 269753/3670. Let 0 + 12*j**2 + 0*j + p*j**5 - 78*j**3 + 105*j**4 = 0. What is j?
-2, 0, 2/7
Let k(r) = r**2 - 3*r - 2. Let x be k(4). Let f(z) be the second derivative of 1/60*z**5 + 0*z**3 + 0 - 1/36*z**4 - x*z + 0*z**2. Factor f(t).
t**2*(t - 1)/3
Suppose -37 - 14 = -17*r. Let k(c) be the first derivative of -1/15*c**3 + r - 4/5*c + 2/5*c**2. Factor k(x).
-(x - 2)**2/5
Let c(r) = -8*r**3 - r**2 + 23*r. Let d(w) = -4*w**3 - w**2 + 11*w. Let b(f) = -3*c(f) + 7*d(f). Factor b(i).
-4*i*(i - 1)*(i + 2)
Suppose -5 = -c - 2*v + 3*v, 2 = -2*v. Factor w**4 - c*w**4 - 3*w + 9*w + 4*w**2 + 5*w**2.
-3*w*(w - 2)*(w + 1)**2
Let k(w) be the first derivative of w**4/78 + 2*w**3/39 + w**2/13 - 5*w - 6. Let s(b) be the first derivative of k(b). Suppose s(d) = 0. Calculate d.
-1
Let b(s) be the second derivative of 5*s**7/42 + s**6/6 - 5*s**5/4 - 25*s**4/12 + 10*s**3/3 + 10*s**2 + 2*s. Solve b(w) = 0 for w.
-2, -1, 1, 2
Let o = -1444/3 + 482. Let 2/3*z + 0 - o*z**2 = 0. Calculate z.
0, 1
Let g(i) be the first derivative of -i**4/4 + i**3/3 + i**2 - 5. Factor g(p).
-p*(p - 2)*(p + 1)
Suppose -3*r + 2*s + 80 = 4*s, 5*r + 4*s - 130 = 0. Let u be (-4)/10 + 36/r. Solve -2/5*c**5 + 0 + 0*c**2 + 0*c**4 - 2/5*c + u*c**3 = 0 for c.
-1, 0, 1
Let u(s) be the second derivative of s**4/4 - 11*s**3 + 363*s**2/2 + 18*s. Factor u(o).
3*(o - 11)**2
Suppose -p + 5 = -b, p = -p + 4*b + 20. Let h(n) be the third derivative of 0*n + p - 1/180*n**5 - n**2 - 1/9*n**3 + 1/24*n**4. Factor h(j).
-(j - 2)*(j - 1)/3
Let g(w) be the third derivative of 0*w**3 + 1/24*w**4 - 1/120*w**6 - 1/210*w**7 + 0*w + 1/60*w**5 + 3*w**2 + 0. Factor g(s).
-s*(s - 1)*(s + 1)**2
Let a = 77 + -72. Let w(z) be the second derivative of 0 + 0*z**4 + 2/7*z**2 - 2*z - 1/70*z**a + 1/7*z**3. Determine m, given that w(m) = 0.
-1, 2
Find f, given that -6*f**3 + 2*f**3 + 2*f - f + 3*f = 0.
-1, 0, 1
Suppose 0 = -2*j + 8, -3*b = -4*b + j + 20. Factor 8 - b*q**3 - 18*q**3 + 8*q**2 + 24*q - 34*q**2.
-2*(q + 1)*(3*q - 2)*(7*q + 2)
Let z(f) = 6*f**2 - 6*f. Let k(b) = 13*b**2 - 12*b - 1. Let q(g) = -3*k(g) + 7*z(g). Suppose q(h) = 0. Calculate h.
1
Let g(c) be the first derivative of c**5/300 - c**4/60 + c**3/30 + 3*c**2/2 - 4. Let d(r) be the second derivative of g(r). Determine y so that d(y) = 0.
1
Let j(h) = -h**3 + 5*h**2 + 5*h + 8. Let l be j(6). Suppose l*b + 0*b = 0. Factor 2/5*i**5 - 2/5*i**4 + 0 + b*i + 2/5*i**2 - 2/5*i**3.
2*i**2*(i - 1)**2*(i + 1)/5
Let h(f) be the first derivative of -f**4/12 - 2*f**3/9 - f**2/6 - 5. Suppose h(v) = 0. What is v?
-1, 0
Let h(b) = -12*b**2 - 6*b - 3. Let o = 4 + -1. Let l(v) = -12*v**2 - 7*v - 4. Let c(q) = o*l(q) - 4*h(q). Let c(n) = 0. What is n?
-1/4, 0
Let r(o) = 3*o**2 - o + 6. Let c(t) = 2*t**2 - t + 4. Let u(y) = -8*c(y) + 5*r(y). Factor u(d).
