3*j**4 - 3*j**5 + 0 - 2/3*j**m + 0*j - 5/3*j**3 = 0.
-2/9, 0, 1
Let t(i) be the third derivative of -i**8/5040 - i**7/2520 - i**3/2 + 4*i**2. Let l(s) be the first derivative of t(s). Determine a, given that l(a) = 0.
-1, 0
Let i(t) be the first derivative of -t**6/15 - t**5/10 + t**4/6 + t**3/3 - 2*t + 1. Let n(k) be the first derivative of i(k). Solve n(s) = 0 for s.
-1, 0, 1
Let s(z) be the third derivative of -z**9/3780 - z**8/1120 - z**7/1120 - z**6/2880 - z**4/24 + z**2. Let h(t) be the second derivative of s(t). Factor h(y).
-y*(y + 1)*(4*y + 1)**2/4
Solve -28*c**4 + 39*c**3 - 17*c**4 - 10*c**2 + 16*c**3 = 0 for c.
0, 2/9, 1
Determine l so that l**2 - 2*l**2 - 1 + 5*l - 8*l + l = 0.
-1
Let q = -2 - -2. Suppose q = 2*c - 4 - 2. Find b, given that -2/9*b**c + 0*b + 0 + 4/9*b**2 = 0.
0, 2
Factor -1/5*g**2 + 2/5*g**3 - 1/5*g**4 + 0*g + 0.
-g**2*(g - 1)**2/5
Let u = 2 + 0. Factor -2 - 2 - 21 - 3*n**2 - 18*n - u.
-3*(n + 3)**2
Let g(f) be the first derivative of 3*f**6/80 - f**5/20 - f**4/16 - f**2 - 3. Let h(s) be the second derivative of g(s). Let h(l) = 0. Calculate l.
-1/3, 0, 1
Let b = 4 + 8. Suppose -2*d - b = -5*f, -f + 18 - 2 = 3*d. Suppose -q**d - q**5 + 2*q**2 - 5*q**4 + 5*q**5 = 0. What is q?
-1/2, 0, 1
Let t be -3 - -1 - -12 - 1. Suppose 0 = 4*n - t*n + 15. Factor -11*f**2 + 5*f + 75*f**5 + 90*f**4 + 7*f - 25*f**2 - 33*f**n.
3*f*(f + 1)**2*(5*f - 2)**2
Let v(m) be the second derivative of -m**5/90 - m**4/24 - m**3/18 + 3*m**2/2 - 4*m. Let f(u) be the first derivative of v(u). Determine i, given that f(i) = 0.
-1, -1/2
Let s(k) = 3*k**2 + 1. Let f be s(1). Find h, given that 3*h**3 + 11*h**4 + 3*h + 3 - 6*h - 5*h**f - 9*h**2 = 0.
-1, 1/2, 1
Suppose -2*m = m - 0*m. Determine f, given that m - 2/5*f - 2/5*f**2 = 0.
-1, 0
Let i(z) = -z**3 + 5*z**2 + 8*z + 10. Let n be i(7). Let m = 97/3 + n. Suppose 0 + 0*r + m*r**3 + 0*r**2 = 0. Calculate r.
0
Let f be 1/1 - (-4)/8. Factor -3/2*n**2 - f - 3*n.
-3*(n + 1)**2/2
Suppose 0 = 11*k - 13*k. Suppose k*u + 1/2*u**2 - 1/2 = 0. Calculate u.
-1, 1
Let a(v) = 2*v**3 - 3*v**2 - v + 1. Let h(n) = n**2 - n + 1. Let k = -4 - -3. Let f(r) = k*a(r) - h(r). Factor f(c).
-2*(c - 1)**2*(c + 1)
Let k(v) be the third derivative of v**7/525 + v**6/100 + v**5/75 - 35*v**2. Find i such that k(i) = 0.
-2, -1, 0
Suppose 4*n + i + 0*i = 216, 253 = 5*n - 3*i. What is o in -39*o + 10*o - 91*o - 94*o**5 - 705*o**3 - 12 - n*o**5 - 525*o**4 - 435*o**2 = 0?
-1, -2/7
Let a be 7/20 + (-12)/16. Let z = 1/10 - a. Factor 5/4*o**3 + z*o + 0 + 7/4*o**2.
o*(o + 1)*(5*o + 2)/4
Let a(s) = s**3 - 6*s**2 - 7*s - 1. Let g be a(7). Let q be g/(-10)*60/8. Factor -1/2*b**2 + q*b**3 + 1/2*b**4 + 0 + 0*b.
b**2*(b + 2)*(2*b - 1)/4
Factor -3/7*b + 6/7*b**2 - 3/7*b**3 + 0.
-3*b*(b - 1)**2/7
Let d(f) be the third derivative of -2*f**7/105 + 13*f**6/120 - f**5/4 + 7*f**4/24 - f**3/6 - 35*f**2. Factor d(y).
