Let w be -5 + 3/(6/10). Let h(q) be the second derivative of 0 - 3/100*q**5 + w*q**3 + 1/50*q**6 + 0*q**2 + 0*q**4 - q. Factor h(c).
3*c**3*(c - 1)/5
Factor -1/5*q**3 + 1/5*q**2 - 1/5 + 1/5*q.
-(q - 1)**2*(q + 1)/5
Suppose 4*u - 39 + 13 = -3*k, -5*k - 3*u + 25 = 0. What is g in 0 + 7/4*g**2 - 4*g**4 - 1/4*g - k*g**3 = 0?
-1, 0, 1/4
Let w = 0 + 2. Factor 8/9*u - 2/9*u**w - 8/9.
-2*(u - 2)**2/9
Let o = 20 - 27. Let n(a) = -a**2 - 7*a + 3. Let i be n(o). Factor -24/7*f**i + 18/7*f**2 + 0 - 4/7*f + 10/7*f**4.
2*f*(f - 1)**2*(5*f - 2)/7
Let h be ((-4)/6)/(8/(-108)). Suppose h*i = 4*i + 10. Factor 3*k - 2 + 3*k**5 - i*k**5 - 4*k**3 - k**2 + 3*k**2.
(k - 1)**3*(k + 1)*(k + 2)
Let w(v) be the first derivative of 2*v**6/3 - 32*v**5/5 + 21*v**4 - 24*v**3 + 41. Let w(k) = 0. Calculate k.
0, 2, 3
Let g(d) be the first derivative of d**3/6 - d**2/2 + d/2 + 32. Factor g(x).
(x - 1)**2/2
Let h(q) = -4*q**3 - 22*q**2 - 12*q - 6. Let z(b) = b**3 - b**2 - 1. Let s(t) = h(t) - 4*z(t). Factor s(w).
-2*(w + 1)**2*(4*w + 1)
Suppose -24*q**2 + 2*q**3 + 8*q**2 - 4 + 8*q**2 + 10*q = 0. Calculate q.
1, 2
Let t = 13 + -5. Let z be (t/(-3))/(4/(-12)). Suppose 8*v - v**2 + 6*v**2 + z - 3*v**2 = 0. What is v?
-2
Let u(b) = 5*b**2 + b. Let h be (1 - 3) + (-2 - 2). Let s(r) = r**2 - r. Let o(d) = 5*d. Let y(i) = o(i) + 4*s(i). Let m(q) = h*y(q) + 5*u(q). Factor m(g).
g*(g - 1)
Let d(x) be the second derivative of -x**5/10 + 5*x**4/12 + 2*x**3/3 - 3*x**2/2 + 4*x. Let d(p) = 0. Calculate p.
-1, 1/2, 3
Let m(v) = -v**3 + 8*v**2 + 7*v + 22. Let t be m(9). Find j, given that 1/5*j**2 + 0*j - 6/5*j**3 + 0 + j**t = 0.
0, 1/5, 1
Let v(a) be the third derivative of a**8/840 - 2*a**7/525 + a**6/300 + 3*a**2. Determine g so that v(g) = 0.
0, 1
Let n(j) be the first derivative of -1/15*j**3 + 2 + 2/5*j**2 - 4/5*j. Suppose n(q) = 0. What is q?
2
Let j(o) = -1 - 8 + 1 + o**2 + 9*o. Let i be j(-10). Determine h, given that -2*h**5 + 4*h**2 + h**4 + 2*h**3 - 4*h**2 + 2*h**i - 3*h**4 = 0.
-1, 0, 1
Let -6/13*u**4 + 14/13*u**2 + 0 + 6/13*u**3 - 2/13*u**5 - 12/13*u = 0. Calculate u.
-3, -2, 0, 1
Let j(f) be the second derivative of -f + 1/36*f**4 - 1/9*f**3 + 1/6*f**2 + 0. Factor j(w).
(w - 1)**2/3
Let a(t) be the third derivative of t**8/560 - t**7/420 + t**6/720 - t**5/60 - 3*t**2. Let i(b) be the third derivative of a(b). Factor i(y).
(6*y - 1)**2
Let f(m) be the first derivative of 2*m**3/39 + 6*m**2/13 + 18*m/13 - 3. Let f(d) = 0. Calculate d.
-3
Let j be (-28)/9 - (7 + -11). Factor -2/9*d**4 + 8/3*d - j + 4/3*d**3 - 26/9*d**2.
-2*(d - 2)**2*(d - 1)**2/9
Let h = 2 - 0. Find v such that 30*v**3 - 108*v**h + 110*v - 41*v - 3*v**4 - 81 + 93*v = 0.
1, 3
Determine f so that 2/11*f**5 + 16/11*f**2 - 16/11*f**4 + 30/11*f**3 - 32/11*f + 0 = 0.
-1, 0, 1, 4
Let p(b) be the third derivative of b**6/40 + b**5/30 - b**4/4 + b**3/6 - 3*b**2. Let g(k) = k - 1. Let u(s) = 3*g(s) + p(s). Let u(o) = 0. What is o?
-1, -2/3, 1
Let y(a) be the first derivative of a**6/240 - a**5/10 + a**4 - 16*a**3/3 + 4*a**2 - 8. Let m(f) be the second derivative of y(f). Find c, given that m(c) = 0.