-(d - 2)*(d - 1)
Let s be 10/4*(-40)/25. Let k be 10/(-4)*s/5. Factor 2/7 - 2/7*m - 24/7*m**k.
-2*(3*m + 1)*(4*m - 1)/7
Suppose -4*y + 13 = -5*g, 4*y - g + 6 = 15. Factor -2*f + f**2 + 0*f + 3*f**2 - 4 - 2*f**y.
2*(f - 2)*(f + 1)
Let o(z) be the third derivative of -z**8/1176 + 4*z**7/735 - z**6/84 + z**5/105 - 7*z**2. Find s, given that o(s) = 0.
0, 1, 2
Let z(a) be the first derivative of -1/3*a**2 - 2 - 1/3*a - 1/9*a**3. Let z(o) = 0. What is o?
-1
Suppose 0 = -3*b - 2*b + 15. Factor -c - 1 - c**2 - b*c + 2*c.
-(c + 1)**2
Let j(a) = 9*a**3 - 19*a**2 - 7*a. Let h(y) = 18*y**3 - 37*y**2 - 13*y. Let q(m) = 3*h(m) - 5*j(m). Determine g, given that q(g) = 0.
-2/9, 0, 2
Suppose 29*f = -3*n + 27*f + 10, -4*f = -4*n. Find j such that 3/2*j + 3/4*j**n + 3/4 = 0.
-1
Let g(y) be the first derivative of -16*y**6/3 + 16*y**5 - y**4/2 - 76*y**3/3 + 17*y**2 - 4*y + 5. Find d, given that g(d) = 0.
-1, 1/4, 1, 2
Let x(g) be the first derivative of -g**4/6 + 10*g**3/27 - 2*g**2/9 + 2. Suppose x(d) = 0. Calculate d.
0, 2/3, 1
Suppose -6*p**2 + 6*p**3 + 0*p - 3/2*p**4 + 0 = 0. What is p?
0, 2
Let c(v) be the second derivative of -1/2*v**2 + 0 + 0*v**3 - 1/30*v**5 + 0*v**4 + v. Let a(l) be the first derivative of c(l). Factor a(y).
-2*y**2
Factor -4*p - 10*p - 2*p**4 + 14*p + 2*p**2.
-2*p**2*(p - 1)*(p + 1)
Let y be 3/((-15)/2) + 1242/230. Solve 2/3*v**2 + 0*v + 0 - 2/3*v**4 - 4/3*v**y + 4/3*v**3 = 0 for v.
-1, -1/2, 0, 1
Let f(n) = -n**3 + n**2 + n. Let w(j) = -j**3 - 9*j**2 - 3*j + 2. Suppose 5*c - 3*d = 0, -2*d + 5*d - 9 = 2*c. Let u(a) = c*f(a) + w(a). Solve u(h) = 0 for h.
-1, 1/2
Let c(o) = -4*o**4 - 15*o**3 + 44*o**2 - 25*o - 1. Let x(f) = -f**4 + f**2 + 1. Let z(t) = c(t) + x(t). Factor z(r).
-5*r*(r - 1)**2*(r + 5)
Suppose 0 = -u - 3*u - 3*x + 14, -5*u + 5*x = 0. Let -3 + 0 - u*d**2 + 5 = 0. Calculate d.
-1, 1
Let g(z) be the third derivative of -z**8/4480 - z**7/1260 - z**6/1440 + z**4/8 - 3*z**2. Let r(x) be the second derivative of g(x). Find w such that r(w) = 0.
-1, -1/3, 0
Suppose 11 = 2*j - 9. Let f = j + -8. Suppose 6*z**2 - 6*z - 8*z**f + 5*z**2 = 0. What is z?
0, 2
Let k(f) = 7 - 3 - f + 5 - 2. Let q be k(3). What is z in 2*z**2 - 2*z - z**2 + q*z = 0?
-2, 0
Let s(q) = -q**2 + 3*q. Let m(r) = r**2 + r. Let v(a) = 3*a**2 - 4*a. Let t(h) = m(h) - v(h). Let y(u) = -5*s(u) + 3*t(u). Solve y(f) = 0.
0
Let f(a) be the second derivative of 25*a**4/12 - 20*a**3/3 + 8*a**2 + 12*a - 2. Solve f(k) = 0 for k.
4/5
Let x(v) be the second derivative of 0*v**2 + 1/42*v**4 + 1/21*v**3 + 2*v + 0. What is c in x(c) = 0?
-1, 0
Let a = 20 + -11. Let s be 1/36 - (-2)/a. Factor -1/4*m + s*m**2 + 0.
m*(m - 1)/4
Let u(t) = 2*t**2 + 50*t - 50. Let m be u(-26). What is n in -5/4*n**3 + n + 2*n**m + 0 = 0?
