. Let k(z) be the third derivative of 1/300*z**6 + 0*z**4 - 1/525*z**7 + g*z**3 + 2*z**2 + 0*z + 0 + 0*z**5. Factor k(n).
-2*n**3*(n - 1)/5
Let d(m) be the first derivative of -2*m**5 - 13*m**4/2 - 8*m**3/3 + 4*m**2 - 42. Solve d(t) = 0.
-2, -1, 0, 2/5
Let a(v) be the second derivative of -v**5/20 - v**4/6 - v**3/6 + 3*v. Factor a(q).
-q*(q + 1)**2
Let k(i) be the first derivative of 0*i - 8/3*i**2 - 2 - 57*i**4 + 184/9*i**3 + 54*i**5. Factor k(x).
2*x*(5*x - 2)*(9*x - 2)**2/3
Solve 15*b + 10*b**2 - 15*b**3 + 26*b**3 - 16*b**3 = 0.
-1, 0, 3
Let u(m) be the first derivative of -m**2 + 0*m + 1/18*m**4 - 1/9*m**3 - 1/90*m**5 - 3. Let n(h) be the second derivative of u(h). What is g in n(g) = 0?
1
Factor 0*l**2 + 21*l + 3*l**2 - 9*l.
3*l*(l + 4)
Let b(n) be the second derivative of -n**7/28 + 3*n**5/20 - n**3/4 + 3*n. Let b(t) = 0. What is t?
-1, 0, 1
Let s(b) = b**3 + 6*b**2 + 5. Let r be s(-6). Let k = -3 + r. Find h such that -4*h - 1 + 3 + h**2 + k = 0.
2
Let x(c) be the third derivative of -1/10*c**5 - 1/105*c**7 + 0 - 4*c**2 - 1/20*c**6 - 1/12*c**4 + 0*c**3 + 0*c. Factor x(p).
-2*p*(p + 1)**3
Let d(s) be the third derivative of -s**10/50400 + s**9/20160 + s**8/6720 - s**7/1680 - s**5/30 - 5*s**2. Let f(o) be the third derivative of d(o). Factor f(m).
-3*m*(m - 1)**2*(m + 1)
Find i such that 204*i**3 - 90*i**4 - 698/5*i**2 - 8/5 + 136/5*i = 0.
2/15, 1
Suppose 33 - 13 = 5*b. Let y(o) be the third derivative of 1/30*o**5 + 0*o**3 + 0*o - 1/24*o**b + 0 - o**2 - 1/120*o**6. Factor y(t).
-t*(t - 1)**2
Let r(q) be the first derivative of -q**4/36 + 3*q + 2. Let f(o) be the first derivative of r(o). Factor f(u).
-u**2/3
Let j(t) be the first derivative of 0*t**4 + 0*t**2 + 3 - 1/20*t**5 + 0*t**3 + 0*t. Let j(c) = 0. What is c?
0
Let r = 13 + -11. Factor 2*k**2 + 2*k**2 - 4 + 2*k - 5*k**r + 2*k.
-(k - 2)**2
Let u(j) be the second derivative of j**9/45360 + j**8/20160 + j**4/6 - 2*j. Let d(r) be the third derivative of u(r). Let d(k) = 0. Calculate k.
-1, 0
Let 1/3*w**2 - 1/3 + 0*w = 0. Calculate w.
-1, 1
Suppose 4*u + 6 = 18. Let f(a) be the first derivative of -2/25*a**5 + 0*a + 0*a**2 + 0*a**u + 0*a**4 - 1. Let f(m) = 0. Calculate m.
0
Let f(t) = -6*t**2 - 2*t - 1. Let s(m) = 5*m**2 + 2 + 2*m + 0*m + 3 - 4. Let d = -2 - -6. Let z(c) = d*f(c) + 5*s(c). Factor z(o).
(o + 1)**2
Let s(g) be the first derivative of g**8/252 + g**7/63 + g**6/45 + g**5/90 - 3*g**2/2 - 1. Let u(p) be the second derivative of s(p). Factor u(h).
2*h**2*(h + 1)**2*(2*h + 1)/3
Let l(d) be the first derivative of -64*d**5/5 + 20*d**4 + 32*d**3 + 2*d**2 - 8*d + 27. Solve l(s) = 0 for s.
-1/2, 1/4, 2
Let k(p) = -4*p**3 - 2*p**2 + 5*p. Let m(j) = 7*j**3 + 3*j**2 - 11*j. Let u(d) = -7*k(d) - 3*m(d). Determine v, given that u(v) = 0.
-1, 0, 2/7
Let a(o) = -o**3 + 2*o**2 - o. Let u be a(1). Suppose c - 2 + 9 = g, -4*g + 3*c + 27 = u. What is n in n**3 + 3*n**3 + n + n**5 - g*n**3 = 0?
