*3/6 - 2*g**2. Let d(h) be the first derivative of y(h). Factor d(p).
-3*p**2*(p + 1)
Find a such that -4/7 - 2/7*a**2 + 6/7*a = 0.
1, 2
Let h be -1*(0 - (-4 + 3))/(-2). Determine m, given that 0*m**2 - h*m**4 - 3/4*m**5 + 1/4*m**3 + 0*m + 0 = 0.
-1, 0, 1/3
Let y be 14/(-36)*12/(-84). Let m(u) be the third derivative of 0*u**4 - 1/180*u**5 + 0*u + u**2 + 0 + y*u**3. Factor m(g).
-(g - 1)*(g + 1)/3
Let i be -10*((-54)/(-15) - (2 - -2)). Factor -i*l - 20/3*l**2 + 12 - 4/3*l**3.
-4*(l - 1)*(l + 3)**2/3
Let b(v) be the second derivative of v**9/2520 - v**8/672 + v**7/1260 + v**6/360 + v**4/6 + 2*v. Let q(o) be the third derivative of b(o). Factor q(t).
2*t*(t - 1)**2*(3*t + 1)
Let n(k) be the first derivative of 0*k + 1 + 4/21*k**3 - 3/7*k**2 + 5/14*k**4. Find b, given that n(b) = 0.
-1, 0, 3/5
Let l(z) be the second derivative of z**5/20 - z**4/12 + 16*z. Factor l(m).
m**2*(m - 1)
Let q(p) be the second derivative of -1/30*p**4 + 0 - 3/5*p**2 - 5*p - 4/15*p**3. Solve q(u) = 0 for u.
-3, -1
Suppose 1/2*m**3 + 5/2 + 7/2*m**2 + 11/2*m = 0. Calculate m.
-5, -1
Let g(w) = w**3 - 7*w**2 + w + 5. Let u be g(4). Let x = u + 119/3. Factor -4/9*c**3 + 2/3*c + x*c**4 - 4/9*c**2 - 2/9*c**5 - 2/9.
-2*(c - 1)**4*(c + 1)/9
Let j(p) be the first derivative of -4*p**3/3 - 6*p**2 + 6. Factor j(x).
-4*x*(x + 3)
Suppose 8*u - 3*u - 20 = 0. Factor -2*m**u - 2*m + 6*m**3 - 2*m**5 - 2*m**2 - 2 + 6*m**2 - 2*m**3.
-2*(m - 1)**2*(m + 1)**3
Let d(a) be the third derivative of -3/160*a**6 - 1/40*a**5 + 0*a**3 + 0*a**4 + 0 + 0*a - 1/280*a**7 + 6*a**2. Factor d(j).
-3*j**2*(j + 1)*(j + 2)/4
Let a(f) = -f - 12. Let w be a(-14). Let t(u) be the third derivative of 0 - w*u**2 + 1/840*u**7 + 0*u**5 + 0*u**6 + 0*u**3 + 0*u**4 + 0*u. Factor t(r).
r**4/4
Let k(f) be the second derivative of 2/9*f**3 + 3*f - 1/6*f**2 - 1/12*f**4 + 0. Factor k(z).
-(z - 1)*(3*z - 1)/3
Let o(x) = x**2 - x + 1. Let c(s) be the second derivative of s**4/6 - s**3/3 + s**2/2 - s. Let d(u) = -c(u) + o(u). Let d(i) = 0. Calculate i.
0, 1
Solve 242/19 + 44/19*k + 2/19*k**2 = 0.
-11
Suppose -5*w = -5*l + 65, 37 = 5*l + 2*w - 0*w. Suppose l*r - 5*r - 16 = 0. Suppose 0*f + 0 + 0*f**2 - 3/2*f**3 - 3/2*f**5 + 3*f**r = 0. Calculate f.
0, 1
Let l(u) be the second derivative of u**4/3 + 4*u**3 + 10*u**2 - 11*u. Factor l(w).
4*(w + 1)*(w + 5)
Factor -2/9 + 2/9*g**3 + 2/9*g**2 - 2/9*g.
2*(g - 1)*(g + 1)**2/9
Let u(o) = 3*o**2 - 6*o + 11. Let x(p) = 2*p**2 - 4*p + 7. Let d(v) = -5*u(v) + 8*x(v). Factor d(s).
(s - 1)**2
Let k = 8 + -5. Solve 5*r**3 - r - 4*r**4 - 6*r**2 + 2*r**4 + k*r + r**3 = 0.
0, 1
Let v(l) be the second derivative of l**6/105 + l**5/35 + 36*l. Solve v(j) = 0.
-2, 0
Let o(r) be the first derivative of -1/15*r**3 + 1/10*r**2 - 2 + 0*r. What is y in o(y) = 0?