-2/5, 0, 2
Suppose -2 + 4 = c. Suppose -3*p + 5*o + 20 = 0, 2*o = -5*p - c*o + 58. What is m in 0 + 4 + p*m**3 + m**4 - 5*m**4 - 10*m = 0?
-1, 1/2, 1, 2
Let g = 403 - 2006/5. Factor 9/5*r**2 + 3/5*r**4 + 3/5*r + g*r**3 + 0.
3*r*(r + 1)**3/5
Let k(n) be the second derivative of -6*n**6/5 - 6*n**5 - 13*n**4/3 + 40*n**3/3 - 8*n**2 - 6*n. Let k(h) = 0. What is h?
-2, 1/3
Let r(v) = -5*v - 3. Let x be r(-1). Let y = 1 + x. Factor 0 - 2/5*u**y + 2/5*u**5 + 2/5*u**2 + 0*u - 2/5*u**4.
2*u**2*(u - 1)**2*(u + 1)/5
Factor d**5 - 2*d**5 + 2*d - 5*d**3 + 6*d**4 - 3*d**4 - 3*d**2 + 4*d**3.
-d*(d - 2)*(d - 1)**2*(d + 1)
Let o(b) = 2*b**2 - 2*b - 9. Let k(f) = -3*f**2 + 3*f + 14. Let q(r) = -5*k(r) - 8*o(r). Factor q(d).
-(d - 2)*(d + 1)
Let m be (-792)/(-231) + (-3)/7. Factor -f**2 + 1/6*f**m + 0 + 3/2*f.
f*(f - 3)**2/6
Factor 25*v**2 + 32 - 12 - 14*v**3 + 40*v + 19*v**3.
5*(v + 1)*(v + 2)**2
Let n = 29/4 - 311/44. Factor 0 + 0*c + n*c**2.
2*c**2/11
Let x = 6 - 10. Let y = x + 4. Factor r**5 + r**3 - 2*r**5 + y*r**3.
-r**3*(r - 1)*(r + 1)
Let g = -253 + 258. Factor 13/5*h**3 - 6/5*h**4 + 0 - 12/5*h**2 + 4/5*h + 1/5*h**g.
h*(h - 2)**2*(h - 1)**2/5
Let c(b) be the first derivative of b**7/105 - 2*b**6/75 + b**4/15 - b**3/15 + 5*b - 5. Let a(d) be the first derivative of c(d). Suppose a(o) = 0. What is o?
-1, 0, 1
Let m(x) be the first derivative of -2*x**5/5 - 2*x**4 - 2*x**3 + 13. Suppose m(j) = 0. Calculate j.
-3, -1, 0
Factor 5/4*d**3 - 15/4*d**2 - 5/4 + 15/4*d.
5*(d - 1)**3/4
Let f(u) be the second derivative of 7*u + 0 + 27/2*u**2 - 3/20*u**5 - 3/2*u**3 - 5/4*u**4. Solve f(d) = 0.
-3, 1
Let c(n) = -n**3 + 16*n**2 - n + 20. Let j be c(16). Factor 16/7 - 2/7*b**j - 10/7*b**3 + 8/7*b - 12/7*b**2.
-2*(b - 1)*(b + 2)**3/7
Let n = -34 - -21. Let q = -9 - n. Determine w, given that 6*w**2 + 8*w**5 + 2*w**2 - w**4 - 4*w - 6*w**3 - 7*w**q + 2*w = 0.
-1, 0, 1/2, 1
Suppose 5*a = 0, 2*w + 0*w - 4*a = 0. Let o = w - -4. Factor -v**3 - 4*v**o - 2*v**2 + 2*v**2 + v + v**2 + 3*v**4.
-v*(v - 1)*(v + 1)**2
Let m(y) be the second derivative of -1/12*y**4 + 1/3*y**3 - 2*y**2 + 3*y + 0 + 1/120*y**5. Let j(k) be the first derivative of m(k). Solve j(h) = 0.
2
Let t(h) be the third derivative of 1/48*h**4 - 1/120*h**5 + 0*h + 6*h**2 + 0 + 0*h**3. Determine i, given that t(i) = 0.
0, 1
Let x(b) be the first derivative of 2*b**6/3 + 16*b**5/5 + 2*b**4 - 16*b**3/3 - 6*b**2 - 4. Factor x(j).
4*j*(j - 1)*(j + 1)**2*(j + 3)
Let z be (-1 + 16/10)*(-784)/(-42). Factor -8/5 - 98/5*j**2 - z*j.
-2*(7*j + 2)**2/5
Let v(z) be the first derivative of z**4/12 - 2*z**3/9 + z**2/6 - 15. Factor v(t).
t*(t - 1)**2/3
Let z(c) be the second derivative of -c**8/56 + 3*c**7/70 - c**5/20 - c**2/2 - 4*c. Let u