5/100 - k**4/120 - k**3/10 + 18*k**2. Determine q, given that a(q) = 0.
-3, -1, 1
Let l be (-48)/80*(-5)/12. Factor -1/4*u + 0 - l*u**2.
-u*(u + 1)/4
Let a(x) be the third derivative of x**7/4200 + x**6/1800 - x**3/6 - 6*x**2. Let p(g) be the first derivative of a(g). Suppose p(q) = 0. Calculate q.
-1, 0
Let g(f) be the first derivative of f**9/3024 - f**8/840 + f**7/840 - f**3/3 - 8. Let s(j) be the third derivative of g(j). Factor s(n).
n**3*(n - 1)**2
Let o(s) be the third derivative of s**6/180 - s**5/90 - s**2. Suppose o(v) = 0. Calculate v.
0, 1
Let o be (-2 - 1)/(3/3). Let m = o - -3. Factor m*y**3 + 4/7*y**2 + 2/7*y - 2/7*y**5 - 4/7*y**4 + 0.
-2*y*(y - 1)*(y + 1)**3/7
Suppose -5*x = -2*l + 9, 3*x + 21 = -2*x - 2*l. Let c be x/9 - 48/(-9). Factor -4*a**3 + c*a**3 + 5*a**3 + 4*a**4 - 4*a**3 + 2*a**5.
2*a**3*(a + 1)**2
Factor 2 + 2/3*g**2 - 8/3*g.
2*(g - 3)*(g - 1)/3
Let q be 19/19*2/5. Factor 4/5 + q*c**2 - 6/5*c.
2*(c - 2)*(c - 1)/5
Let u be (11/3 + -3)*3. Let m be (3/u)/(3/4). Factor 4/3*t - 4/3 - 1/3*t**m.
-(t - 2)**2/3
Suppose -4*g - 14 + 14 = 0. Let y(u) be the first derivative of -2 + 3/10*u**4 + 2/25*u**5 + g*u + 2/5*u**3 + 1/5*u**2. Factor y(d).
2*d*(d + 1)**3/5
Let o(c) be the second derivative of -c**7/6300 + c**6/900 - c**5/300 + c**4/12 - c. Let l(v) be the third derivative of o(v). Factor l(h).
-2*(h - 1)**2/5
Let b(g) = -g**2 - 7*g - 5. Let p be b(-5). Factor -5*j**2 - 2*j + 3*j**2 - j**3 - 4*j + p*j.
-j*(j + 1)**2
Suppose -20*c + 11*c**5 + 10*c**4 - 40*c**2 - 180*c**3 + 165*c**3 - 6*c**5 = 0. Calculate c.
-2, -1, 0, 2
Factor 14 - 4*k - k + 16 - 7*k**2 + 2*k**2.
-5*(k - 2)*(k + 3)
Let y(t) be the first derivative of 2*t**3/9 - 2*t**2/3 - 3. Find q such that y(q) = 0.
0, 2
Suppose 0 = -p + 3*d - 6, 0 = 2*p + 3*p + d - 18. Let -a**2 - a**4 - 3*a**4 - 2*a**2 + 3*a**p + 7*a**4 - 3*a = 0. What is a?
-1, 0, 1
Let w be (14 - 17) + 18/3. Let x(i) be the first derivative of -1/9*i**w + 1/3*i**2 + 0*i - 1. Factor x(o).
-o*(o - 2)/3
Let p(l) be the third derivative of l**5/75 + l**4/20 + l**3/15 + 7*l**2. Suppose p(r) = 0. Calculate r.
-1, -1/2
Factor 0 + 15/2*l**3 + 3*l - 21/2*l**2.
3*l*(l - 1)*(5*l - 2)/2
Let u(m) = m**3 + 21*m**2 - 47*m - 23. Let n be u(-23). Factor -1/5*d**4 + 0*d**3 + 2/5*d**2 - 1/5 + n*d.
-(d - 1)**2*(d + 1)**2/5
Let d(n) be the first derivative of -n**3/7 + n**2/14 + 2*n/7 + 1. Determine c so that d(c) = 0.
-2/3, 1
Let q(h) be the third derivative of h**6/60 + 2*h**5/15 + 5*h**4/12 + 2*h**3/3 + 3*h**2. Factor q(o).
2*(o + 1)**2*(o + 2)
Let u(k) be the second derivative of k**9/45360 - k**8/10080 - k**4/12 - 5*k. Let h(v) be the third derivative of u(v). Solve h(m) = 0 for m.
0, 2
Let b = -4 - -7. Let n be (6/(-54))/(0 + 2/(-4)). What is l in 0*l + n*l**4 - 2/9*l**2 + 0*l**b + 0 = 0?
