*7/105 + t**6/60 - t**5/30 - t**4/12 + 15*t**2. Factor u(r).
2*r*(r - 1)*(r + 1)**2
Let a(w) = -w**3 + 14*w**2 + 15*w + 4. Let r be a(15). Suppose 0 + 1/6*k**r + 1/2*k**3 - 1/6*k**5 - 5/6*k**2 + 1/3*k = 0. Calculate k.
-2, 0, 1
Determine x, given that 2/5*x**2 + 0*x**4 + 0*x + 0 - 3/5*x**3 + 1/5*x**5 = 0.
-2, 0, 1
Suppose 10*a + 2*h - 4 = 13*a, 0 = 5*a + 4*h - 8. Factor 1/6*s + a - 1/6*s**5 + 1/3*s**4 + 0*s**3 - 1/3*s**2.
-s*(s - 1)**3*(s + 1)/6
Let z(o) be the first derivative of 4*o**3/3 + 4*o**2 - 11. Factor z(g).
4*g*(g + 2)
Suppose 0 = 12*w + 3*w - 90. Let o(m) be the first derivative of 0*m - 4*m**3 - w*m**2 - 3/4*m**4 - 3. Solve o(q) = 0.
-2, 0
Let y(r) be the first derivative of 0*r**2 + 2/15*r**3 + 0*r + 1/25*r**5 - 3/20*r**4 + 1. Factor y(v).
v**2*(v - 2)*(v - 1)/5
Let j(s) = 2*s - 4. Let f be j(10). Let a = 19 - f. Factor 28/5*b**2 - 8/5*b + 0 - 22/5*b**a + b**4.
b*(b - 2)**2*(5*b - 2)/5
Let d(k) = 49*k**4 - 195*k**3 + 154*k**2 - 30*k - 11. Let w(f) = 10*f**4 - 39*f**3 + 31*f**2 - 6*f - 2. Let h(u) = -2*d(u) + 11*w(u). Factor h(a).
3*a*(a - 2)*(a - 1)*(4*a - 1)
Let v(x) be the third derivative of 2*x**7/525 + x**6/200 - x**5/25 - x**4/120 + x**3/5 - 25*x**2. Find h such that v(h) = 0.
-2, -3/4, 1
Find z, given that -1/2*z**4 + z**2 + 0*z + 0 - 1/2*z**3 = 0.
-2, 0, 1
Let w(z) be the first derivative of z**6/120 - z**5/20 + z**4/8 - 7*z**3/3 - 4. Let f(v) be the third derivative of w(v). Factor f(s).
3*(s - 1)**2
Suppose 4*w = 5*w + 5. Let c(b) = -2*b - 5. Let l be c(w). Factor -1 + l - 3*m**3 + m**4 - 4 + 2*m**2.
m**2*(m - 2)*(m - 1)
Let f(p) = -12*p - 10. Let b(j) = -j**2 + 25*j + 21. Let z(q) = 2*b(q) + 5*f(q). Suppose z(o) = 0. What is o?
-4, -1
Let c(i) = i**4 - 24*i**3 - 60*i**2 - 44*i - 15. Let n(v) = -25*v**3 - 60*v**2 - 45*v - 15. Let j(w) = 5*c(w) - 6*n(w). Factor j(h).
5*(h + 1)**3*(h + 3)
Let s be (-1)/3*(-270)/25. Determine x so that -12/5*x - s - 2/5*x**2 = 0.
-3
Let i = 0 + 2. Let c(l) = -13*l - 12. Let k be c(-2). Let 4 - 2*r**2 + 9*r**i - 8*r**3 + r**2 + k*r = 0. Calculate r.
-1/2, 2
Let t be (-234)/(-52) + -4*1. Determine j so that 1/2*j**2 + 0*j + t*j**3 + 0 = 0.
-1, 0
Let z(o) be the second derivative of 3*o**5/50 + o**4/6 + o**3/15 - o**2/5 + 20*o. Factor z(p).
2*(p + 1)**2*(3*p - 1)/5
Factor 0 + 2*u - 1/2*u**2.
-u*(u - 4)/2
Factor 6*o**3 + 996*o**4 - 3*o - 996*o**4 - 3*o**5.
-3*o*(o - 1)**2*(o + 1)**2
Let a(b) be the third derivative of b**8/420 - b**7/210 - b**6/90 + b**5/30 + b**3/6 - 2*b**2. Let v(d) be the first derivative of a(d). Factor v(q).
4*q*(q - 1)**2*(q + 1)
Let s = -285863486/27027 + 285586/27. Let t = s + -2/143. Factor t*x**2 + 0*x + 0 + 2/7*x**3.
2*x**2*(x + 1)/7
Let j = 10 - 14. Let c = 7 + j. Find b such that 3/4*b + 1/4 + 1/4*b**c + 3/4*b**2 = 0.