0, 1
Let c = -1406/765 - -32/17. Let i(w) be the first derivative of 1/6*w**4 - 2/27*w**6 + c*w**5 - 2/27*w**3 - 2 + 0*w - 1/9*w**2. What is p in i(p) = 0?
-1, -1/2, 0, 1
Let z(s) be the second derivative of 1/18*s**3 + 0*s**2 + 0 + 8*s + 1/36*s**4. Factor z(a).
a*(a + 1)/3
Let g(b) be the third derivative of -b**7/630 + b**6/180 + b**5/180 - b**4/36 + b**2. Determine t, given that g(t) = 0.
-1, 0, 1, 2
Let t(u) be the second derivative of u**5/10 + u**4/3 + u**3/3 - 14*u. Factor t(q).
2*q*(q + 1)**2
Let x(a) be the second derivative of -a**9/1512 - a**8/420 - 5*a**3/6 + 4*a. Let f(g) be the second derivative of x(g). Determine t so that f(t) = 0.
-2, 0
Let d = -6 + 9. Factor 6*w**3 - 3*w**3 + w**3 - d*w**3 - w.
w*(w - 1)*(w + 1)
Suppose 1/11*n**2 - 6/11*n + 9/11 = 0. Calculate n.
3
Determine r so that -9*r**2 + 5*r**2 - 65*r - 6*r**2 + 35 = 0.
-7, 1/2
Factor 2*x**3 - 44*x**2 + 2*x**3 + 3*x**3 + 5*x**3 + 48*x - 16.
4*(x - 2)*(x - 1)*(3*x - 2)
Let u(a) be the second derivative of -1/135*a**6 + 0 - 1/189*a**7 + 2*a + 0*a**2 + 0*a**3 + 1/90*a**5 + 1/54*a**4. Factor u(b).
-2*b**2*(b - 1)*(b + 1)**2/9
Factor 128/9 - 2/9*p**5 + 28/9*p**4 - 352/9*p + 344/9*p**2 - 146/9*p**3.
-2*(p - 4)**3*(p - 1)**2/9
Let h = 11/2289 - -1/872. Let i(p) be the third derivative of h*p**8 + 0 + 1/15*p**6 - 2*p**2 - 1/12*p**4 - 1/30*p**5 + 0*p + 1/6*p**3 - 1/30*p**7. Factor i(l).
(l - 1)**4*(2*l + 1)
Suppose -4*a - 13 = -33. Let q(t) be the first derivative of t**2 - 23/14*t**4 + 16/21*t**6 - 16/35*t**a + 2/7*t - 1 + 2/3*t**3. Suppose q(y) = 0. Calculate y.
-1, -1/4, 1
Let z(s) be the second derivative of s**6/40 - 3*s**4/16 - s**3/4 - 3*s. Factor z(q).
3*q*(q - 2)*(q + 1)**2/4
Let o(p) be the second derivative of -p**4/16 + p**3/4 - 3*p**2/8 - 19*p. Factor o(b).
-3*(b - 1)**2/4
Let k = 5293/2271 - -2/757. Let v(g) be the first derivative of -11*g**2 + 4*g + 28/3*g**3 - 1 - 32/5*g**5 + k*g**6 + 2*g**4. Factor v(n).
2*(n - 1)**3*(n + 1)*(7*n - 2)
Let l be 4/2 + 6 + 6. Let v(n) = 4*n**3 - 14*n**2 + 16*n - 20. Let h(m) = m**3 - 3*m**2 + 3*m - 4. Let y(s) = l*h(s) - 3*v(s). Factor y(a).
2*(a - 1)**2*(a + 2)
Let i(s) = -s**2 + 15*s - 24. Let m be i(13). Find t, given that -6/5*t**m - t**3 - 1/5*t + 0 = 0.
-1, -1/5, 0
Let o(q) be the second derivative of -q**5/70 + q**4/42 + 3*q. Factor o(d).
-2*d**2*(d - 1)/7
Let h(z) be the second derivative of 0 - 14/9*z**3 - 4*z + 4/3*z**2 + 7/15*z**5 - 2/9*z**4. Suppose h(g) = 0. Calculate g.
-1, 2/7, 1
Let l = 13 + -10. Suppose 0*g + 28 = l*z + 4*g, 28 = 4*z + 3*g. Suppose 0*c**z + 2/3*c**5 + 0*c**2 - 2/3*c**3 + 0 + 0*c = 0. What is c?
-1, 0, 1
Let o(m) be the second derivative of 2/9*m**4 + 0*m**6 + 1/5*m**5 - 2/63*m**7 - 5*m + 0*m**2 + 0*m**3 + 0. Factor o(f).