-1, 0, 1
Let u(p) be the third derivative of 0 + p**2 + 1/32*p**4 - 1/80*p**5 + 0*p**3 + 0*p. Factor u(k).
-3*k*(k - 1)/4
Let r = 131/10 + -13. Let q(a) be the second derivative of 2*a + 1/2*a**4 + 0 + a**3 + r*a**5 + a**2. Determine l, given that q(l) = 0.
-1
Let v(u) = 3*u**4 + u**3 + 10*u**2 - 17. Let j(n) = n**4 + 3*n**2 - 6. Let m(g) = -17*j(g) + 6*v(g). Find x, given that m(x) = 0.
-3, 0
Let u(o) be the second derivative of -o**9/52920 + o**8/11760 - o**7/8820 - o**4/12 - o. Let b(s) be the third derivative of u(s). Factor b(a).
-2*a**2*(a - 1)**2/7
Let t = -6 + 4. Let j = t + 4. Find w such that w + 2 + 2*w**j - 2*w - 3*w**2 = 0.
-2, 1
Let t(u) = 5*u**4 - u**3 - 5*u**2 + 5*u - 4. Let y(b) = -5*b**4 + 5*b**2 - 5*b + 5. Let s(z) = -5*t(z) - 4*y(z). Factor s(l).
-5*l*(l - 1)**2*(l + 1)
Factor -2 + y - 3*y**2 + 0*y**2 + 3*y + y**2.
-2*(y - 1)**2
Let x be (-8)/(-10)*120/48. Let 2/13*s**5 + 0 - 6/13*s**3 + 2/13*s**4 - 4/13*s - 10/13*s**x = 0. What is s?
-1, 0, 2
Suppose 0 = -3*o - 0*o - 3. Let l be ((-5 + o)/(-3))/1. Factor -1/4*d**3 + 0 + 0*d**l + 1/4*d.
-d*(d - 1)*(d + 1)/4
Let t = -25 - -27. Suppose 2*q - 6 = 0, 0 = -f - 4*q + 1 + 17. Find k, given that f*k**t - 7*k**2 + 4*k - 2*k = 0.
0, 2
Let n(s) = -3*s**2 - 15*s + 6. Let k(x) = 6*x**2 + 29*x - 11. Suppose -13 = -4*z + 11. Let l(i) = z*k(i) + 11*n(i). Solve l(g) = 0.
-3, 0
Let u be ((-9)/(-2) - 3)*2. Factor -u*c**2 + 4*c - c + 6*c**4 - 2*c**3 - 3*c**4 - c**3.
3*c*(c - 1)**2*(c + 1)
Let b = -79/6 - -83/6. Let 0*l**2 + 2/3*l**3 - b*l + 0 = 0. Calculate l.
-1, 0, 1
Let d(u) be the third derivative of 2*u**7/105 + u**6/30 + 6*u**2. Factor d(k).
4*k**3*(k + 1)
Suppose 5*d - 39 = m, -4*d + 6*d - 103 = 5*m. Let z be (-2)/m + 279/57. Let 0 - 3/5*l**3 + 9/5*l**2 + 6/5*l - 9/5*l**4 - 3/5*l**z = 0. Calculate l.
-2, -1, 0, 1
Let l(n) be the second derivative of n**6/480 + n**5/80 - n**3/6 - n**2/2 - 4*n. Let j(s) be the first derivative of l(s). Factor j(a).
(a - 1)*(a + 2)**2/4
Let c(n) be the third derivative of -n**2 + 0*n + 0*n**3 + 0*n**4 - 1/90*n**5 + 0. Factor c(o).
-2*o**2/3
Factor -24*k**2 + 5*k**4 - 8 - 5*k - 15*k**3 + 8 + 39*k**2.
5*k*(k - 1)**3
Let f(a) = a**3 - a**2 + a - 4. Let i be f(0). Let m = -4 - i. Find g such that 4*g**2 + m + 0 + 6*g**3 = 0.
-2/3, 0
Let w(l) be the first derivative of 1/12*l**3 + 0*l**2 - 1/40*l**5 + 9 + 0*l**4 - 1/8*l. Factor w(z).
-(z - 1)**2*(z + 1)**2/8
Let a(g) be the first derivative of 1/4*g**4 - 3 - 1/3*g**3 + 0*g**2 + 0*g. Find n, given that a(n) = 0.
0, 1
Let l(j) be the third derivative of -1/12*j**3 + 1/480*j**6 + 5/96*j**4 - 6*j**2 + 0 - 1/60*j**5 + 0*j. Determine p, given that l(p) = 0.
1, 2
Let t(v) = 2*v**2 + 7*v + 3. Let x(g) = -18*g**2 - 62*g - 26. Let f(c) = -52*t(c) - 6*x(c). Factor f(n).
