0 - 9*c - 3*c - 3*c**2 - a - c**2.
-4*(c + 1)*(c + 2)
Let p = 1/70 + 11/210. Let i(r) be the second derivative of -1/5*r**4 + 0*r**2 - 9/50*r**5 + 2*r - p*r**3 + 0. Solve i(y) = 0.
-1/3, 0
Let 3 - 90*p**3 - 551*p**4 + 251*p**2 - 95*p**2 + 615*p**4 - 37*p - 150*p**3 = 0. Calculate p.
1/4, 3
Factor 72*a**2 + 176*a**3 + 21*a**4 - 117*a**4 + 18*a**5 - 200*a**2 + 32*a.
2*a*(a - 2)**2*(3*a - 2)**2
Let z(n) be the first derivative of -4*n**3/3 + 4*n**2 + 34. Factor z(i).
-4*i*(i - 2)
Suppose 0 = 5*o + 4 + 11. Let c = -1 - o. Suppose -u**c + u**4 + u**3 - u + 8 - 8 = 0. Calculate u.
-1, 0, 1
Factor -2*l**4 + 10 + 5*l**3 + 7*l**4 - 75*l**2 + 60*l**2 - 5*l.
5*(l - 1)**2*(l + 1)*(l + 2)
Factor -h**3 - 15*h + 10*h**2 - 5*h**3 + 11*h**3.
5*h*(h - 1)*(h + 3)
Let k(b) be the third derivative of 3*b**7/490 + b**6/280 - 2*b**5/35 + b**4/14 - 2*b**2. Determine l so that k(l) = 0.
-2, 0, 2/3, 1
Let i be -3*(-2 + 1 + 0). Let -2*y**2 + y + i*y**2 + 0*y**3 - 2*y**3 = 0. What is y?
-1/2, 0, 1
Suppose 96 - 96 = k. Let a(h) be the first derivative of -4 + 0*h**2 + k*h + 1/20*h**5 + 0*h**4 - 1/12*h**3. Factor a(m).
m**2*(m - 1)*(m + 1)/4
Factor -1/7*s**4 + 1/7*s + 1/7*s**2 + 0 - 1/7*s**3.
-s*(s - 1)*(s + 1)**2/7
Let f(n) = 7*n**2 - 9*n + 2. Let l(p) = -14*p + 3 + 6*p**2 + 9*p**2 + 2*p**2 - 6*p**2. Let r = 12 - 4. Let c(x) = r*f(x) - 5*l(x). Factor c(j).
(j - 1)**2
Let u be 5*(-16)/(-30)*(-27)/(-36). Let w(j) be the third derivative of 0*j + 1/75*j**5 + 0*j**3 - 1/60*j**4 + 0 + j**u - 1/300*j**6. What is g in w(g) = 0?
0, 1
Let m be (-4 - -10)/((3 + -4)*-2). Factor 0*v**2 + 3/4*v + 0 - 3/4*v**m.
-3*v*(v - 1)*(v + 1)/4
Let 8/5 - 12/5*r + 4/5*r**2 = 0. Calculate r.
1, 2
Let q = 86 - 341/4. Let y(u) be the first derivative of -3*u**2 + q*u**4 + u**3 - 3 + 0*u. Factor y(k).
3*k*(k - 1)*(k + 2)
Solve 43*u**4 + 36*u**2 + 1 + 24*u**3 - 1 - 39*u**4 = 0.
-3, 0
Let x(o) be the second derivative of 0 + 0*o**2 - o + 1/12*o**4 + 0*o**3. Solve x(q) = 0 for q.
0
Let z(g) be the first derivative of 4*g**5/5 + g**4 - 4*g**3 - 10*g**2 - 8*g + 25. Factor z(r).
4*(r - 2)*(r + 1)**3
Let u(q) be the second derivative of -q**5/10 + 4*q**3/3 + 32*q. Let u(o) = 0. Calculate o.
-2, 0, 2
Let i(x) = x**2 - 6*x - 2. Let m be i(6). Let a be 4/(-5)*1/m. Let 0 + 0*u - a*u**2 = 0. What is u?
0
Suppose 0 = -2*r + r - 1. Let v(c) = -c + 1. Let d be v(r). Solve -6*y - 2*y**3 - 2 + 5*y**3 - y**3 + 4*y + d*y**2 = 0 for y.
-1, 1
Let f(o) be the third derivative of -o**5/30 - o**4/12 + 8*o**2. Factor f(z).
-2*z*(z + 1)
Let s = 1 + 0. Let n(p) = 1. Let f(q) = -q**2 + 1. Let z(t) = s*f(t) - n(t). Factor z(v).
-v**2
Suppose -4 = 3*g + 2. Let c be g/(-72) - 6/(-27). Factor 0 - c*w**3 + 0*w**2 + 1/4*w.
