4 + 0 + 0*z**3 + 2/3*z**2 + k*z**5 = 0.
-1, 0, 1
Let x(c) be the first derivative of -c**6/9 - 7*c**5/15 - 3*c**4/4 - 5*c**3/9 - c**2/6 - 9. Factor x(m).
-m*(m + 1)**3*(2*m + 1)/3
Factor -21*c**2 - 44 + 75*c**2 - 14*c**3 + 3*c**4 + 38*c**3 - 37.
3*(c - 1)*(c + 3)**3
Let s(h) be the second derivative of 1/48*h**4 - 1/160*h**5 + 1/1440*h**6 - 1/6*h**3 - 2*h + 0*h**2 + 0. Let w(m) be the second derivative of s(m). Factor w(f).
(f - 2)*(f - 1)/4
Suppose -1347 + 3*r + 14*r**2 + 1333 - 2*r**3 - r = 0. What is r?
-1, 1, 7
Let d(y) = -35*y**2 - 685*y - 3485. Let b(t) = 5*t**2 + 98*t + 498. Let c(k) = -15*b(k) - 2*d(k). Factor c(a).
-5*(a + 10)**2
Let o(w) be the first derivative of w**3/3 - w**2 - 3*w + 3. Let q be o(-2). Factor -v**2 - 2*v + q + 3*v**2 - 5.
2*v*(v - 1)
Let z(v) be the third derivative of 1/60*v**6 + 1/24*v**4 + 1/24*v**5 + 0 + 0*v**3 - 5*v**2 + 1/420*v**7 + 0*v. What is k in z(k) = 0?
-2, -1, 0
Suppose -30 = -3*c - 3*c. Find p such that -2*p**5 + 8*p**4 - 2*p**3 + 4*p**3 - 4*p**2 - 4*p**c = 0.
-2/3, 0, 1
Let b = 901 - 6305/7. Factor 0*g + 0 - b*g**3 + 4/7*g**2.
-2*g**2*(g - 2)/7
Let z(p) = -3*p**2 - 2*p - 29. Let s(r) = r**2 + r + 10. Let w(n) = -17*s(n) - 6*z(n). Solve w(j) = 0.
1, 4
Let d = 8/49 + -47/588. Let h(g) be the second derivative of -1/24*g**4 - d*g**3 + 0 + 4*g + 0*g**2. Determine v, given that h(v) = 0.
-1, 0
Let t(w) be the second derivative of -1/24*w**3 + 4*w + 0*w**2 + 1/168*w**7 + 0 + 0*w**5 + 1/60*w**6 - 1/24*w**4. Factor t(g).
g*(g - 1)*(g + 1)**3/4
Let -2*t**4 - 46/3*t**3 + 22/3*t**2 + 46/3*t - 16/3 = 0. Calculate t.
-8, -1, 1/3, 1
Let o(d) be the third derivative of -d**7/5040 + d**6/1440 - d**4/8 + 3*d**2. Let r(q) be the second derivative of o(q). Factor r(l).
-l*(l - 1)/2
Let j = 12 - 7. Suppose -z + 3*z**5 - 6*z**4 - 2*z + z**2 + j*z**2 = 0. What is z?
-1, 0, 1
Let h(m) be the first derivative of -2*m + 1 - 2*m**2 - 2/3*m**3 - 1/12*m**4. Let i(w) be the first derivative of h(w). Factor i(z).
-(z + 2)**2
Let k(z) be the second derivative of -z**5/50 - z**4/5 - 46*z. Factor k(g).
-2*g**2*(g + 6)/5
Let q(l) = 5*l**2 - 65*l. Let z(s) = 2*s**2 - 33*s. Let r(a) = -3*q(a) + 5*z(a). Find w, given that r(w) = 0.
0, 6
Let y(c) be the second derivative of -2/27*c**3 + 6*c + 0 - 1/9*c**2 - 1/54*c**4. What is t in y(t) = 0?
-1
Factor -15*j + 2*j**2 + j**2 + j**2 - 9*j**2.
-5*j*(j + 3)
Suppose -12 = -v + 4*n - n, v + 3*n + 12 = 0. Solve -4/7*r**2 + v - 2/7*r**3 - 2/7*r = 0 for r.
-1, 0
Let o = -989/3 - -331. Factor 0*z + o*z**2 - 2/3*z**3 + 0.
-2*z**2*(z - 2)/3
Suppose -3*f + 2 = f - 2*u, -4*f - 4*u = -20. Let 8/5 + 12/5*o + 4/5*o**f = 0. Calculate o.
-2, -1
Let y = 335 - 235. Let h = y + -698/7. Let 2/7 - 2/7*u**2 - h*u + 2/7*u**3 = 0. Calculate u.