4*n*(n + 2)
Suppose -j + 4*d + 27 = 0, -5*j - 8 = -3*d - 75. Let s = -1 + j. What is q in -2 + 21*q - 72*q**2 + s*q**3 + 83*q**3 - 12*q**3 = 0?
2/9, 1/3
Let l = -17 - -19. Let i(w) be the first derivative of -1 + 1/4*w + 1/3*w**3 - 5/8*w**l. Solve i(k) = 0 for k.
1/4, 1
Suppose 2*r = -r + 2*q + 13, 15 = -3*q. Let m(x) be the first derivative of 0*x + 1/3*x**3 + 0*x**2 - r. Determine w, given that m(w) = 0.
0
Factor -4 - 2 + 3 - 3*b**3 - 9*b**2 - 9*b.
-3*(b + 1)**3
Let g(c) be the third derivative of -c**8/504 - c**7/315 + c**6/60 + c**5/18 + c**4/18 - 39*c**2. Suppose g(d) = 0. What is d?
-1, 0, 2
Let z(n) = -2*n**2 - 7*n. Let i be z(-3). Solve -5*w + 3*w - 6*w**2 - 6*w**i + 0*w**3 - 2*w**4 = 0 for w.
-1, 0
Let y(q) be the first derivative of 8/25*q**5 + 2/5*q**4 + 0*q + 1/15*q**6 + 4 + 0*q**2 + 0*q**3. Factor y(m).
2*m**3*(m + 2)**2/5
Let b(q) be the first derivative of q**7/168 + q**6/40 + 3*q**5/80 + q**4/48 + 3*q - 2. Let x(p) be the first derivative of b(p). Let x(l) = 0. What is l?
-1, 0
Let d = 6331/30 - 211. Let w(j) be the second derivative of 0 - 2/5*j**2 + 1/5*j**3 - d*j**4 - 2*j. Find p such that w(p) = 0.
1, 2
Find m, given that 22/9*m**2 - 14/9*m**4 - 8/9 - 8/3*m + 8/3*m**3 = 0.
-1, -2/7, 1, 2
Let a(j) = -j**3 + 3*j**2 + 3*j + 7. Let c = 0 + 1. Suppose 0 = -4*g + 3 + c. Let u(z) = z + 1. Let h(t) = g*a(t) - 6*u(t). Factor h(s).
-(s - 1)**3
Suppose 10 = 5*n + 2*z, 4*n + 4 + 21 = 5*z. Determine v, given that 3/2*v**3 + 0*v - 1/2*v**4 + n - v**2 = 0.
0, 1, 2
Let a(d) = -d**3 + 8 + 4*d + 2*d + 3*d + 3*d**2. Let r be a(5). Determine q so that 4/9*q**r + 0 - 2/9*q**5 + 0*q**4 - 2/9*q + 0*q**2 = 0.
-1, 0, 1
Let o(m) be the first derivative of 2*m**3/9 - 2*m**2 + 6*m - 10. Factor o(c).
2*(c - 3)**2/3
Let m(n) be the third derivative of -n**5/60 + n**4/8 + 11*n**2. Let d be m(3). Factor d - 8/7*k**3 + 6/7*k**4 + 2/7*k**2 + 0*k.
2*k**2*(k - 1)*(3*k - 1)/7
Let c(z) be the first derivative of z**4 + 4*z**3/3 - 2*z**2 - 4*z - 36. Factor c(q).
4*(q - 1)*(q + 1)**2
Suppose -6 = -2*n - a, -4*n + 8 = -3*n + 3*a. Factor 0 + 2/7*c**5 + 2/7*c**3 + 0*c**n + 0*c - 4/7*c**4.
2*c**3*(c - 1)**2/7
Let y = 32 - 28. Let b be (-9)/(-4) - (-2 - -4). Factor 1/4*k**3 + 0 - 1/4*k**y + b*k**2 - 1/4*k.
-k*(k - 1)**2*(k + 1)/4
Solve -10/3*c**2 + 16/3*c + 2/3*c**3 - 8/3 = 0 for c.
1, 2
Factor 8/15*g + 2/15*g**2 + 8/15.
2*(g + 2)**2/15
Let v(m) = -m**3 - 1. Let l(i) = 5*i**3 - 2*i**2 - 2*i + 5. Let y(t) = l(t) + 3*v(t). Factor y(p).
2*(p - 1)**2*(p + 1)
Factor u**5 + 10*u**4 + 5*u + 2*u**5 - 8*u**5 - 10*u**2.
-5*u*(u - 1)**3*(u + 1)
Let b = -172/3 - -58. Let j(v) be the first derivative of 2/9*v**3 - 2/3*v**2 - 1 + b*v. Find t such that j(t) = 0.
1
Suppose 15 = 5*