*p**2 - p = 0. Calculate p.
0, 2
Let l = -1775 - -154423/87. Let z = l + 184/435. Determine m, given that 0 + z*m**3 - 2/5*m**2 + 0*m = 0.
0, 1
Let w(g) be the second derivative of 3*g**5/40 - 3*g**4/16 - g**3/4 - 11*g. Factor w(f).
3*f*(f - 2)*(2*f + 1)/4
Let h(n) be the second derivative of -n**5/4 - 5*n**4/12 + 2*n. Determine b, given that h(b) = 0.
-1, 0
Let c(t) be the first derivative of -2*t**6/3 + 8*t**5/5 + t**4 - 8*t**3/3 + 7. Find q such that c(q) = 0.
-1, 0, 1, 2
What is j in 143*j**5 - 1525*j**5 - 16*j**2 - 264*j**3 - 1452*j**4 - 1280*j**5 = 0?
-2/11, 0
Let o(t) be the second derivative of -3*t**5/160 + 5*t**4/16 - 17*t**3/16 + 3*t**2/2 - 7*t. Suppose o(s) = 0. Calculate s.
1, 8
Factor 8/5*z - 8/5 - 2/5*z**2.
-2*(z - 2)**2/5
Let p(z) be the third derivative of z**5/20 - 2*z**3 + 6*z**2. Factor p(s).
3*(s - 2)*(s + 2)
Let o = -310 - -312. Factor -1/2 + z**o - 7/4*z.
(z - 2)*(4*z + 1)/4
Let n(q) be the second derivative of -3*q + 0 + 2/15*q**3 + 0*q**2 + 1/30*q**4. Suppose n(f) = 0. Calculate f.
-2, 0
Let y(c) be the first derivative of c**4/12 - c**3/3 - 2*c + 5. Let l(q) be the first derivative of y(q). Find f, given that l(f) = 0.
0, 2
Let s(l) be the second derivative of l**5/300 + l**4/60 + l**3/30 + 3*l**2/2 + l. Let j(q) be the first derivative of s(q). Factor j(c).
(c + 1)**2/5
Suppose 5*a = 3*k - 2 + 6, -k + 5*a - 8 = 0. Suppose -x - k*x = 0. Factor 0*c**2 + 1/2*c**4 + 0*c**3 + 0 + x*c + 1/2*c**5.
c**4*(c + 1)/2
Factor -b - 1/3*b**2 - 2/3.
-(b + 1)*(b + 2)/3
Factor 0 + 3/4*q**5 + 0*q + 3/4*q**2 + 9/4*q**4 + 9/4*q**3.
3*q**2*(q + 1)**3/4
Let f = -1/28 - -227/84. Let p = -13/6 + f. Factor -3/2*c**2 - 1/2 - p*c**3 - 3/2*c.
-(c + 1)**3/2
Let w(j) = -5*j**3 - j**2 + 13*j - 11. Let m(u) = -21*u**3 - 3*u**2 + 51*u - 45. Let x(y) = -2*m(y) + 9*w(y). Factor x(k).
-3*(k - 1)**2*(k + 3)
Suppose -3*m + 6 = 5*f, f + 2*m = 2*f + 4. Let 0*d - 1/7*d**3 + 1/7*d**5 - 1/7*d**2 + f + 1/7*d**4 = 0. Calculate d.
-1, 0, 1
Solve -4*j**2 - 48 + j**2 + 3*j + 18*j + 3*j = 0.
4
Let n(w) be the second derivative of 0 + 0*w**3 + 1/18*w**4 - 1/3*w**2 + 2*w. Determine s so that n(s) = 0.
-1, 1
Let i(p) = -2*p - 2. Let t be i(-2). Let s(l) be the second derivative of 0 - 1/15*l**3 - 2*l + 1/5*l**t + 1/50*l**5 - 1/30*l**4. Factor s(d).
2*(d - 1)**2*(d + 1)/5
Let s(n) be the first derivative of -n**6/2 + 1. Determine f so that s(f) = 0.
0
Let f(q) = -23*q**3 + 43*q**2 - 21*q - 1. Let v(t) = -11*t**3 + 22*t**2 - 11*t. Let w(a) = 2*f(a) - 5*v(a). Factor w(p).
(p - 2)*(3*p - 1)**2
Let l(y) = 20*y**2 + 14*y - 6. Let w(i) = 40*i**2 + 29*i - 13. Let j(z) = -13*l(z) + 6*w(z). What is c in j(c) = 0?
-2/5, 0
Let z(i) be the first derivative of 0*i**5 - 2/3*i**3 + 1/900*i**6 + 0*i**2 + 0*i**4 - 1 + 0*i. Let u(q) be the third derivative of z(q). Factor u(w).
