uppose 0 = 57*p + 40*p + 37*p - 402. Factor 1/3*d**p + 8/3*d + 4/3 + 5/3*d**2.
(d + 1)*(d + 2)**2/3
Let j(s) be the third derivative of -s**7/6300 - s**6/360 - s**5/50 - 5*s**4/12 + 19*s**2. Let a(u) be the second derivative of j(u). Factor a(f).
-2*(f + 2)*(f + 3)/5
Let l be (-24)/(-96) - 90/(-24). Factor 0 + 9*v**3 + 3/2*v**5 - 6*v**l + 3/2*v - 6*v**2.
3*v*(v - 1)**4/2
Let f(u) be the third derivative of 1/5*u**5 + 0*u**3 - 1/3*u**4 - 1/20*u**6 - 3*u**2 + 0 + 0*u + 1/210*u**7. Find p, given that f(p) = 0.
0, 2
Let l = 22/105 - -214/315. Solve 8/9*j**4 + 0 - 8/9*j + 2/3*j**3 + 2/9*j**5 - l*j**2 = 0.
-2, -1, 0, 1
Factor 222*s + 1266*s**2 + 4 + 583*s**2 - 50*s.
(43*s + 2)**2
Let a = 292 + -292. Let v(k) be the third derivative of a*k + 4/105*k**7 + 0 + 2*k**2 - 1/8*k**4 + 1/12*k**3 + 1/10*k**6 + 1/120*k**5. Let v(b) = 0. What is b?
-1, 1/4
Let v(t) = 54*t**3 + 36*t**2 - 20*t - 44. Let i(q) = 7*q**2 + 13*q + 2 + 11*q**3 - 11 - 17*q. Let g(n) = 14*i(n) - 3*v(n). Solve g(j) = 0 for j.
-1, 3/4
Let d(m) be the first derivative of -5*m**3/3 - 95*m**2/2 - 170*m + 4. Let d(n) = 0. Calculate n.
-17, -2
Let p(f) = f**3 + 8*f**2 + 2*f. Let s(w) = 2*w**2 + w. Let j(v) = -p(v) + 5*s(v). Suppose j(i) = 0. Calculate i.
-1, 0, 3
Suppose -4*r + 4*c - 4 = 0, -2*r = c - 6*c - 4. Let n be (-12)/(-4)*r/(-21). Factor -27/7*b - n*b**5 - 6/7 - 18/7*b**4 - 48/7*b**2 - 6*b**3.
-3*(b + 1)**4*(b + 2)/7
Let s(v) be the first derivative of -v**4/28 - 2*v**3/21 + v**2/2 - 4*v/7 + 25. Suppose s(o) = 0. Calculate o.
-4, 1
Suppose -4*z + 3*f + 27 = -2, z = -f + 9. Let v be -5 + 4/z - -5. Determine g, given that -v*g**3 + 0 - g + 3/2*g**2 = 0.
0, 1, 2
Let d(h) be the third derivative of h**7/70 - 3*h**6/20 - 3*h**5/20 + 7*h**4 - 24*h**3 + 727*h**2. Factor d(a).
3*(a - 4)**2*(a - 1)*(a + 3)
Let y be 0*(16/(-616)*-11 - (-5)/7). Factor -1/7*c**4 + y*c**2 + 2/7*c**3 + 1/7 - 2/7*c.
-(c - 1)**3*(c + 1)/7
Let m(x) be the third derivative of x**7/70 + 9*x**6/40 + 11*x**5/10 - 16*x**3 + 35*x**2. Find n, given that m(n) = 0.
-4, -2, 1
Let c = 310/1173 + 27/391. Factor -1/6*q + c - 1/6*q**2.
-(q - 1)*(q + 2)/6
Let s be (((-5)/20)/1)/((-1)/(-4)). Let l be 2/12*(9 + s). Factor -1/3*o**3 - 1/3*o**2 + 4/3 + l*o.
-(o - 2)*(o + 1)*(o + 2)/3
Let n(m) = m**4 + 6*m**3 - 22*m + 15. Let j(h) = h**2 - 2*h + 1. Let q(p) = 24*j(p) - 3*n(p). Find c, given that q(c) = 0.
-7, -1, 1
Let m(b) be the third derivative of b**8/1848 + 2*b**7/1155 - b**6/110 - 4*b**5/165 + 5*b**4/132 + 2*b**3/11 - 64*b**2. Determine c, given that m(c) = 0.
-3, -1, 1, 2
Let z = -66 - -71. Solve z*k - 6*k - 5*k**2 + k = 0 for k.
0
Let w(q) = q**3 + 7*q**2 - 6*q + 21. Let f be w(-8). Suppose -4*o - o + 15 = 0. Let 2*n**2 + 21*n**5 - n**o + 7*n**3 - 19*n**f + 6*n**4 = 0. What is n?