4
Let t(v) = 5*v**4 + 10*v**3 - 3*v**2 - 3*v. Let c(o) = 15*o**4 + 30*o**3 - 8*o**2 - 8*o. Let p(q) = -3*c(q) + 8*t(q). Let p(j) = 0. What is j?
-2, 0
Let i(h) = -4*h**3 - 3*h**2 - 3*h + 3. Let z(n) = -18*n**3 - 14*n**2 - 14*n + 14. Let j(p) = -28*i(p) + 6*z(p). Find x, given that j(x) = 0.
0
Let v(b) = -3*b. Let a be v(-1). Factor 8*l + 2*l**3 + 4*l**2 + 5 - a - l**3 - 3*l.
(l + 1)**2*(l + 2)
Factor 930 - 8*s + 0*s**4 - 4*s**4 + 12*s**2 - 930.
-4*s*(s - 1)**2*(s + 2)
Find c, given that -1/3*c**2 - 1/3*c + 1/3 + 1/3*c**3 = 0.
-1, 1
Let b(s) = -20*s**2 - 76*s + 88. Let h(m) = 13*m**2 + 51*m - 59. Let w(c) = -5*b(c) - 8*h(c). Factor w(i).
-4*(i - 1)*(i + 8)
Let p = -23 - -14. Let v be (p + 7)*1/(-4). Solve 2*m**3 + 2*m - 3*m**2 - 1/2*m**4 - v = 0 for m.
1
Let p(w) be the first derivative of -w**3 + 9*w**2 - 27*w + 4. Factor p(r).
-3*(r - 3)**2
Let m be (-2)/(-1) + 48/(-4). Let g(p) = -p - 6. Let f be g(m). Suppose 0*v**2 + 2/3*v**f - 2/9*v**5 + 0*v - 4/9*v**3 + 0 = 0. Calculate v.
0, 1, 2
Let h(u) be the third derivative of 2*u**7/105 - u**6/30 - u**5/15 + u**4/6 + 7*u**2. Determine n so that h(n) = 0.
-1, 0, 1
Let y(k) = -k**3 + 10. Let s be y(0). Suppose -6 = i - 4*i, 3*f = -2*i + s. Let -6*q - 4*q**2 + 2*q**2 + f*q - 2 = 0. Calculate q.
-1
Let w(x) be the second derivative of 2*x**5/5 - x**4/6 - 4*x**3/3 + x**2 + 2*x. Determine k so that w(k) = 0.
-1, 1/4, 1
Let d(u) be the third derivative of -u**8/1344 + u**7/280 + u**6/480 - 11*u**5/240 + u**4/8 - u**3/6 - 20*u**2. Determine r so that d(r) = 0.
-2, 1, 2
Let n(c) be the second derivative of c**7/2520 + c**6/360 + c**4/4 + 7*c. Let t(q) be the third derivative of n(q). Factor t(g).
g*(g + 2)
Suppose -4*n - 5*x = -14 - 18, -25 = -n + 3*x. Let f = n + -7. Determine t so that 5*t**2 - 13*t**2 - f + 6*t + 8 = 0.
-1/4, 1
Let b(q) be the second derivative of 0 - 1/20*q**5 - 2/3*q**3 + 1/3*q**4 + 0*q**2 + 9*q. Solve b(n) = 0.
0, 2
Let f(n) be the third derivative of -1/1344*n**8 + 0*n + 1/420*n**7 + 6*n**2 + 0*n**3 + 0*n**5 + 0*n**4 + 0 + 0*n**6. Factor f(v).
-v**4*(v - 2)/4
Let y(z) = -z**5 + 25*z**4 + 41*z**3 + 23*z**2 + 8*z. Let l(p) = 12*p**4 + 20*p**3 + 12*p**2 + 4*p. Let x(w) = -5*l(w) + 2*y(w). Suppose x(u) = 0. Calculate u.
-2, -1, 0
Suppose -7 = 3*f + 2. Let m(u) = u**2 - 9*u - 7. Let r(h) = -8*h - 6. Let s(l) = f*r(l) + 2*m(l). Factor s(w).
2*(w + 1)*(w + 2)
Let v = -11/24 + 5/8. Let d(i) be the second derivative of -v*i**4 + 0 - 1/3*i**3 + 1/10*i**5 - 3*i + i**2. Factor d(b).
2*(b - 1)**2*(b + 1)
Let x be (-1)/(-1)*(-10 + 13). Suppose 1/2*a**4 + 1/2*a**5 + 0 - 1/2*a**2 + 0*a - 1/2*a**x = 0. Calculate a.
-1, 0, 1
Factor 18*n**2 - 5*n - 16*n**2 + 5*n - 8.
2*(n - 2)*(n + 2)
Factor 4/5*u**4 - 8/5*u**2 - 8/5*u**3 + 4/5*u**5 + 4/5*u + 4/5.
4*(u - 1)**2*(u + 1)**3/5
Suppose 3*c = -12 - 3, -3*w = -4*c - 26. Determine o, given that 1 - o**w - 4 + o**3 + 4 - o = 0.
-1, 1
Let x(d) be the first derivative of 15*d*