-w*(w - 1)*(w + 1)/4
Suppose -b + 0*b = -2. What is w in w**b - 3*w**2 - 7*w**3 + 2*w**3 + 4*w**2 = 0?
0, 2/5
Let u(o) be the first derivative of 7 + 0*o + 1/15*o**3 + 1/10*o**2. What is d in u(d) = 0?
-1, 0
Let o(d) = 7*d**2 + 4*d + 2. Let x(j) = 11*j**2 + 6*j + 3. Let a = 18 - 26. Suppose 8 + 12 = 4*i. Let g(b) = a*o(b) + i*x(b). Let g(f) = 0. What is f?
-1
Factor 4/7 + 2/7*b**2 - 6/7*b.
2*(b - 2)*(b - 1)/7
Let f be 3/(15/20*12/9). Find h such that -2/7*h**f + 0 + 2/7*h**2 + 0*h = 0.
0, 1
Let f(y) be the first derivative of -4*y**5 - 3*y**4 + 8*y**3/3 - 6. Let f(z) = 0. Calculate z.
-1, 0, 2/5
Let k(u) be the first derivative of 1 - 21/2*u**2 + 9*u**3 - 6*u. Factor k(t).
3*(t - 1)*(9*t + 2)
Suppose -8*s = -2*s - 24. Let w(j) be the third derivative of 0*j**s - 1/70*j**5 + 0 + 0*j + 1/21*j**3 + 1/210*j**6 - 2*j**2. Let w(z) = 0. Calculate z.
-1/2, 1
Solve 2 + 7*j + 6*j - 12*j**5 + 4*j**3 + 6*j**2 - 23*j**4 - 5*j**3 + 15*j**2 = 0 for j.
-1, -2/3, -1/4, 1
Factor 2/9*m + 0*m**2 + 0 - 2/9*m**3.
-2*m*(m - 1)*(m + 1)/9
Let l(u) = -3*u**2 - 4*u - 11. Let a(t) = -4*t**2 - 3*t - 12. Let r be -1*1/(-3)*12. Let b(f) = r*a(f) - 6*l(f). Factor b(n).
2*(n + 3)**2
Let w(d) be the first derivative of -d**6/240 + d**5/40 - d**4/24 + d**2 - 5. Let c(q) be the second derivative of w(q). What is m in c(m) = 0?
0, 1, 2
Let v(z) = z**3 - 4*z**2 - 3*z - 7. Let y be v(5). Suppose g - 5*g = -y*j - 2, j - 10 = -4*g. Factor j - 1 - 3*k**3 - 7*k + k + 7*k**2 + k.
-(k - 1)**2*(3*k - 1)
Solve -4 + a + 20*a**4 - a**2 + 4 - a**3 - 19*a**4 = 0 for a.
-1, 0, 1
Let f(k) be the second derivative of k**7/84 - k**6/12 + k**5/4 - 5*k**4/12 + 5*k**3/12 - k**2/4 + 9*k. Factor f(l).
(l - 1)**5/2
Let c(o) = -5*o**2 + o + 2. Let x(q) = 2*q**2 - q - 1. Let i(n) = 2*c(n) + 4*x(n). Factor i(w).
-2*w*(w + 1)
Let b(z) be the second derivative of -z**6/32 - 13*z**5/240 - z**4/48 + 5*z**2/2 - z. Let g(k) be the first derivative of b(k). Factor g(n).
-n*(3*n + 2)*(5*n + 1)/4
Let i(l) = 7*l**3 + 61*l**2 + 293*l + 243. Let k(b) = 6*b**3 + 60*b**2 + 294*b + 243. Let o(s) = -3*i(s) + 4*k(s). What is x in o(x) = 0?
-9, -1
Let w(l) be the first derivative of l**3 - 3*l**2 - 9*l + 6. Factor w(s).
3*(s - 3)*(s + 1)
Factor 4*w**3 + 0*w**2 - 11*w**2 + 7*w**2.
4*w**2*(w - 1)
Solve 7/3*w - 13/6 - 1/6*w**2 = 0 for w.
1, 13
Factor 20*h**2 - 3*h**2 + 5*h**3 + 34 - 24 + 3*h**2 + 25*h.
5*(h + 1)**2*(h + 2)
Let x(t) = 5*t**4 + 2*t**3 - 4*t**2 + 2*t + 5. Let c(v) = -6*v**4 - 3*v**3 + 3*v**2 - 3*v - 6. Let k(p) = 2*c(p) + 3*x(p). Factor k(z).
3*(z - 1)**2*(z + 1)**2
Let b(k) = -9. Let z(d) = 6*d**2 + 0*d - 5*d**2 + 10 - 2*d + d. Let f(o) = 4*b(o) + 3*z(o). Factor f(t).
3*(t - 2)*(t + 1)
Suppose -2*h = 3*h. Let q = -20/9 + 89/36. Determine t, given that q*t**2 + h - 1/4*t**3 + 0*t = 0.