2*w**2/5
Let g(w) = w + 6. Let u be g(-6). Factor 2/5*q**2 + 2/5*q**3 + u - 2/5*q - 2/5*q**4.
-2*q*(q - 1)**2*(q + 1)/5
Let p(t) be the third derivative of 0 - 3*t**2 - 1/70*t**5 - 1/735*t**7 + 0*t + 4/21*t**3 + 1/21*t**4 - 1/105*t**6. Determine r so that p(r) = 0.
-2, -1, 1
Let k(q) = q**5 - 5*q**4 - 24*q**3 + 7*q**2 + 23*q - 17. Let n(s) = -3*s**4 - 12*s**3 + 3*s**2 + 12*s - 9. Let z(p) = 3*k(p) - 5*n(p). Factor z(x).
3*(x - 1)**3*(x + 1)*(x + 2)
Let f(z) = -z**2 + 16*z + 11. Let p(y) = -8*y - 6. Let c(h) = 4*f(h) + 10*p(h). Factor c(a).
-4*(a + 2)**2
Let t(s) = -s**3 - s - 2. Let b(m) = 2*m**3 - 20*m**2 + 30*m - 20. Let f(i) = b(i) - 2*t(i). Factor f(d).
4*(d - 2)**2*(d - 1)
Factor 6*o + 5*o**3 + 4 - o**3 - 6*o**3.
-2*(o - 2)*(o + 1)**2
Let a(r) = 2*r - 4. Let q be a(3). Factor n**4 - n**q - 7*n + 6*n - n**4 + n**3 + n**4.
n*(n - 1)*(n + 1)**2
Suppose 0 = -6*h + h + 15. Suppose 6*t**3 + 3*t**h - 4*t**3 - 3*t**3 = 0. Calculate t.
0
Let b be (15/(-3 - 0))/(20/(-8)). Factor 0*s**b + 0*s**3 + 3/4*s**5 + 0 - 3/4*s**4 + 0*s.
3*s**4*(s - 1)/4
Let x(y) be the third derivative of -y**10/529200 + y**8/35280 - y**6/2520 - y**5/30 + 2*y**2. Let j(c) be the third derivative of x(c). What is v in j(v) = 0?
-1, 1
Suppose -2/5*m**3 + 6/5*m**4 + 0 - 6/5*m**2 + 2/5*m = 0. What is m?
-1, 0, 1/3, 1
Factor 108/5 + 3/5*u**2 + 36/5*u.
3*(u + 6)**2/5
Factor 3/5*b - 3/5*b**2 + 0.
-3*b*(b - 1)/5
Let a(c) be the first derivative of c**6/12 + c**5/5 - 7*c**4/8 + 2*c**3/3 + 13. Factor a(l).
l**2*(l - 1)**2*(l + 4)/2
Let a(h) be the third derivative of -h**6/40 + h**5/10 + 9*h**2. Factor a(c).
-3*c**2*(c - 2)
Let r(m) = -15*m**4 - 33*m**3 - 42*m**2 + 12. Let p(k) = -6*k**4 - 13*k**3 - 17*k**2 + 5. Let a(c) = 12*p(c) - 5*r(c). Factor a(x).
3*x**2*(x + 1)*(x + 2)
Let j = -34 + 37. Let o(b) be the first derivative of 3/2*b**3 + b + 7/4*b**2 + 5/8*b**4 - j + 1/10*b**5. Factor o(h).
(h + 1)**3*(h + 2)/2
Let s be (2/(-4))/(18/(-4) - -3). Factor -1/3*i + 1/3 + 1/3*i**3 - s*i**2.
(i - 1)**2*(i + 1)/3
Let t = -247 + 2225/9. Let c = 90 - 808/9. Let 0*n - 2/9*n**4 - t*n**5 + 2/9*n**2 + 0 + c*n**3 = 0. What is n?
-1, 0, 1
Factor -59 + 3*m**2 + 3*m + 59.
3*m*(m + 1)
Let f(x) be the third derivative of x**8/616 + 2*x**7/385 - x**5/55 - x**4/44 + 17*x**2. Solve f(d) = 0.
-1, 0, 1
Let j = 73 + -70. Suppose -1/8 + 1/8*b**4 + 0*b**2 + 1/4*b - 1/4*b**j = 0. Calculate b.
-1, 1
Let k(s) = s**3 + 8*s**2 - s - 5. Let u be k(-8). What is d in 2*d**3 - 3*d**3 + 2*d**u - d**5 = 0?
-1, 0, 1
Let o(i) be the second derivative of 14*i**4/3 + i**3/3 - 2*i**2 + 34*i. Factor o(g).
2*(4*g - 1)*(7*g + 2)
Let m be ((-4)/4 - 3)/(-5). Let c(k) be the first derivative of -3/5*k**2 + 6/25*k**5 + 2/5*k**3 + 2 + 7/10*k**4 - m*k. Factor c(x).