-4*f**2*(f - 2)*(f + 1)**2/3
Let m be 4/(132/171) - (-12)/(-66). Let 6*y**3 + 3/2*y**m + 5*y**4 + 0 + 3*y**2 + 1/2*y = 0. Calculate y.
-1, -1/3, 0
Let m(r) = 2*r**2 - 2*r - 1. Let g = -5 + 7. Let i be m(g). Solve -u + u**3 + 2*u - 2*u**i = 0.
-1, 0, 1
Suppose 0*q - 40 = 4*q. Let u be (-1 + -1)*1/q. Factor 1/5*p**2 + 1/5*p - 1/5*p**3 - u.
-(p - 1)**2*(p + 1)/5
Let m(o) = -20*o**4 - 34*o**3 - 25*o**2 + o + 6. Let a(t) = -20*t**4 - 33*t**3 - 25*t**2 + 2*t + 7. Let n(c) = 6*a(c) - 7*m(c). Factor n(g).
5*g*(g + 1)*(2*g + 1)**2
Let r(q) be the third derivative of -2*q**2 + 2/9*q**3 + 0 - 7/36*q**5 + 1/18*q**4 + 0*q. Factor r(d).
-(5*d - 2)*(7*d + 2)/3
Let j = 78 + -542/7. Suppose 0*b**4 - j*b**3 + 0*b**2 + 2/7*b + 2/7*b**5 + 0 = 0. Calculate b.
-1, 0, 1
Let l(f) = 6*f**2 - 5*f**3 + 2*f**3 - 5*f - 6*f**2 + 4*f**2. Let x(d) = 4*d**3 - 5*d**2 + 6*d. Let q(v) = 5*l(v) + 4*x(v). Determine r, given that q(r) = 0.
-1, 0, 1
Let g(t) = -t**3 + t**2 + 12*t + 5. Let l(b) = b**3 - b**2 - 18*b - 8. Let n(x) = -8*g(x) - 5*l(x). Suppose n(m) = 0. What is m?
-1, 0, 2
Find i, given that 8/11*i + 0 + 42/11*i**3 - 18/11*i**4 - 32/11*i**2 = 0.
0, 2/3, 1
Let x(m) be the first derivative of m**5/80 - m**4/16 + m**2/2 + 4*m - 4. Let s(c) be the first derivative of x(c). Suppose s(r) = 0. Calculate r.
-1, 2
Suppose 55*x = 53*x + 10. Let p(u) be the first derivative of 0*u**2 + 2 + 2/5*u**x + 0*u - 1/9*u**6 + 0*u**3 - 1/3*u**4. Factor p(w).
-2*w**3*(w - 2)*(w - 1)/3
Let x(a) = -a**3 + 2*a**2 + 3*a - 3. Let u be x(2). Let v = 12 - u. Factor t**3 - 3*t**2 + 4*t + t**3 + v*t**2.
2*t*(t + 1)*(t + 2)
Let v(r) be the third derivative of 0*r**4 + 0*r - 1/1344*r**8 - 1/480*r**6 + 0 - 4*r**2 + 0*r**3 + 0*r**5 + 1/420*r**7. Factor v(t).
-t**3*(t - 1)**2/4
Suppose -l + 3*d + 23 = -2*d, 3*d = -4*l. Let a be (2/8)/(29/174). Determine h, given that 2*h**4 + 0 + a*h**l - 1/4*h - 3/4*h**2 = 0.
-1, -1/4, 0, 1/2
Let j(c) be the first derivative of -c**6/1440 - c**5/240 - c**4/96 - c**3/3 + 6. Let u(n) be the third derivative of j(n). Factor u(y).
-(y + 1)**2/4
Determine i so that -82 - 169 - 2*i**2 + 36*i + 89 = 0.
9
Let b(c) be the first derivative of c**3/12 + 7*c**2/4 + 49*c/4 + 14. Find q, given that b(q) = 0.
-7
Let l = 0 - -4. Let u(k) be the first derivative of 4/3*k - 10/9*k**3 + 2/5*k**5 + 1/6*k**l - 1/3*k**2 + 2. Solve u(s) = 0.
-1, 2/3, 1
Determine u so that 2/5 + 2/5*u**2 - 4/5*u = 0.
1
Let c(k) be the third derivative of k**10/529200 - k**8/35280 + k**6/2520 + k**5/30 + k**2. Let z(s) be the third derivative of c(s). Factor z(m).
2*(m - 1)**2*(m + 1)**2/7
Let 4*w**3 + 8/9 + 8/9*w**2 - 2/3*w**5 - 16/9*w**4 - 10/3*w = 0. What is w?
-4, -1, 1/3, 1
Let m(i) = 8*i**5 + 2*i**4 + 4*i**3 + 4*i**2. Let a(b) = b**5 + b**3 + 