-1, 0
Suppose 32*o - 27*o - k = 10, 0 = -3*k. Factor 0*q + 0 - 2/9*q**3 - 4/9*q**o.
-2*q**2*(q + 2)/9
Let a(w) = -3*w**2 - 12*w + 3. Let l(n) = -8*n**2 - 36*n + 10. Let u(r) = -17*a(r) + 6*l(r). What is b in u(b) = 0?
1, 3
Let g(o) be the third derivative of o**8/840 - o**6/300 + 466*o**2. Factor g(c).
2*c**3*(c - 1)*(c + 1)/5
Let i(r) = -r**2 + r + 1. Let h be (5/25)/((-2)/10). Let c(a) = -a**5 - a**4 + a**3 + a + 1. Let k(m) = h*i(m) + c(m). Determine b so that k(b) = 0.
-1, 0, 1
Let y(z) = -6*z**3 - 4*z**2 + 4*z + 2. Let t be y(3). Let l = t - -187. Suppose -4/9*n + 4/9*n**l + 0*n**2 - 2/9*n**4 + 2/9 = 0. What is n?
-1, 1
Determine c so that -6042*c**4 + 4 - 18*c + 15*c**2 + 5*c - 7*c**3 + 6043*c**4 = 0.
1, 4
Factor -12*z**2 + 13*z**4 - 13*z**4 + 3*z**5 + 81*z**3 - 69*z**2 - 27*z**4.
3*z**2*(z - 3)**3
Let u be 392/32*(-16 + (-354)/(-21)). Factor 27*a - 12 + 99/2*a**2 + u*a**3.
3*(a + 1)*(a + 4)*(7*a - 2)/2
Let t(c) be the second derivative of -4*c - 5*c**3 + 5/12*c**4 + 45/2*c**2 + 0. Factor t(g).
5*(g - 3)**2
Let d(w) = -w**2 + w. Let p(b) be the first derivative of 2*b**3 - 3*b**2/2 + 17. Let g(s) = 5*d(s) + p(s). Find m such that g(m) = 0.
-2, 0
Factor -6/13*h**2 - 28/13*h + 10/13.
-2*(h + 5)*(3*h - 1)/13
Let j(v) = -5*v**2 - 28*v + 73. Let q(k) = 10*k**2 + 55*k - 145. Let s(a) = 5*j(a) + 3*q(a). Factor s(l).
5*(l - 2)*(l + 7)
Suppose o + 14 = 4*o - 5*t, 3*t = -3. Suppose 0 = -3*f + 3*l + 9, 2*f - l - 7 = 2*l. Factor -1/6*q**4 - 11/3*q**f - 3/2 - 4*q - 4/3*q**o.
-(q + 1)**2*(q + 3)**2/6
Let t(i) = -60*i**2 - 5*i + 4. Let q be t(1). Let h = 63 + q. Factor -2 - 2*d - 1/2*d**h.
-(d + 2)**2/2
Let a be (-90)/(-40) - 1/4. Factor r**a + 2*r**2 + 6*r - 9*r**2 + 9*r**2.
3*r*(r + 2)
Factor -14 + 4/3*u**3 + 40/3*u + 86/3*u**2.
2*(u + 1)*(u + 21)*(2*u - 1)/3
Let c = 26 - 28. Let r be (0 - 0)/((-6)/(-3)) - c. Find k, given that -2/7*k - 4/7 + 4/7*k**r + 2/7*k**3 = 0.
-2, -1, 1
Let w(x) be the third derivative of x**8/16 + 10*x**7/7 + 7*x**6 - 72*x**5 - 810*x**4 - 864*x**3 - 142*x**2. Find n, given that w(n) = 0.
-6, -2/7, 4
Let u(c) be the third derivative of 2/255*c**5 + 0*c - 1/51*c**4 - 28*c**2 + 0 + 0*c**3 + 1/1020*c**6 - 1/1785*c**7. Solve u(o) = 0.
-2, 0, 1, 2
Suppose f = 13 - 9. Let z be (f/(-10))/((-9)/45). Find m such that 0*m**2 - 5*m**z - 4*m**2 - 4*m**4 + 5*m**2 + 8*m**3 = 0.
0, 1
Factor 1/8*c**2 - 45/8 - 11/2*c.
(c - 45)*(c + 1)/8
Determine j, given that 0 + 16/3*j**2 - 2/9*j**3 + 0*j = 0.
0, 24
Suppose 3*m - 22 = -2*i, -5*m - 1 + 6 = -3*i. Let f be 42/(-56) + 27/m + -2. Let 1/5 + x**f + 2*x**2 + 1/5*x**5 + 2*x**3 + x = 0. Calculate x.
-1
Suppose 42*c + 30*c - 9*c**2 - 93*c + 8 + 10 = 0. Calculate c.