-(y - 1)**3*(4*y - 1)
Let c(n) be the first derivative of n**4/16 + n**3/12 - n**2/8 - n/4 - 7. Factor c(g).
(g - 1)*(g + 1)**2/4
Let h(y) be the first derivative of 8*y + 1 + 2*y**2 - 4/3*y**3. Factor h(m).
-4*(m - 2)*(m + 1)
Determine z so that 41*z**3 - 27*z**3 + 20*z - 4*z**2 - 18*z**3 - 12 = 0.
-3, 1
Let c(t) be the second derivative of t**6/21 + 4*t**5/35 + t**4/42 - 2*t**3/21 + 4*t. Factor c(h).
2*h*(h + 1)**2*(5*h - 2)/7
Let c(l) be the third derivative of -1/28*l**4 + 5*l**2 + 0 + 0*l - 2/21*l**3 - 1/210*l**5. Factor c(x).
-2*(x + 1)*(x + 2)/7
Let t be ((-3)/48*-6 + 0)/9. Let a(x) be the third derivative of 0*x**3 + 2*x**2 + 0 + 0*x + 1/60*x**5 - t*x**4. Suppose a(b) = 0. Calculate b.
0, 1
Determine b, given that -3/5*b - 9/5*b**5 + 0 - 6/5*b**2 + 6/5*b**4 + 12/5*b**3 = 0.
-1, -1/3, 0, 1
Let o(n) be the second derivative of -n**7/14 - 9*n**6/10 - 24*n**5/5 - 14*n**4 - 24*n**3 - 24*n**2 - 6*n. Factor o(x).
-3*(x + 1)*(x + 2)**4
Let t(y) be the third derivative of 3*y**5/20 - 17*y**4/12 - 4*y**3/3 - 8*y**2. Solve t(q) = 0.
-2/9, 4
Let m = 4/59 + 27/472. Let z(b) be the first derivative of -2 - 1/6*b**3 - 1/4*b**2 + m*b**4 + 1/2*b. Factor z(k).
(k - 1)**2*(k + 1)/2
Find g such that -3 + 3/2*g**2 + 87/2*g**4 - 15*g**5 - 75/2*g**3 + 21/2*g = 0.
-1/2, 2/5, 1
Let n(r) be the first derivative of -12*r**5/35 - r**4/4 + 11*r**3/21 + r**2/2 + r/7 + 5. Solve n(y) = 0 for y.
-1, -1/3, -1/4, 1
Let q(z) = -17*z**4 - 13*z**3 - 9*z**2 - 13*z + 13. Let b(f) = 8*f**4 + 6*f**3 + 4*f**2 + 6*f - 6. Let t(p) = 13*b(p) + 6*q(p). Factor t(v).
2*v**2*(v - 1)*(v + 1)
Let n(m) be the third derivative of -m**5/20 - m**4/8 + 10*m**2. Factor n(a).
-3*a*(a + 1)
Let x(z) be the first derivative of z**4/2 - 2*z**3/3 - 2. Factor x(m).
2*m**2*(m - 1)
Suppose 3*p + 60 = 6. Let u be 4/p*1*-9. Factor 1/2 + 3/2*n - u*n**2.
-(n - 1)*(4*n + 1)/2
Find u, given that -240*u - 33 - 396*u**2 - 196*u**3 - 108*u**2 + 1 = 0.
-2, -2/7
Let g = 1 + 3. Suppose -g - 8 = -4*d. Factor d*k**5 - 3*k**3 - k**3 - 5*k**5 + 6*k**4.
-2*k**3*(k - 2)*(k - 1)
Factor 7*q - 60*q**2 - 20*q**4 + 131*q**3 - 56*q**3 - 27*q.
-5*q*(q - 2)**2*(4*q + 1)
Suppose 0 = 4*n - 6 - 2. Let m(v) be the second derivative of 1/15*v**6 + 1/6*v**4 - 1/5*v**5 + 0*v**n + 0*v**3 + 0 + v. Factor m(j).
2*j**2*(j - 1)**2
Let 3*v + 2*v**4 + 2 - 41*v**2 + 37*v**2 + 2*v**3 + 2*v**5 - 4*v - 3*v**5 = 0. What is v?
-1, 1, 2
Let v(w) be the first derivative of -w**6/1440 - w**5/480 + w**4/48 - w**3 + 1. Let c(q) be the third derivative of v(q). Factor c(b).
-(b - 1)*(b + 2)/4
Let m(q) be the first derivative of -2*q**5/15 - q**4/2 + 2*q**3/9 + q**2 - 36. Solve m(l) = 0.
-3, -1, 0, 1
Let l = 83/2 + -41. Find f such that -l - 1/2*f**4 - 2*f - 3*f**2 - 2*f**3 = 0.