-1, 1
Let t(y) = -11*y**3 + 12*y**2 - 20*y - 8. Let i(l) = -7*l**3 + 8*l**2 - 13*l - 5. Let m(g) = -8*i(g) + 5*t(g). Suppose m(c) = 0. Calculate c.
0, 2
Let b(y) be the first derivative of y**4/14 + 2*y**3/21 - 6. Determine o, given that b(o) = 0.
-1, 0
Let u(x) be the first derivative of -x**9/3024 + x**7/840 + x**3/3 - 1. Let b(q) be the third derivative of u(q). Factor b(g).
-g**3*(g - 1)*(g + 1)
Let m(h) be the first derivative of -2*h**3/27 - 2*h**2/9 - 25. Factor m(x).
-2*x*(x + 2)/9
Suppose 3*h - 12 = -h. Suppose -62*z**h + 64*z**3 + z - 3*z = 0. Calculate z.
-1, 0, 1
Suppose -3*l - 2*b - 3 = -5*b, 2*l - 2 = -2*b. Suppose 0*r + 4*r = l. Solve r*h**3 + 0*h**3 - h**4 + h**2 = 0.
-1, 0, 1
Let i(l) be the second derivative of l**6/60 + 3*l**5/40 - 3*l**4/8 - 23*l**3/12 - 3*l**2 + 35*l. What is a in i(a) = 0?
-4, -1, 3
Let o = 60491/11 - -11073/22. Factor 140*l + o*l**4 + 16807/4*l**5 + 980*l**2 + 8 + 3430*l**3.
(7*l + 2)**5/4
Let d = 14 + -9. Suppose d*x - 4*s = 11, 5*x + 5*s + 11 = 31. Factor -4*r**2 + 2*r + 4*r**2 - r**2 + x*r**2.
2*r*(r + 1)
Let 4/5 - 1/5*t**2 + 3/5*t = 0. Calculate t.
-1, 4
Let r(t) = -3*t**3 + 8*t**2 + 3*t - 4. Let y(a) = 4*a**3 - 9*a**2 - 3*a + 5. Let v(u) = 5*r(u) + 4*y(u). Solve v(x) = 0 for x.
-3, -1, 0
Let t(y) be the first derivative of -1 + 1/24*y**4 - 1/18*y**3 - 1/12*y**2 + 1/6*y. Factor t(n).
(n - 1)**2*(n + 1)/6
Let a = -231 - -2081/9. Factor a + 0*o - 2/9*o**2.
-2*(o - 1)*(o + 1)/9
Let t(n) be the second derivative of 1/6*n**3 - 3*n + 0 + 0*n**2 + 1/20*n**5 + 1/6*n**4. Factor t(i).
i*(i + 1)**2
Let r = -1/26 - -7/13. Factor 1 + r*i - 1/2*i**2.
-(i - 2)*(i + 1)/2
Suppose 0 = -4*t - 10*d + 7*d + 3, 4 = -7*t + 4*d. Solve 1/2*k**4 - 3/4*k**5 + k + 9/4*k**3 + t - 3*k**2 = 0 for k.
-2, 0, 2/3, 1
Factor -4 - 27*n**2 - 13*n - 2 + 6*n**2 - 14*n.
-3*(n + 1)*(7*n + 2)
Let o(j) be the third derivative of -j**6/60 - j**5/15 - j**4/12 - 8*j**2. Find m, given that o(m) = 0.
-1, 0
Let f(x) be the second derivative of -x**6/10 + 9*x**5/20 - 3*x**4/4 + x**3/2 - 7*x. Factor f(i).
-3*i*(i - 1)**3
Let l(k) be the third derivative of -1/420*k**7 + 0*k + 1/32*k**4 + k**2 + 0 + 1/240*k**5 + 1/24*k**3 - 1/160*k**6. Solve l(q) = 0 for q.
-1, -1/2, 1
Let h(z) be the third derivative of -z**8/20160 + z**7/15120 + z**5/30 + 3*z**2. Let v(x) be the third derivative of h(x). Factor v(s).
-s*(3*s - 1)/3
Suppose 8*l - 32 - 1/2*l**2 = 0. What is l?
8
Let c(s) = 4*s**2 - 2*s - 1. Let o be c(2). Let w = o + -8. Determine u so that 6/7*u**w - 8/7*u**4 - 2/7 - 6/7*u + 10/7*u**2 = 0.
-1, -1/4, 1
Suppose 15 = -2*p + k, -k = -p - 3*k + 5. Let n be (-12)/20 + (-3)/p. Factor 2/5*b**2 + 0*b + n + 2/5*b**3.
2*b**2*(b + 1)/5
Let h(f) = 55*f**4 - 25*f**3 - 35*f**2 - 25*f + 55. Let l(c) = 9*c**4 - 4*c**3 - 6*c**2 - 4*c + 9. Let t(k) = 4*h(k) - 25*l(k). Determine w so that t(w) = 0.