-1, 0, 1
Let w(c) be the third derivative of -c**6/480 - c**5/120 + c**4/96 + c**3/12 + c**2 + 27. Determine h, given that w(h) = 0.
-2, -1, 1
Suppose 48 = 3*i - 3*x, 4*i - 55 = 5*x + 13. Let h be (-1 - 1)*(10 - i). Factor 4/3*j**2 + 0 + 1/3*j**3 - 1/3*j - 4/3*j**h.
-j*(j - 1)*(j + 1)*(4*j - 1)/3
Let m = 20 + -20. Let j(h) be the first derivative of -3 + m*h + 2/35*h**5 + 1/7*h**4 + 0*h**2 + 2/21*h**3. Factor j(l).
2*l**2*(l + 1)**2/7
Let k(l) = -4*l**3 + 8*l**2 + 2*l. Let m(i) = -i**3 + i**2 + i. Let a(t) = -k(t) + 6*m(t). Factor a(b).
-2*b*(b - 1)*(b + 2)
Let w(u) be the first derivative of 1/3*u**3 + 4 + 0*u + 1/18*u**4 - 2/45*u**5 - 1/120*u**6 + 0*u**2. Let m(z) be the third derivative of w(z). Factor m(k).
-(k + 2)*(9*k - 2)/3
Suppose 5*r - 143 - 132 = 0. Suppose -5*i - r = -5*n, n - 4*i - 2 = 21. Let n*s**4 - 5*s**4 + 2*s**2 + 0*s**2 + 4*s**3 = 0. What is s?
-1, 0
Let o be (-1)/(-4)*(-12)/30*-3. Let r(c) be the second derivative of 0*c**4 + 0*c**2 + o*c**5 + 1/15*c**6 + 4*c - 4/3*c**3 + 0. What is z in r(z) = 0?
-2, 0, 1
Suppose -6*w - g - 4 = -w, w + 8 = -2*g. Let h be (-130)/50 - 1*-3*1. Factor w + 2/5*d**2 + 0*d + h*d**3.
2*d**2*(d + 1)/5
Let n(v) be the third derivative of v**6/600 + v**5/300 - 22*v**2. Let n(q) = 0. What is q?
-1, 0
Suppose -4*x - x + 15 = 0. Factor -x*q**4 + 4*q**3 + 0*q**3 + q**5 - 3 + q + 6*q**2 - 6*q**3.
(q - 3)*(q - 1)**2*(q + 1)**2
Suppose 4*v - 3*m - 9 = 18, 30 = 4*v - 2*m. Let c be 47/v - 20/90. Factor 0*j**3 - 2*j**4 + 2*j**5 + j**3 - c*j**3.
2*j**3*(j - 2)*(j + 1)
Let b(r) = 2*r**3 - 14*r**2 + 10*r + 14. Suppose 3*x + 0*y - 2 = -2*y, 3*y = 4*x - 31. Let s(u) = -u - 4 + u**2 - 1 + x. Let z(f) = b(f) + 12*s(f). Factor z(o).
2*(o - 1)**2*(o + 1)
Let a(s) be the second derivative of 3*s**6/50 + 3*s**5/25 - s**4/10 - 2*s**3/5 - 3*s**2/10 - s. Find n, given that a(n) = 0.
-1, -1/3, 1
Let -1/2*i**3 + 11/2*i**2 + 25/2 - 35/2*i = 0. Calculate i.
1, 5
Let s = 15 - 11. Let m(v) be the first derivative of -7*v**3 - 2*v - v**5 + 11/2*v**2 + 2 + 17/4*v**s. Factor m(k).
-(k - 1)**3*(5*k - 2)
Let t(d) = 5*d**2 + 5*d + 4. Let y(b) = b**2 + b + 1. Let m be (-2)/(-8) - 14/(-8). Suppose s + s = m. Let i(l) = s*t(l) - 4*y(l). Factor i(q).
q*(q + 1)
Let f(w) be the third derivative of w**9/25200 - w**8/11200 + w**4/8 - 2*w**2. Let t(p) be the second derivative of f(p). Let t(v) = 0. What is v?
0, 1
Factor 5*z**4 + 195*z**2 + 720 + 290*z**2 - 1320*z + 118*z**3 - 8*z**3.
5*(z - 1)**2*(z + 12)**2
Suppose -4*n + u + 23 = n, 0 = 3*n + 2*u - 19. Suppose -8 = -4*r, n + 1 = -2*w + 5*r. Find j such that -32*j**2 + 31*j**w + j - 2*j + 2 = 0.