-1
Suppose 4*i + 56 = 5*y, -3*y + y + 2*i + 24 = 0. Factor y*m + m**2 + m**2 + 5 + 1.
2*(m + 1)*(m + 3)
Let y(q) be the second derivative of 0 + 1/60*q**6 - 1/12*q**4 + 0*q**5 + 0*q**3 - 4*q + 1/4*q**2. Factor y(n).
(n - 1)**2*(n + 1)**2/2
Suppose 2*p - 3 = -p, 0 = -4*z - p + 9. Let b = 17 + -14. Factor 2*t**3 + z*t**3 - 10*t**2 - 12 - 2*t**b + 4 + 16*t.
2*(t - 2)**2*(t - 1)
Let l(p) = p**2 - p + 1. Let i(x) = 3*x**2 + 7*x + 9. Let r(f) = 2*i(f) - 2*l(f). Factor r(t).
4*(t + 2)**2
Factor -92/3*d**2 - 50/3*d**4 - 2/3 + 8*d + 40*d**3.
-2*(d - 1)**2*(5*d - 1)**2/3
Suppose 2*n + 4 = -t - 0*n, -5*t + 2 = -n. Let z be (2 - 4) + 16/6. Solve 0 + 0*l - z*l**5 + 0*l**3 - 2/3*l**4 + t*l**2 = 0.
-1, 0
Let o(m) be the first derivative of -m**5/25 - 3*m**4/10 - 11*m**3/15 - 3*m**2/5 - 44. Let o(w) = 0. What is w?
-3, -2, -1, 0
Suppose -3*j - 2*j**2 + 13 + j - 9 + 4*j = 0. What is j?
-1, 2
Solve -38/17*i + 2/17*i**2 + 36/17 = 0 for i.
1, 18
Let m(b) be the second derivative of -3*b**5/40 + b**4/8 + 5*b**3/4 + 9*b**2/4 + 67*b. Factor m(p).
-3*(p - 3)*(p + 1)**2/2
Let f(y) be the first derivative of y**2 + 0*y**3 + 0*y + 1/42*y**4 - 1/210*y**5 + 1. Let j(u) be the second derivative of f(u). Factor j(w).
-2*w*(w - 2)/7
Let a(n) be the third derivative of -n**7/490 - n**6/140 - n**5/140 - 40*n**2. Solve a(t) = 0 for t.
-1, 0
Let c(u) be the third derivative of -u**6/30 + u**5/5 - u**4/2 + 2*u**3/3 - 23*u**2. Factor c(r).
-4*(r - 1)**3
Let m be (-68)/(-16) - ((-4)/(-1) + -1). Let -m*q + 9/4*q**2 - 7/4*q**4 + 5/4*q**3 - 1/2 = 0. Calculate q.
-1, -2/7, 1
Find b, given that -10/11*b - 2/11*b**4 - 12/11 + 14/11*b**2 + 10/11*b**3 = 0.
-1, 1, 6
Suppose -17*u + 6*u = -22. Factor 26/5*f**4 + 8/5*f**5 + 14/5*f**u + 0 + 6*f**3 + 2/5*f.
2*f*(f + 1)**3*(4*f + 1)/5
Let z(p) be the first derivative of -5*p**3/3 - 27*p**2/2 - 10*p + 10. Factor z(a).
-(a + 5)*(5*a + 2)
Let m be -3 + 1/(-14)*-50. Factor 0 + 0*p**4 + m*p**3 - 2/7*p + 0*p**2 - 2/7*p**5.
-2*p*(p - 1)**2*(p + 1)**2/7
Let d = -17067845/3317476 - -4/43651. Let n = 2/19 - d. Solve -y + 0 + n*y**4 + 6*y**2 - 41/4*y**3 = 0 for y.
0, 2/7, 2/3, 1
Let n(i) be the first derivative of -i**3/12 + i**2/8 - 7. Find w, given that n(w) = 0.
0, 1
Let b(s) = 1. Let p(z) = z**2 - 4*z + 1. Let m(c) = -c - 1. Let n(x) = 4*m(x) - p(x). Suppose -4*w = -3 - 1. Let l(q) = w*n(q) + 6*b(q). Solve l(g) = 0.
-1, 1
Let k(a) be the second derivative of 2/21*a**3 - 2*a + 1/14*a**4 + 0*a**2 - 1/105*a**6 + 0*a**5 + 0. Factor k(p).
-2*p*(p - 2)*(p + 1)**2/7
Suppose -g = -0*g - 2. Factor -3*o**2 - 2 + 2 - o - g*o + 3*o**3 + 3*o**4.
3*o*(o - 1)*(o + 1)**2
Let y(x) be the second derivative of -x**5/20 + x**3/6 - x**2/2 - 7*x. Let l(m) = -10*m**3 + 24*m**2 - 30*m - 6. Let f(b) = l(b) - 6*y(b). Factor f(r).
