e third derivative of -l**5/60 - l**4/24 - 4*l**2. Let j(a) = 0. Calculate a.
-1, 0
Let c be 66/(-825) + 33/100. Factor j**3 - 3/2*j**2 + j - c*j**4 - 1/4.
-(j - 1)**4/4
Let -10*h**2 + 3*h**3 + 2*h**5 + 3*h**5 + 12*h**3 - 10*h**5 = 0. Calculate h.
-2, 0, 1
Find b, given that -b**3 + 1/3*b**5 + 0 + 4/3*b + 2/3*b**4 - 4/3*b**2 = 0.
-2, 0, 1
Let f(w) be the first derivative of -1/10*w**4 + 2/5*w - 4 + 1/5*w**2 - 2/15*w**3. Factor f(h).
-2*(h - 1)*(h + 1)**2/5
Let p(k) = -k**4 + k**3 + k**2 - 1. Let v(y) = 5*y**4 - 4*y**3 - 7*y**2 + 2*y + 4. Let g(u) = -4*p(u) - v(u). Suppose g(c) = 0. What is c?
-2, 0, 1
Solve 6*b + 15*b + b**2 - b - 28 + 7*b**2 = 0 for b.
-7/2, 1
Let i(b) be the second derivative of -b**5/90 - b**4/54 - 4*b. Factor i(j).
-2*j**2*(j + 1)/9
Let o(q) = q**3 + 7*q**2 + 7*q + 8. Let i be o(-6). Suppose -2*k - 12 - k**i - 2*k**2 - 10*k = 0. Calculate k.
-2
Let c(x) be the second derivative of 0*x**2 + 0*x**6 + 0*x**3 + 0*x**4 - 1/90*x**5 + 1/189*x**7 + 0 - 2*x. Factor c(r).
2*r**3*(r - 1)*(r + 1)/9
Let q(g) be the third derivative of 2*g**7/105 - g**6/30 - g**5/15 + g**4/6 + g**2. Find i, given that q(i) = 0.
-1, 0, 1
Let f(y) be the first derivative of 3*y**5 + 9*y**4/4 - 7*y**3 - 9*y**2/2 + 6*y + 17. Factor f(t).
3*(t - 1)*(t + 1)**2*(5*t - 2)
Suppose 10*k - 16*k = -24. Let x(y) = -y + 1. Let i be x(-2). What is n in 2/3*n**k + 0*n**2 + 2/3*n**i + 0 + 0*n = 0?
-1, 0
Solve 5/2*m - 25/2 - 1/8*m**2 = 0.
10
Let y = 562 - 3918/7. Find r such that 10/7*r**3 + 8/7*r + 0 + y*r**2 + 2/7*r**4 = 0.
-2, -1, 0
Let q = 10 - 7. Determine k, given that 3*k**2 - 18*k**q - 24 + 24 + 24*k**4 = 0.
0, 1/4, 1/2
Let c(y) be the first derivative of y**3/3 - y**2/2 - 8. Let c(o) = 0. Calculate o.
0, 1
Let o be 3/7*32/48. Let p be 4/(-35) - 4/(-10). Factor p*u + o*u**2 - 4/7.
2*(u - 1)*(u + 2)/7
Let w = 1459897/77 + -18960. Let r = 3/11 - w. Suppose -r*d**2 + 0 + 2/7*d + 2/7*d**3 = 0. What is d?
0, 1
Suppose -5*p**2 + 6*p**4 + 9*p**3 + p**4 - 2*p - 2*p**4 - 7*p**5 = 0. Calculate p.
-1, -2/7, 0, 1
Let q = 185/4 + -91/2. Factor 1/4*t**3 + q*t - 3/4*t**2 - 1/4.
(t - 1)**3/4
Let j(h) be the first derivative of 2*h**3/15 - h**2/5 + 9. Factor j(r).
2*r*(r - 1)/5
Let y(i) = 3*i**3 + 3*i - 3. Suppose 21 = -4*s + 1. Let l(a) = -6*a**3 - a**2 - 5*a + 5. Let w(z) = s*y(z) - 3*l(z). Let w(o) = 0. Calculate o.
-1, 0
Let y = -3/122 + 253/366. Factor -y + 10/3*p - 8/3*p**2.
-2*(p - 1)*(4*p - 1)/3
Let v = -350 + 353. Factor -1/3*c**v + 0 + 1/3*c**2 + 0*c.
-c**2*(c - 1)/3
Let x = 61/5 - 12. Let d(m) be the first derivative of 0*m + 1/3*m**3 + 1/25*m**5 - x*m**4 - 1/5*m**2 - 1. What is r in d(r) = 0?
0, 1, 2
Let o(g) be the first derivative of 2*g**3/3 + 3*g**2 + 4*g + 18. Factor o(a).
2*(a + 1)*(a + 2)
Let o(r) = -7*r + 56. Let f be o(8). Factor 0 + f*q**2 + 0*q - 2/5*q**3 + 2/5*q**4.