-2, 1
Suppose -4*s = -6*s + 48. Let c = -22 + s. Factor -1/5*g + 0 + 1/5*g**c.
g*(g - 1)/5
Let z(m) be the third derivative of 5/168*m**4 + 0 - 6*m**2 + 0*m + 1/840*m**6 - 1/105*m**5 - 1/21*m**3. What is w in z(w) = 0?
1, 2
Let m(w) = -5*w**4 - 7*w**3 + 2*w**2. Let a(q) be the first derivative of -q**5/5 - q**4/4 + q**3/3 - 7. Let b(z) = -4*a(z) + m(z). Factor b(d).
-d**2*(d + 1)*(d + 2)
Let a(u) = u**3 + u + 0*u**3 - 2*u**3 - u**4 - u**2. Let z(m) = 5*m**4 + 6*m**3 + 5*m**2 - 4*m. Let b(i) = 4*a(i) + z(i). Factor b(o).
o**2*(o + 1)**2
Let a(w) be the first derivative of -4*w**6/15 - 9*w**5/10 - w**4 - w**3/3 + 2*w - 2. Let j(z) be the first derivative of a(z). Factor j(i).
-2*i*(i + 1)**2*(4*i + 1)
Suppose 3*n - 1 = w, -3 = -4*n - w + 10. Factor 15*x**4 + x**3 - 6*x + 6*x - n*x**2.
x**2*(3*x - 1)*(5*x + 2)
Let m(f) be the first derivative of -f**4/4 + 2*f**3/3 - f**2/2 + 12. Find y, given that m(y) = 0.
0, 1
Let y(h) be the first derivative of -2 + 0*h + 1/16*h**4 + 0*h**2 + 1/12*h**3. Find s such that y(s) = 0.
-1, 0
Suppose 5*x - 72 = -62. What is r in -r - 1/3*r**3 + 1/3 + r**x = 0?
1
Let i be (-2)/(-3)*9*(-1)/(-12). Factor 0*r + 0 + 1/2*r**2 + i*r**4 - r**3.
r**2*(r - 1)**2/2
Let t(i) = i**3 + 7*i**2 - 9*i - 6. Let g be t(-8). Determine b, given that -2*b - 10*b**2 - 14*b**2 - 42*b**3 - 34*b**4 - g*b - 10*b**5 + 2*b**2 = 0.
-1, -2/5, 0
Let h(o) = o**3 + o**2 - 13*o - 1. Let f(q) = q**3 + 2*q**2 - 14*q. Let u(n) = 4*f(n) - 5*h(n). Let s(l) be the first derivative of u(l). Solve s(y) = 0.
-1, 3
Let m(g) = g. Let k(u) = 5*u**2 + 20*u - 10. Let p(i) = k(i) - 25*m(i). Factor p(q).
5*(q - 2)*(q + 1)
Let f(d) be the third derivative of -d**9/393120 + d**8/131040 + d**5/20 + 2*d**2. Let n(c) be the third derivative of f(c). Find z such that n(z) = 0.
0, 1
Let s(o) be the first derivative of -o**6/2 + 9*o**5/5 - 3*o**4/2 - 2*o**3 + 9*o**2/2 - 3*o - 1. Factor s(x).
-3*(x - 1)**4*(x + 1)
Let u(l) be the first derivative of -1/36*l**4 + 0*l**3 + 0*l**2 - 3*l - 1 - 1/60*l**5. Let j(n) be the first derivative of u(n). Factor j(m).
-m**2*(m + 1)/3
Let h = 86 + -171/2. Factor -y**2 + 0 + 1/2*y**3 + h*y.
y*(y - 1)**2/2
Let f(k) = -4*k - 3. Let j be f(-2). Find n such that 0*n**3 + n**4 - 5*n**3 + n**3 + 2*n**j - 3*n**4 = 0.
-1, 0, 2
Let c be 6 + 0/(-1 + 2). Let q be (-35)/(-15) + c/9. Factor 0 + 0*x**2 + 1/2*x**q - 1/2*x.
x*(x - 1)*(x + 1)/2
Let 2*x**3 - 8/3*x + 8/3*x**2 + 0 = 0. What is x?
-2, 0, 2/3
Let y(p) = 8*p**4 - 10*p**3 - 14*p**2 + 4*p. Let h(f) = 25*f**4 - 29*f**3 - 42*f**2 + 12*f. Let d(i) = -6*h(i) + 17*y(i). Factor d(l).
-2*l*(l - 1)*(l + 1)*(7*l - 2)
Suppose 0*i = -11*i + 22. Factor 6/5*b**3 + 0 + 0*b - 4/5*b**i.
2*b**2*(3*b - 2)/5
Let y(d) = d**3 - 2*d