-4*r*(r - 3)**2
Let b(o) be the third derivative of 3*o**2 + 0 + 0*o**3 + 1/12*o**4 - 1/60*o**5 + 0*o. Factor b(r).
-r*(r - 2)
Let r(h) be the third derivative of -2*h**2 - 1/90*h**5 + 0*h - 1/45*h**6 + 0*h**3 + 0 - 1/63*h**7 + 0*h**4 - 1/252*h**8. Factor r(w).
-2*w**2*(w + 1)**2*(2*w + 1)/3
Find b such that -27/4*b**2 - 2 - 1/4*b**4 + 11/4*b**3 + 25/4*b = 0.
1, 8
Let d(n) be the first derivative of -1/15*n**3 + 0*n - 3/10*n**2 + 5. Factor d(u).
-u*(u + 3)/5
Let k be 2/(-5) + (1 - 15/25). Factor 1/2*v**2 + k - 1/4*v**3 + 0*v.
-v**2*(v - 2)/4
Factor -x + 5*x + 3*x**2 + 2*x**2 - 9*x.
5*x*(x - 1)
Let r(h) be the third derivative of h**5/30 - h**4/24 - h**3/6 - 2*h**2. Let g be r(-1). Factor -2*t**2 - 4*t**2 - 4 + 4*t + 5*t**g.
-(t - 2)**2
Let z(k) = -k - 3. Let h be z(-7). Let m be 8/h*(1 - -1). Factor 4*p**5 + 5/4*p**2 - 1/4 + 25/4*p**3 - 5/4*p - 10*p**m.
(p - 1)**3*(4*p + 1)**2/4
Suppose 0 = 2*i + 4*q - 22, 6*q - 2*q = 4*i + 4. What is p in 9/2*p**4 + p**i + 0*p + 0*p**2 + 0 = 0?
-2/9, 0
Let q(d) = 4 - 2 - 5 + 3*d**2 + 4. Let b = 10 + -14. Let j(c) = c**2. Let f(w) = b*j(w) + q(w). What is y in f(y) = 0?
-1, 1
Let g(n) be the third derivative of 5*n**8/336 - n**7/105 - n**6/24 + n**5/30 + 27*n**2. Factor g(c).
c**2*(c - 1)*(c + 1)*(5*c - 2)
Let a(p) be the second derivative of -p**6/90 - p**5/12 - p**4/6 + 2*p**3/9 + 4*p**2/3 + 10*p. Solve a(j) = 0.
-2, 1
Let g(h) be the third derivative of -h**6/300 - h**5/50 - h**4/30 + 7*h**2. Factor g(s).
-2*s*(s + 1)*(s + 2)/5
Let q be 1 + (2 - (6 + -3)). Factor 8/7 + 12/7*v + q*v**2 - 4/7*v**3.
-4*(v - 2)*(v + 1)**2/7
Suppose o - 24 = -3*o + 3*a, -2*a = 3*o - 1. What is c in -2/3*c**o + 2/3*c + 0 + 0*c**2 = 0?
-1, 0, 1
Suppose 0*w - w = 0. Let g(r) be the third derivative of -3*r**2 + 1/90*r**5 - 1/180*r**6 + 0 + 0*r**4 + w*r**3 + 0*r. Suppose g(h) = 0. Calculate h.
0, 1
Factor 1/9*q**5 + 0*q**2 + 0*q**3 - 1/3*q**4 + 0*q + 0.
q**4*(q - 3)/9
Let m(y) = y**2 + y - 1. Let o be m(2). What is n in 32*n - 4*n**2 - 3*n - o*n - 36 = 0?
3
Let h = -8 + 11. Let d(m) = -2*m + 1. Let g be d(-2). Factor 0*n**3 - 2*n**2 + 1 - 3*n**4 - 2*n**3 + 3*n + n**2 + h*n**2 - n**g.
-(n - 1)*(n + 1)**4
Let n(z) be the third derivative of -1/12*z**4 + 0*z + 1/120*z**5 + 1/3*z**3 + 0 - 3*z**2. Determine q so that n(q) = 0.
2
Let o(h) be the third derivative of -h**6/60 + h**5/15 - h**4/12 + 15*h**2. Let o(a) = 0. What is a?
0, 1
Let v(u) be the second derivative of u**4/90 + u**3/45 - 22*u. Factor v(k).
2*k*(k + 1)/15
Let v(s) be the third derivative of -s**10/30240 + s**8/2240 + s**7/1260 - s**4/24 - 3*s**2. Let c(a) be the second derivative of v(a). Let c(z) = 0. What is z?
-1, 0, 2
Let q(y) = y + 1. Suppose 0 = -2*f, 5*k + 3*f - 3 = 2. Let d(