-1
Suppose -291*s = -290*s. Factor s*m**2 + 0 + 0*m - 8/7*m**5 - 4/7*m**3 + 12/7*m**4.
-4*m**3*(m - 1)*(2*m - 1)/7
Let k(d) be the first derivative of 2/27*d**3 + 0*d + 1/18*d**4 - 2/45*d**5 - 3 - 1/9*d**2. Factor k(i).
-2*i*(i - 1)**2*(i + 1)/9
Suppose x = -4*x + 15. Suppose 0*w + 3 = -w - 3*q, -x*q = 6. Solve 2*v**5 + 0 + 14/3*v**4 + 10/3*v**w + 0*v + 2/3*v**2 = 0 for v.
-1, -1/3, 0
Let w(j) be the third derivative of 3*j**2 + 0*j - 1/240*j**6 - 1/4*j**4 + 0 + 2/3*j**3 + 1/20*j**5. Find r, given that w(r) = 0.
2
Let c = 99 + -97. Factor 2*p - 4/7 - 6/7*p**c.
-2*(p - 2)*(3*p - 1)/7
Let b = 91/9 + -10. Let l(f) be the second derivative of 0 + 7/36*f**4 - 1/12*f**5 + f - b*f**3 + 0*f**2. Solve l(m) = 0.
0, 2/5, 1
Let 0 - 2/3*g**2 + 0*g - 2/3*g**3 = 0. Calculate g.
-1, 0
Let y(p) = -3*p - 22. Let f be y(-8). Let k(m) be the first derivative of -f - 2*m - 1/6*m**3 + m**2. Factor k(l).
-(l - 2)**2/2
Solve 1/2*x + 0 - 1/4*x**2 = 0 for x.
0, 2
Let i = -3 + 6. Suppose m - i + 1 = 0. Factor -1/3*c + 1/3*c**5 + 0 + 2/3*c**m + 0*c**3 - 2/3*c**4.
c*(c - 1)**3*(c + 1)/3
Let q(s) be the second derivative of -s**6/120 - 3*s**5/80 - s**4/16 - s**3/24 + 4*s. Solve q(b) = 0 for b.
-1, 0
Let c(t) = -t**3 + 5*t**2 + 24*t - 38. Let k(d) = 4*d**3 - 26*d**2 - 120*d + 191. Let f(p) = 11*c(p) + 2*k(p). Suppose f(i) = 0. What is i?
-3, 2
Let v = -1499/4 + 375. Suppose -1/2*t**3 - 1/4*t**2 + 1/2*t**5 + 0*t + v*t**4 + 0 = 0. What is t?
-1, -1/2, 0, 1
Let w(a) be the second derivative of -a**5/20 - a**4/2 - a**3 - 5*a**2/2 + 7*a. Let d be w(-5). Factor d + 1/5*l**2 - 2/5*l.
l*(l - 2)/5
Let v(p) = -3*p**2 + 14*p + 45. Let d(z) = z**2 + 1. Let x(k) = -4*d(k) - v(k). Factor x(n).
-(n + 7)**2
Suppose 0 = -5*a + 3*h + 4, 0 = 3*a + h + 2*h - 12. Let p(q) be the second derivative of -1/6*q**4 + 0 + 0*q**a - 3*q - 1/3*q**3. Factor p(o).
-2*o*(o + 1)
Let d(y) be the third derivative of -2*y**2 + 1/21*y**3 + 0*y**4 + 0 - 1/210*y**5 + 0*y. Suppose d(o) = 0. What is o?
-1, 1
Let a = 0 + 5. Factor 8*y**3 - 4*y**3 - 9*y**5 + 4*y**3 - 24*y**4 + 27*y**a.
2*y**3*(3*y - 2)**2
Factor -2/3*o**2 - 4/9 + 14/9*o.
-2*(o - 2)*(3*o - 1)/9
Let t(z) be the third derivative of -z**7/945 - z**6/270 + z**4/54 + z**3/27 - 8*z**2. Determine j so that t(j) = 0.
-1, 1
What is l in l**2 - 2*l**4 + l**2 - 4*l**2 + 4*l**2 = 0?
-1, 0, 1
Let l(u) = -u**3 + 2*u**2 - 5*u. Let r(n) = 4*n**3 - 6*n**2 + 16*n. Let g(y) = 14*l(y) + 4*r(y). Factor g(v).
2*v*(v - 1)*(v + 3)
Suppose -5*f - 7 = -27. Determine b so that -3*b**f - 2*b**5 + b**5 - 2*b**2 + 1 + 4*b**2 + 0*b**2 - 2*b**3 + 3*b = 0.
-1, 1
Find r, given that 0 + 1/7*r**2 - 6/7*r = 0.
0, 6