0, 1
Suppose w - 5*w = -16. Let a = 8 - -1. Factor -o**2 + a*o**4 + 2*o**3 + 2*o**3 - 9*o**2 + o**w - 4*o.
2*o*(o - 1)*(o + 1)*(5*o + 2)
Let o(a) be the first derivative of -a**4/4 + a**3 - 4*a + 54. Factor o(g).
-(g - 2)**2*(g + 1)
Let x(o) be the second derivative of o**9/1680 + o**8/1120 - o**7/840 + 5*o**4/12 - 5*o. Let z(y) be the third derivative of x(y). What is r in z(r) = 0?
-1, 0, 1/3
Let k(h) be the second derivative of h**7/105 + 2*h**6/15 + 33*h**5/50 + 4*h**4/3 + 16*h**3/15 - 25*h. Factor k(d).
2*d*(d + 1)**2*(d + 4)**2/5
Let b(g) be the first derivative of g**7/5460 - g**5/780 + g**3/3 + 4. Let v(j) be the third derivative of b(j). Factor v(p).
2*p*(p - 1)*(p + 1)/13
Suppose 0 = 2*k - 2 - 14. Let i be (6/k)/(9/36). Factor -n**i + 1/2*n**2 + 0 + 0*n + 1/2*n**4.
n**2*(n - 1)**2/2
Let x = 1/7 + 5/14. Let y = 52 - 51. Factor -x*u**2 + 1/2*u + y.
-(u - 2)*(u + 1)/2
Let y be ((-2)/(2 + -10))/(3 - 2). Find z, given that -y*z - 5/4*z**3 + 2*z**2 - 1/2 = 0.
-2/5, 1
Let x(n) = 3*n + 30. Let j be x(-10). Factor 2/3*o + 2/3*o**5 - 4/3*o**3 + 0 + 0*o**2 + j*o**4.
2*o*(o - 1)**2*(o + 1)**2/3
Let j(g) = 4*g**5 - 2*g**3 - 6*g**2 + 4*g. Let r(n) = -5*n**5 + n**4 + n**3 + 7*n**2 - 5*n + 1. Let u(v) = 3*j(v) + 2*r(v). Factor u(o).
2*(o - 1)**2*(o + 1)**3
Let n(w) be the first derivative of 1 + 2/13*w - 10/39*w**3 + 4/13*w**2. Factor n(k).
-2*(k - 1)*(5*k + 1)/13
Let m(b) be the second derivative of b**5/20 - b**4/12 - b**3/3 - 6*b. Factor m(r).
r*(r - 2)*(r + 1)
Let o be (-2395)/(-45) - (-2)/(-9). What is j in -o + 53 - 3*j - 3*j**2 = 0?
-1, 0
Let u = 9/8 + 3/8. Factor 1/4*n + 0 - n**4 - u*n**2 + 9/4*n**3.
-n*(n - 1)**2*(4*n - 1)/4
Let t(w) be the first derivative of 2*w**3/9 - 2*w**2 + 15. Suppose t(b) = 0. Calculate b.
0, 6
Factor 2/13*r**4 - 32/13*r + 0 + 14/13*r**3 + 16/13*r**2.
2*r*(r - 1)*(r + 4)**2/13
Let t(b) be the first derivative of -4 - 4/7*b - 16/21*b**3 - 3/14*b**4 - b**2. Factor t(c).
-2*(c + 1)**2*(3*c + 2)/7
Let j = 95 + -95. Suppose j + 8/5*f**2 - 2/5*f**3 - 8/5*f = 0. What is f?
0, 2
Let h(u) be the second derivative of u**6/30 + u**5/10 - u**4/12 - u**3/3 + 48*u. Solve h(f) = 0 for f.
-2, -1, 0, 1
Let c(f) be the second derivative of f**6/6 - 3*f**5/4 - 25*f**4/4 - 85*f**3/6 - 15*f**2 - 35*f. Factor c(v).
5*(v - 6)*(v + 1)**3
Let x(v) be the second derivative of -v**6/15 + 7*v**5/10 - 5*v**4/6 - 7*v**3/3 + 6*v**2 + 4*v - 1. Suppose x(p) = 0. Calculate p.
-1, 1, 6
Let k(f) be the third derivative of f**2 - 1/180*f**5 + 0 - 1/18*f**3 - 1/36*f**4 + 0*f. Find n such that k(n) = 0.
-1
Suppose -8*u = -3*u - 10. Factor -3*d**4 + d**u + 2*d**4 + 3*d**3 - 3*d**3.
-d**2*(d - 1)*(d + 1)
Let k(o) = 22 - 8 + 43*o + 10 + 18*o**2 + 3*o**3. Let g(b) = 2*b**3 + 12*b**2 + 29*b + 16. Let j(i) = 7*g(i) -