2*(x + 1)**3*(3*x - 2)/5
Let k be (-2)/(-8) + 748/16. Let d = k - 187/4. Determine q so that 0 + d*q**2 - 1/4*q = 0.
0, 1
Suppose -2*f = -2*b - 6, 0*b - 3*b = 2*f + 9. Let v(j) be the third derivative of -1/105*j**5 + f*j + 1/84*j**4 - 2*j**2 + 0 + 0*j**3 + 1/420*j**6. Factor v(r).
2*r*(r - 1)**2/7
Let u(b) be the first derivative of -b**3/3 + b**2 - 3*b + 2. Let l(a) = -2*a**2 + 4*a - 5. Let r(p) = 6*l(p) - 10*u(p). Determine z so that r(z) = 0.
0, 2
Suppose -3*a + 15 = -21. Let h be (-14)/a - 36/(-24). Factor -s**2 - 2/3*s + 0 - h*s**3.
-s*(s + 1)*(s + 2)/3
Let b(z) be the second derivative of 0*z**2 - 9*z + 0*z**5 - 1/84*z**7 + 1/12*z**4 + 0 + 1/12*z**3 - 1/30*z**6. Factor b(a).
-a*(a - 1)*(a + 1)**3/2
Let x(o) = o + 8. Let r be x(-6). Factor -r*v**2 + v**3 - 3*v**3 + 2*v**4 + 0*v**5 + 2*v**5.
2*v**2*(v - 1)*(v + 1)**2
Let i(k) be the first derivative of k**7/6 + k**6/15 - 7*k**5/20 - k**4/6 + 2*k + 1. Let g(x) be the first derivative of i(x). Factor g(p).
p**2*(p - 1)*(p + 1)*(7*p + 2)
Let d be ((-3)/3*6*-1)/2. Determine r, given that -7*r**d + 7/2*r**5 + 1 - 2*r**2 + 7/2*r + r**4 = 0.
-1, -2/7, 1
Factor -5*d**2 - 1317*d + 1317*d + 5*d**3.
5*d**2*(d - 1)
Let k be 64/14 - (2 - 1) - 3. Solve 0 + k*v - 2/7*v**2 = 0.
0, 2
Factor 0 + 3/5*d**4 + 0*d + 6/5*d**2 - 9/5*d**3.
3*d**2*(d - 2)*(d - 1)/5
Let w(a) = 12*a**2 - 1. Let t be w(-1). Suppose -7 = -6*b + t. Factor 0*u - 1/3*u**4 + 0*u**b + 1/3*u**2 + 0.
-u**2*(u - 1)*(u + 1)/3
Let n(f) be the second derivative of -f**5/4 - 5*f**4/6 - 5*f**3/6 + 12*f. Factor n(p).
-5*p*(p + 1)**2
Find g such that -8/3*g + 6*g**3 - 8*g**2 + 0 + 14/3*g**4 = 0.
-2, -2/7, 0, 1
Factor -4/3*o**3 - 1 + 2/3*o**2 + 1/3*o**4 + 4/3*o.
(o - 3)*(o - 1)**2*(o + 1)/3
Let a(f) be the third derivative of -f**6/40 - f**5/20 + f**4/2 + 2*f**3 + 7*f**2. Let a(h) = 0. What is h?
-2, -1, 2
Let i(a) = -a**2 - 10*a - 10. Let c be i(-8). Factor -c*p**2 - 1 + 4*p + 4*p - 1.
-2*(p - 1)*(3*p - 1)
Let y(p) be the third derivative of -p**6/420 - p**5/70 + 5*p**2. Suppose y(g) = 0. What is g?
-3, 0
Let r(g) = -g**2 - 8*g + 20. Let t be r(-10). Suppose 2/5*x**4 + t*x**2 + 0*x**3 - 9/5*x**5 + 0 + 0*x = 0. What is x?
0, 2/9
Let x = -131 - -133. Let o(v) be the first derivative of 2*v**3 + 3/2*v**x - 3/4*v**4 - 1 - 6*v. Suppose o(k) = 0. What is k?
-1, 1, 2
Suppose -2*d - 55 = -61. Solve 6/7*o**d - 4/7*o - 10/7*o**2 + 0 = 0 for o.
-1/3, 0, 2
Let w(y) = -6*y**4 + 10*y**3 + 16*y**2 - 14*y + 14. Let b(i) = i**3 + i**2 - i + 1. Let l(t) = -28*b(t) + 2*w(t). Factor l(a).
-4*a**2*(a + 1)*(3*a - 1)
Let j(q) be the third derivative of 0 + 0*q**3 + 1/36*q**4 + 0*q**5 + 3*q**2 + 0*q - 1/180*q**6. Solve j(s) = 0.
-1, 0, 1
Suppose 0 = 3*r - 16 - 14. Let z