2*q**3*(q - 1)/5
Let v = -88/3 + 713/24. Let s(q) be the first derivative of -3/16*q**4 - v*q**2 + 0*q - 1/2*q**3 - 2. Factor s(u).
-3*u*(u + 1)**2/4
Let m(j) be the second derivative of 3/4*j**4 + 0*j**3 + 0 + 0*j**2 + 1/5*j**6 - 9*j - 21/20*j**5. Factor m(p).
3*p**2*(p - 3)*(2*p - 1)
Let g(s) = -3*s**5 + 5*s**4 + 11*s**3 - 5*s**2 - 3*s. Let f(q) = -8*q**5 + 12*q**4 + 28*q**3 - 12*q**2 - 8*q. Let w(u) = -5*f(u) + 12*g(u). Factor w(c).
4*c*(c - 1)**2*(c + 1)**2
Let 0*b + 3/2*b**2 + 3/2*b**4 + 0 - 3*b**3 = 0. Calculate b.
0, 1
Suppose -7*g + 10 = -2*g. Determine w so that 2*w**2 - w**4 + g*w**4 - 3*w**4 - 4*w + 4*w**3 + 0*w = 0.
-1, 0, 1, 2
Determine j, given that -45*j**3 - 33*j + 130*j**2 + 15*j - 82*j - 40 + 10*j**3 = 0.
-2/7, 2
Let q(c) = c**2 - 8*c + 8. Let x be q(6). Let b = x + 7. Factor -1/5*n**2 + 0*n + 0 + 0*n**b + 1/5*n**4.
n**2*(n - 1)*(n + 1)/5
Let j(z) = -10*z + 5. Let s(g) = -g**2 - 9*g + 6. Let a(n) = -6*j(n) + 5*s(n). Determine m so that a(m) = 0.
0, 3
Let l = 103/11 + -101/11. Factor 2/11*w**4 - 4/11 + 10/11*w - l*w**3 - 6/11*w**2.
2*(w - 1)**3*(w + 2)/11
Suppose -2*z = -5*l - 15, 0 = 3*l + 2*l + 15. Suppose -m + 2 + 0 = z. Let 2/7*x + 2/7*x**m + 0 = 0. Calculate x.
-1, 0
Let w = 520 - 518. Factor -2/5*h**3 + 0 + 0*h**w + 2/5*h.
-2*h*(h - 1)*(h + 1)/5
Let a(u) = u**5 - u**4 - u**3 - u**2 - u - 1. Let c(h) = 2*h**5 - 4*h**4 - h**3 - h**2 - 4*h - 4. Let i(k) = -3*a(k) + c(k). Determine g, given that i(g) = 0.
-1, 1
Suppose -j + j - 4*j = 0. Let l(g) be the first derivative of 1/2*g**3 + 1/4*g**2 - 2 + 3/8*g**4 + j*g + 1/10*g**5. Factor l(z).
z*(z + 1)**3/2
Factor 1/3*t**2 + 0*t - 1/3.
(t - 1)*(t + 1)/3
Find l, given that -2/9*l**2 - 10/9*l - 4/3 = 0.
-3, -2
Let t(j) = 2 - 3*j + j - 9. Let w be t(-5). Factor -1 + 2*s**4 + 4*s**5 + s + s - 3*s + 5*s**2 + s**w - 10*s**4.
(s - 1)**3*(2*s + 1)**2
Let 16/3*u + 0 - 8*u**2 - 2/3*u**4 + 4*u**3 = 0. Calculate u.
0, 2
Let x(j) be the second derivative of -2*j**7/21 - 2*j**6/15 + 3*j**5/5 + 5*j**4/3 + 4*j**3/3 + 2*j. Suppose x(s) = 0. Calculate s.
-1, 0, 2
Let c(z) = 3*z**2 - 8*z - 2. Let m(w) = w**2 - 3*w. Let j(i) = 2*c(i) - 7*m(i). Factor j(s).
-(s - 4)*(s - 1)
Let i be (56/24)/((-1)/(-6)). Solve 4*c**2 - 6*c**5 - i*c**3 - 95 + 95 + 16*c**4 = 0.
0, 2/3, 1
Let o(t) = 5*t**3 + 2*t**2 - 2*t - 2. Let w(k) = -4*k**3 - 2*k**2 + k + 3. Let i(l) = 5*o(l) + 6*w(l). Factor i(v).
(v - 2)**2*(v + 2)
Suppose 0 = -0*j - 2*j + 4. Factor b**j + 6*b**3 - 6*b**2 - 2*b**2 - 2*b**4 + 3*b**2.
-2*b**2*(b - 2)*(b - 1)
Let l(y) be the first derivative of 18*y - 3*y**2 - 15*y + 1 + y**3 + 0. Factor l(b).
3*(b - 1)**2
Let i(f) be the second derivative of 2*f + 0*f**2 - 1/90*f**5 - 1/18*f**4 + 0 + 0*f**3. Factor i(w).
