 -4*b**2 - 4*b**3 - b + 9 - c.
-b*(2*b + 1)**2
Let s(c) be the first derivative of -3*c**5/5 + 5*c**4/4 - c**3/2 + c - 2. Let r(h) be the first derivative of s(h). Factor r(i).
-3*i*(i - 1)*(4*i - 1)
Let k(u) be the second derivative of 3*u**5/20 - 3*u**4 + 24*u**3 - 96*u**2 - u. Determine i, given that k(i) = 0.
4
Suppose 0 = -2*a + 6*a - 2*y - 12, 4*y + 6 = 2*a. Solve 4*v**a + 4*v**2 + 21*v + 4 - 8 - 25*v = 0.
-1, 1
Let s = -15 + 20. Let t(d) be the first derivative of 0*d**4 + 0*d + 1 - 1/6*d**2 + 2/9*d**3 - 2/15*d**s + 1/18*d**6. Solve t(w) = 0.
-1, 0, 1
Let b(z) = z**3 + 5*z**2 - 2*z - 7. Let g be b(-5). Solve h**4 - g*h**4 - 9*h**2 + 2*h - 3*h**4 + 12*h**3 = 0 for h.
0, 2/5, 1
Let o = 210 - 210. Factor -5/3*y**3 + 2/3*y**2 - 7/3*y**4 + 0*y + o.
-y**2*(y + 1)*(7*y - 2)/3
Let l = 122 - 120. Factor -12/7*g + 18/7 + 2/7*g**l.
2*(g - 3)**2/7
Let d = 11 - 13. Let y be d - (-16)/(6 + -2). Factor 2*s**3 + 0 + 4/7*s**y + 16/7*s**4 + 0*s + 6/7*s**5.
2*s**2*(s + 1)**2*(3*s + 2)/7
Find v such that -16*v**2 - 10*v - 12 - 31*v - 2*v**3 + 15*v = 0.
-6, -1
Let d(f) be the third derivative of -1/144*f**8 + 1/9*f**3 + 2*f**2 + 0 - 7/90*f**5 + 0*f + 1/90*f**6 + 1/24*f**4 + 2/105*f**7. Let d(q) = 0. What is q?
-1, -2/7, 1
Let v(b) = -b + 1. Let h be v(-3). Let c(n) = -n**2 + 13*n + 2. Let i(k) = k**2 - k + 1. Let x(z) = h*i(z) + c(z). Factor x(s).
3*(s + 1)*(s + 2)
Let g(d) be the second derivative of d**5/14 + d**4/21 - 5*d**3/21 - 2*d**2/7 - 3*d. Find u, given that g(u) = 0.
-1, -2/5, 1
Suppose 0 = -4*c - 5 + 13. Let k(u) be the third derivative of 0*u - 1/24*u**4 + c*u**2 + 0*u**3 + 0 + 1/120*u**6 - 1/210*u**7 + 1/60*u**5. Factor k(n).
-n*(n - 1)**2*(n + 1)
Suppose -2/3*p + 2*p**2 - 4/3 = 0. Calculate p.
-2/3, 1
Suppose -h = -1 + 5. Let d be h/10 + (-152)/(-180). Factor -10/9*z**2 + d + 2/3*z.
-2*(z - 1)*(5*z + 2)/9
Let j(t) = -t - 11. Suppose 3*y - 15 = -2*s - 35, 0 = 2*s - 2*y + 30. Let l be j(s). Factor -12/7*w - 2/7*w**l - 18/7.
-2*(w + 3)**2/7
Let r = 22/3 - 6. Let h(p) be the third derivative of 1/10*p**6 - 1/3*p**4 + 11/30*p**5 - r*p**3 + 0*p - p**2 - 3/35*p**7 + 0. Factor h(s).
-2*(s - 1)**2*(3*s + 2)**2
Let f(w) be the first derivative of w**4/16 + w**3/2 + 16. Find d such that f(d) = 0.
-6, 0
Let u(p) be the first derivative of p**5/5 + p**4/4 - p**3 - p**2/2 + 2*p - 7. Factor u(v).
(v - 1)**2*(v + 1)*(v + 2)
Let i(j) be the second derivative of 1/27*j**3 - 1/90*j**5 - 1/9*j**2 + 0 - 3*j + 1/54*j**4. Determine q so that i(q) = 0.
-1, 1
Let y(w) be the first derivative of 0*w**3 + 1/180*w**6 + 0*w**5 + 0*w**2 - 4*w + 3 - 1/72*w**4. Let r(l) be the first derivative of y(l). Solve r(v) = 0 for v.
-1, 0, 1
Let t(x) be the third derivative of x**8/168 + 3*x**7/35 + 7*x**6/15 + 6*x**5/5 + 4*x**4/3 - 35*x**2. Factor t(l).