-1, 1
Let m be (9 + -10)*1/(-4). Let x(s) be the second derivative of 2*s + 0 - 1/24*s**4 + m*s**3 - 1/2*s**2. Factor x(k).
-(k - 2)*(k - 1)/2
Suppose -4*i + 28 = 4*j, 5*i - 38 = -j - 11. Solve -3 - o**j + 3 - o = 0.
-1, 0
Factor 0*c + 1/2*c**2 - 1/2.
(c - 1)*(c + 1)/2
Let l = -7 + 13. Suppose 5*i = 9 + l. Suppose 2/3 - 4/3*n + 4/3*n**i - 2/3*n**2 = 0. What is n?
-1, 1/2, 1
Suppose g - n = 4, -4*g - 3*n = n. Let x = -28/15 - -34/15. Factor -2/5*o**g - x + 4/5*o.
-2*(o - 1)**2/5
Let c = 3/91 - -7/13. Factor 0*d**3 + 2/7*d**5 - 2/7*d + 0 + 4/7*d**4 - c*d**2.
2*d*(d - 1)*(d + 1)**3/7
Determine v, given that 0*v + 0*v**2 - 2/9*v**5 + 0 + 0*v**3 + 2/9*v**4 = 0.
0, 1
Let z(p) be the third derivative of p**6/40 - 2*p**2. Determine c, given that z(c) = 0.
0
Let r(z) be the third derivative of z**6/15 - 7*z**5/45 - 2*z**4/9 + 10*z**3/9 + 10*z**2 - 1. Find n, given that r(n) = 0.
-5/6, 1
Let o(c) be the first derivative of 0*c + 1/12*c**3 + 0*c**2 + 1. Factor o(d).
d**2/4
Suppose 2*m + 4*k - k + 3 = 0, 3*m = -5*k - 6. Let c(r) be the third derivative of 0 + 2/9*r**m + 1/4*r**4 + 7/90*r**5 + 0*r + r**2. What is f in c(f) = 0?
-1, -2/7
Factor -4*q**4 - 6*q**2 + 3*q**2 - 4*q**5 + 3*q**2.
-4*q**4*(q + 1)
Let b(g) be the second derivative of -5*g**7/14 + 2*g**6/3 + 2*g**5 - 5*g**4/2 - 25*g**3/6 + 5*g**2 + 2*g - 6. Find c such that b(c) = 0.
-1, 1/3, 1, 2
Let z = -2/41 - -45/82. Factor -5/2*t - z - 7/2*t**3 - t**4 - 9/2*t**2.
-(t + 1)**3*(2*t + 1)/2
Let v = 141/4 - 35. Let d(y) be the second derivative of -2*y - v*y**4 + 0 - 1/30*y**6 + 0*y**2 + 1/6*y**3 + 3/20*y**5. Let d(p) = 0. Calculate p.
0, 1
Suppose -2/7*g**2 + 0 + 2/7*g**4 + 0*g**3 + 0*g = 0. What is g?
-1, 0, 1
Let i be -9*2/4*4/(-6). Let r be (4/(-10))/((-16)/10). Factor 1/2*p**4 + 1/4*p - 1/2*p**2 + 0 - r*p**i.
p*(p - 1)*(p + 1)*(2*p - 1)/4
Let m(c) be the second derivative of c**5/60 - 7*c**4/36 + 11*c**3/18 - 5*c**2/6 + 66*c. Factor m(k).
(k - 5)*(k - 1)**2/3
Solve -22/7*s**3 + 90/7*s**2 - 162/7*s + 108/7 + 2/7*s**4 = 0 for s.
2, 3
Let h(l) = -3*l - 3. Let n be h(-3). Suppose 3*u + 3*k = 6, -5*u + 4*u + k + n = 0. Solve o**3 + 2 - 2*o**u - 5*o**3 + 2*o + 2*o = 0 for o.
-1, 1
Let r = -105 + 421/4. Factor 1/4*b**4 - r*b + 1/4 + 1/2*b**3 - 1/4*b**5 - 1/2*b**2.
-(b - 1)**3*(b + 1)**2/4
Let x(z) be the third derivative of 0 - 1/70*z**5 + 1/42*z**4 - z**2 + 1/420*z**6 + 0*z + 0*z**3. Factor x(i).
2*i*(i - 2)*(i - 1)/7
Let q(a) be the second derivative of -49*a**5/20 - 175*a**4/12 - 44*a**3/3 - 6*a**2 + 9*a. What is f in q(f) = 0?
-3, -2/7
Factor -2/7*j**4 + 4/7 - 10/7*j + 6/7*j**2 + 2/7*j**3.
-2*(j - 1)**3*(j + 2)/7
Let c(m) be the second derivative of 0*m**2 + 0