-3, 2/3
Let l(g) = 16*g**2 - 91*g - 18. Let d(z) = -32*z**2 + 183*z + 34. Let w(p) = 3*d(p) + 5*l(p). Solve w(n) = 0 for n.
-1/8, 6
Factor 0 + 12*l**4 - 1/3*l + 10/3*l**2 - 11*l**3.
l*(3*l - 1)**2*(4*l - 1)/3
Suppose 5*k = 48 + 42. Let b = k - 12. Factor 4*v - 3*v**3 - b + 0*v + v - 2*v + 6*v**2.
-3*(v - 2)*(v - 1)*(v + 1)
Let s = 146 - 91. Factor 117*i**2 + 6 + 33*i**4 + s*i**3 - 160*i**3 + 7580*i - 7631*i.
3*(i - 1)**3*(11*i - 2)
Factor 29 - 19867*c**2 + 19882*c**2 - 48*c - 93 - c**3.
-(c - 8)**2*(c + 1)
Let l(i) be the third derivative of i**6/120 - i**5/4 + 21*i**4/8 - 49*i**3/6 + 18*i**2. Solve l(j) = 0.
1, 7
Let g = 115 + -113. Let y be 1 + (-1 + 3)*4. Factor -6*p + g*p + 11*p**2 + y*p**2.
4*p*(5*p - 1)
Suppose 0 = -4*y + 4*a + 56, -2*y + 6*a = 2*a - 20. Let l = y + -14. Solve 8*v - 30*v**l + 72*v**3 - 2*v - 15*v**4 + 6*v**3 - 39*v**2 = 0.
0, 1/3, 2/5, 1
Let c be 2 + 10 + 2842/(-238). Let d(b) be the second derivative of 0 - 1/102*b**4 + 3*b - 2/51*b**3 - c*b**2. Let d(z) = 0. Calculate z.
-1
Determine m so that -1/2*m**3 + 3/2*m**2 + 0 + 0*m = 0.
0, 3
Let x be (2 - 51/21)*(-546)/117. Let v(o) be the first derivative of -4 + 1/10*o**4 - 2/5*o**3 + 0*o + 2/5*o**x. Factor v(y).
2*y*(y - 2)*(y - 1)/5
Suppose -17*l + 44*l - 81 = 0. Let u(a) be the second derivative of 1/40*a**5 - 1/6*a**l - 4*a + 0*a**2 - 1/24*a**4 + 0. Factor u(c).
c*(c - 2)*(c + 1)/2
Let w(r) be the third derivative of -r**7/630 - r**6/90 + r**4/8 - 12*r**2. Let l(c) be the second derivative of w(c). Factor l(i).
-4*i*(i + 2)
Let y(x) = x**4 + 73*x**3 + 168*x**2 - 139*x - 5. Let d(o) = o**4 + 110*o**3 + 252*o**2 - 208*o - 8. Let i(v) = 5*d(v) - 8*y(v). Factor i(m).
-m*(m + 6)**2*(3*m - 2)
Determine a, given that 0 - 18/7*a**2 + 51/7*a**3 + 0*a + 81/7*a**4 + 12/7*a**5 = 0.
-6, -1, 0, 1/4
Let z be 4/6 + -5*39/(-45). Solve -10*f**2 + 10*f**4 - 10*f**3 + 14*f**3 - 4*f**3 - 5*f + z*f**5 = 0.
-1, 0, 1
Let z(t) be the third derivative of -5*t**8/336 + t**7/21 + 5*t**6/24 - 5*t**5/6 - 5*t**4/6 + 20*t**3/3 - 286*t**2. Suppose z(h) = 0. Calculate h.
-2, -1, 1, 2
Let f(c) be the third derivative of -c**5/270 - 5*c**4/54 + 13*c**3/9 + 301*c**2. Determine v, given that f(v) = 0.
-13, 3
Let c(d) be the first derivative of -5*d**6/6 - 7*d**5 + 75*d**4/2 + 610*d**3/3 + 655*d**2/2 + 225*d - 30. Suppose c(b) = 0. What is b?
-9, -1, 5
Let n(u) = -112*u**3 + 68*u**2 + 390*u - 360. Let r(a) = -75*a**3 + 45*a**2 + 260*a - 240. Let j(o) = -5*n(o) + 7*r(o). Factor j(w).
5*(w - 1)*(w + 2)*(7*w - 12)
Let v be -1*1 + (-16)/16. Let r be (11 + v)*1/12. Factor 1/2 + 0*f**2 + r*f - 1/4*f**3.
-(f - 2)*(f + 1)**2/4
Let o = 40 - -12. Let n = o + -49. Let -27/4*i**n - 3/4 - 9/4*i**2 + 15/4*i = 0. Calculate i.
-1, 1/3
Let v be 6*((-2)/2)/(-3). Let u = -11/28 - -199/364. Factor 0 - 2/13*s**3 - u*s + 4/13*s**v.
-2*s