2*l*(l + 1)*(l + 2)**2*(l + 4)
Let z = 1849/3 - 616. Suppose z*r**4 + 1/3*r + r**3 + 0 + r**2 = 0. What is r?
-1, 0
Let t(j) be the second derivative of -j**4/12 + 5*j**3/6 + 16*j. What is f in t(f) = 0?
0, 5
Suppose -8 = -5*u + 6*u + 5*v, -5*u + 16 = -3*v. What is n in 2*n**u + 2/9 - 4/3*n = 0?
1/3
Factor 6 + 17*n - n**2 + 16*n**3 + 18*n**2 - 9*n**3 + n**4.
(n + 1)**2*(n + 2)*(n + 3)
Let y be ((-1)/2)/((-14)/16). Factor 18/7*p**3 + 2*p**4 + y*p**5 + 0 + 2/7*p + 10/7*p**2.
2*p*(p + 1)**3*(2*p + 1)/7
Factor -4/7*z**4 - 4/7*z**3 - 2*z + 2/7*z**5 + 16/7*z**2 + 4/7.
2*(z - 1)**4*(z + 2)/7
Suppose 33 = 4*p + 5*o, 0*p + 5*o = 2*p + 21. Factor 3 - 4 + 3*b**p + 12*b + 13.
3*(b + 2)**2
Let w(r) be the first derivative of -1/3*r**6 + 4/3*r**3 - 4 + r**4 - 2/5*r**5 - 2*r - r**2. Factor w(z).
-2*(z - 1)**2*(z + 1)**3
Let n(k) be the first derivative of 1/5*k**2 - 2 + 1/15*k**3 + 0*k - 1/25*k**5 + 1/30*k**6 - 3/20*k**4. Solve n(l) = 0.
-1, 0, 1, 2
Let m be (-3 + 3)/(6/(-3)). Factor 2/5*s**4 - 2/5*s - 6/5*s**3 + 6/5*s**2 + m.
2*s*(s - 1)**3/5
Let b(i) be the second derivative of -i**4/48 - i**3/24 + 7*i. Suppose b(l) = 0. Calculate l.
-1, 0
Let r(t) be the first derivative of 64*t**6/3 - 288*t**5 + 870*t**4 + 3170*t**3/3 + 420*t**2 + 72*t - 15. Factor r(q).
2*(q - 6)**2*(4*q + 1)**3
Suppose 4*q + 3 = -5*y, 0*q + 3*q = -y + 6. Let -1/4*t - 1/4*t**5 + 1/2*t**q - 1/4*t**4 + 1/2*t**2 - 1/4 = 0. What is t?
-1, 1
Suppose 0*z - 32 = -4*z. Find g, given that -2*g + 18*g + 36 + 4*g**2 + z*g = 0.
-3
Let u(b) be the first derivative of b**3/3 + 3*b**2/2 - 5*b - 3. Let t be u(-5). Factor -2*l + l**3 + l + t*l - 3*l + 2*l**2.
l*(l + 1)**2
What is s in -32*s + 20/3*s**2 - 1/3*s**5 - s**4 + 64/3 + 16/3*s**3 = 0?
-4, 1, 2
Let m(f) = -36*f**3 - 48*f**2 + 48*f + 8. Let i(v) = 12*v**3 + 16*v**2 - 16*v - 3. Let g(z) = -8*i(z) - 3*m(z). Factor g(j).
4*j*(j + 2)*(3*j - 2)
Let h(y) be the second derivative of -y**7/70 + 2*y**6/25 - 3*y**5/25 - y**4/10 + y**3/2 - 3*y**2/5 + 6*y. Find u such that h(u) = 0.
-1, 1, 2
Let t(x) be the third derivative of x**5/100 + 13*x**4/20 + 169*x**3/10 - 7*x**2. Factor t(s).
3*(s + 13)**2/5
Solve -1/4*a**2 - 3/4 + a = 0.
1, 3
Suppose 6*z = -23*z + 87. Solve -2/3*o**z - 2/15*o**5 + 4/15*o**2 + 0 + 0*o + 8/15*o**4 = 0 for o.
0, 1, 2
Let y = 13 + -10. Factor -y*g**3 + 15*g**2 + 5 - 2 + 12*g + 9*g**3.
3*(g + 1)**2*(2*g + 1)
Let r be 0/(56/(-26) - 14/(-91)). Suppose 2/3*g**5 + 0 - 4/3*g**4 - 2/3*g**3 + 4/3*g**2 + r*g = 0. What is g?
-1, 0, 1, 2
Suppose -4*z - f + 14 = -0*z, -z - 3 = -3*f. Factor -2 + 2*a - 2*a**z - 2*a**2 + 4 - 1 + a**2.
-(a - 1)*(a + 1)*(2*a + 1)
Let o(d) be the third derivative of -1/9*d**3 - 1/90*d**6 + 1/504*d**8 + 0*d + 1/36*d**4 - 2*d**2 - 1/315*d**7 + 0 + 1/45*d**5. Factor o(g).