-2*w**2*(w + 3)/9
Let k be ((-4)/(-3))/(3/(-18)). Let q be k/(-10)*140/21. Determine z, given that -8*z - 2/3*z**3 - q - 4*z**2 = 0.
-2
Let k be 3*(3/(-30))/(27/(-225)). Solve 4*z**4 + 33/4*z**2 + 10*z**3 + 1/4 + k*z = 0 for z.
-1, -1/4
Factor -125 + 175*o - 18*o**2 + 5*o**3 - 6*o**2 - 3*o**2 - 28*o**2.
5*(o - 5)**2*(o - 1)
Let k = 164/3 + -54. Solve -3*u**2 + 10/3*u**3 + k - u = 0 for u.
-1/2, 2/5, 1
Let a(l) be the first derivative of l**3 + 20. Let a(v) = 0. Calculate v.
0
Suppose 0 = -5*f + f. Factor 2*d**2 - d**2 + f*d**2 + 2*d.
d*(d + 2)
Factor 4/3*l**2 + 10/3*l**4 + 0 + 14/3*l**3 + 0*l.
2*l**2*(l + 1)*(5*l + 2)/3
Let j(x) be the second derivative of 2*x**5/15 + 7*x**4/18 - 2*x**3/9 + 13*x. Factor j(q).
2*q*(q + 2)*(4*q - 1)/3
Suppose 126/13*m + 4 - 10/13*m**2 = 0. What is m?
-2/5, 13
Let u(r) = -1 + 0*r + 4*r + 5 + 3*r**3 - 3*r**2 - 4*r**3. Let y be u(-4). Factor 2/7*g**2 - 4/7*g**3 + 2/7*g**y + 0*g + 0.
2*g**2*(g - 1)**2/7
Let l(t) = 3*t**5 - 10*t**4 + 4*t**3 + 11*t**2 + 3*t. Let o(h) = h**2 + h. Let j(n) = -4*l(n) + 12*o(n). Find u such that j(u) = 0.
-2/3, 0, 2
Let m(q) be the first derivative of -q**8/840 + q**7/525 + q**6/150 + q**2/2 - 3. Let f(t) be the second derivative of m(t). Suppose f(a) = 0. What is a?
-1, 0, 2
Let i = -3733/60 - -560/9. Let y(t) be the third derivative of -1/120*t**6 + 0*t**4 + 0*t**3 + 0 + 0*t + 3*t**2 - i*t**5. Suppose y(o) = 0. What is o?
-1/3, 0
Let z(t) = -t**2 + 5*t + 7. Let d be z(6). Factor -o - 1/4*o**2 - d.
-(o + 2)**2/4
Factor -3/5*u**3 - 9/5*u**4 - 6/5*u**5 + 0 + 0*u**2 + 0*u.
-3*u**3*(u + 1)*(2*u + 1)/5
Suppose -1 = -d + 8. Let n be (2/30)/(d/30). Find q such that n*q - 2/9*q**2 + 0 = 0.
0, 1
Let b(d) = -11*d**2 + 4*d + 13. Suppose -4*c = -5*c + 13. Let k(l) = -5*l**2 + 2*l + 6. Let r(n) = c*k(n) - 6*b(n). Factor r(p).
p*(p + 2)
Let h(g) be the first derivative of g**4/4 - g**2/2 + 14. Factor h(v).
v*(v - 1)*(v + 1)
Let s(c) = c**2 + 3*c - 6. Let p(u) = -2*u**2 + 5*u**2 - 6*u + 11 - 5*u**2. Let z(x) = 6*p(x) + 11*s(x). Factor z(m).
-m*(m + 3)
Let s(x) be the first derivative of -5/2*x**2 - 4 - x**3 + 2*x. Factor s(z).
-(z + 2)*(3*z - 1)
Factor 2/9*h**4 + 4/9*h**3 + 0*h**2 - 4/9*h - 2/9.
2*(h - 1)*(h + 1)**3/9
Let k(p) be the second derivative of -1/4*p**3 + 9/16*p**4 - 21/80*p**5 + 0 + 0*p**2 + 2*p. Factor k(d).
-3*d*(d - 1)*(7*d - 2)/4
Let w = -159/4 + 40. Factor c**2 + 0 + w*c**3 + c.
c*(c + 2)**2/4
Suppose -3*k + 3*c + 15 = 0, -2*c = -3*k + 3*c + 19. Let q(p) be the second derivative of 1/6*p**k + 3*p + 1/12*p**4 - p**2 + 0. Let q(a) = 0. Calculate a.
-2, 1
Let 0*r**5 - 6*r + 4*r**4 + 3*r**3 + 5*r**3 - r**5 - 4*r**2 - r**5 = 0. What is r?
-1, 0, 1, 3
Let -8/11*k**3 + 6/11*k**2 + 0 + 2/11*k = 0