2*(g - 1)**3*(g + 1)**2/3
Determine g, given that -27*g**3 - 13*g**2 - 4*g - 18*g**4 + 4*g - 5*g**4 - 7*g**5 - 2*g = 0.
-1, -2/7, 0
Let l = -2 - -4. Determine n, given that -1 - 3*n**4 + l - n**2 + 4*n**4 - n**2 = 0.
-1, 1
Factor 2*m**2 - 3*m**2 + 4*m**3 + 37*m**4 - 33*m**4 - 3*m**2 - 4*m.
4*m*(m - 1)*(m + 1)**2
Let j(t) = -7*t**4 - 7*t**3 + 3*t**2 + 3*t. Let p(x) = -15*x**4 - 15*x**3 + 5*x**2 + 5*x. Let d(m) = 5*j(m) - 2*p(m). Let d(r) = 0. Calculate r.
-1, 0, 1
Let s be 18/(-7)*(-39)/9. Let t = -376/35 + s. Let 2/5*n**2 + 0 + t*n = 0. What is n?
-1, 0
Let b(v) = -15*v**2 - 29*v - 3. Let p(s) = -16*s**2 - 30*s - 2. Let y(a) = -6*b(a) + 5*p(a). Let y(f) = 0. Calculate f.
-2, -2/5
Let d(u) be the third derivative of u**7/84 - u**5/8 - 5*u**4/24 + 6*u**2. Factor d(o).
5*o*(o - 2)*(o + 1)**2/2
Find j, given that -44*j**2 - 7 - 26*j**2 + 15*j - 1 + 33*j = 0.
2/7, 2/5
Find u, given that -1/5*u**4 - 1/5*u**3 + 0*u**2 + 0 + 0*u = 0.
-1, 0
Let b be (-2 - -7)/(-1 - -2). Let s(p) be the third derivative of 0*p + 1/180*p**6 - p**2 + 1/36*p**4 - 1/45*p**b + 0 + 0*p**3. Factor s(c).
2*c*(c - 1)**2/3
Let h = 219 + -1529/7. Let t = 12/11 + -40/77. Find k, given that t*k + 1/7*k**2 + h = 0.
-2
Suppose 62*r - 5*l + 20 = 67*r, 0 = -3*r - 4*l + 14. Suppose 0*w**2 - 4/9*w**3 + 0*w + 22/9*w**4 + 0 - r*w**5 = 0. What is w?
0, 2/9, 1
Let m(o) be the third derivative of o**9/272160 + o**5/20 - o**2. Let h(g) be the third derivative of m(g). Let h(i) = 0. What is i?
0
Let r be 3 - ((-11)/(-4) - 0/25). What is t in 3/2*t**2 + 2 - 3*t - r*t**3 = 0?
2
Let u(o) = o**4 - 3*o**3 - 7*o**2 + 5*o + 6. Let c(k) = -2*k**4 + 9*k**3 + 20*k**2 - 16*k - 18. Let f(g) = -2*c(g) - 7*u(g). Factor f(b).
-3*(b - 2)*(b - 1)*(b + 1)**2
Suppose f + 24 = 7*f. Let d(m) be the second derivative of 1/6*m**3 + m - 1/6*m**2 + 1/60*m**5 + 0 - 1/12*m**f. Solve d(y) = 0 for y.
1
Let b(i) = -i**3 - 36*i**2 + 113*i - 108. Let k(y) = y**3 + 18*y**2 - 57*y + 54. Let t(c) = 3*b(c) + 5*k(c). Factor t(u).
2*(u - 3)**3
Let j be (-1)/8 + (-7)/(-28). Let p(y) be the first derivative of 1/6*y**3 - 1/24*y**6 + 1/8*y**4 + 1 - 1/4*y - 1/20*y**5 - j*y**2. Factor p(v).
-(v - 1)**2*(v + 1)**3/4
Let z be ((-32)/210 - 10/(-35))*5. Factor -2/3 + z*p + 6*p**2 + 8/3*p**4 + 22/3*p**3.
2*(p + 1)**3*(4*p - 1)/3
Let -2/5*z**3 + 14/5*z**2 - 32/5 - 16/5*z = 0. What is z?
-1, 4
Let q = 12 - -4. Suppose 0*t = 4*t - q. Determine a so that -2/7*a**3 + 0*a + 0*a**2 + 0 + 0*a**t + 2/7*a**5 = 0.
-1, 0, 1
Let q(d) = -d + 2. Let x be q(-2). Factor 0*h - 5*h**2 + 13*h**2 - x*h - 4*h**3.
-4*h*(h - 1)**2
Let u(i) be the first derivative of -5*i**6/6 + 3*i**5 - 20*i**3/3 + 20. Solve u(x) = 0.
-1, 0, 2
Let f be (-4)/(4*-8) + 39/72. Determ