). Determine h so that 2/5*h**3 - 8/5*h**g - 8/5*h + 0 + 2/5*h**4 = 0.
-2, -1, 0, 2
Let a(j) = j. Let p(q) = -16*q**2 + 22*q + 4. Let i(n) = 10*a(n) - p(n). Factor i(c).
4*(c - 1)*(4*c + 1)
Let r = 78196/39 + -2005. Let c(h) be the third derivative of -2/195*h**5 + 1/780*h**6 + 1/1365*h**7 + 0*h**3 - 12*h**2 + 0*h + 0 - r*h**4. Factor c(v).
2*v*(v - 2)*(v + 1)*(v + 2)/13
Let f(w) be the second derivative of -w**7/126 - w**6/45 + w**5/10 + w**4/9 - 13*w**3/18 + w**2 - 288*w. Determine l so that f(l) = 0.
-3, -2, 1
Let m(y) be the first derivative of -5*y**4/4 + 5*y**3 + 45*y**2/2 + 25*y - 160. Find q such that m(q) = 0.
-1, 5
Find r, given that -33*r**2 - 8*r**2 + 44*r**2 - 6*r**2 - 195*r = 0.
-65, 0
Suppose 18/7*k**3 - 4/7*k + 20/7*k**4 - 6/7*k**2 + 0 = 0. What is k?
-1, -2/5, 0, 1/2
Suppose -4*f - 17 = 5*r, 2*r = 5*f + 1 - 21. Let w(o) be the third derivative of -1/6*o**4 + 0*o + 1/60*o**5 + 0 + f*o**2 + 2/3*o**3. Factor w(l).
(l - 2)**2
Factor -8/7*z**2 + 2/7*z**5 + 16/7*z**3 - 10/7*z**4 + 0*z + 0.
2*z**2*(z - 2)**2*(z - 1)/7
Let a(f) be the third derivative of f**5/45 + 22*f**4/9 + 968*f**3/9 + 73*f**2. Factor a(d).
4*(d + 22)**2/3
Let -80 - 10*a + 20*a**2 + 5/2*a**3 = 0. Calculate a.
-8, -2, 2
Let g = 10099 - 10097. Find n, given that 8*n + 4/5*n**g + 0 = 0.
-10, 0
Let o(i) be the third derivative of i**9/6048 - i**7/840 + i**5/240 - 41*i**3/6 - i**2. Let x(u) be the first derivative of o(u). Find k, given that x(k) = 0.
-1, 0, 1
Let u(l) = -4*l**3 - 44*l**2 + 52*l + 80. Let v(w) = -w**2 - 2. Let d(z) = u(z) - 4*v(z). Suppose d(p) = 0. What is p?
-11, -1, 2
Let v = -3077 - -3079. Let 3/4*l**4 + 3 - 9*l - 9/2*l**3 + 39/4*l**v = 0. What is l?
1, 2
Suppose 0 = 5*s - 17 - 73. Suppose -2 + 3*i - 8*i**4 + 9*i**5 - 12*i**3 - s*i**2 + 20*i**4 + 8 = 0. What is i?
-1, 2/3, 1
Determine x so that 0*x + 3/2*x**3 + 162 - 27/2*x**2 = 0.
-3, 6
Factor 1/5*a**2 - 13/5*a + 8.
(a - 8)*(a - 5)/5
Solve 4225/3 - 130/3*c + 1/3*c**2 = 0 for c.
65
Suppose 79 - 70 = 50*i - 191. Factor -4/5*a**3 + 2/5*a**i - 8/5*a**2 + 0 + 16/5*a.
2*a*(a - 2)**2*(a + 2)/5
Suppose 3*w - 113 = 10. Factor -10*u**4 - 4*u**4 + 36*u**5 + 4*u**4 - w*u**5.
-5*u**4*(u + 2)
Let c(k) = -7*k + 172. Let i be c(24). Let h(f) be the second derivative of -1/18*f**2 + f - 1/54*f**3 + 0 + 1/180*f**5 + 1/108*f**i. Factor h(s).
(s - 1)*(s + 1)**2/9
Let o(u) be the first derivative of -6 - 10*u**2 + 6*u**3 - 7/4*u**4 + 1/5*u**5 + 8*u. Let o(h) = 0. Calculate h.
1, 2
Let w(a) be the first derivative of -3*a**4/20 - 16*a**3/5 - 9*a**2/2 + 19. Let w(m) = 0. What is m?
-15, -1, 0
Let v(u) = -10*u**3 - 10*u**2 + 65*u - 45. Let d(j) = j**4 + 9*j**3 + 10*j**2 - 66*j + 46. Let w(a) = -5*d(a) - 6*v(a). Factor w(p).
-5*(p - 2)**2*(p - 1)*(p + 2)
Let t(g) be the third derivative of -g**6/1500 + g**5/750 + 13*g**4/150 + 8*g**3/25 + 6*g**2 - 21*g. Factor t(d).
-2*(d - 6)*(d + 1)*(d + 4)/25
Suppose 7*c = -38 + 108. Let q be 2*(-3)/(-30)*25/c. What is d in 1 + q*d - 1/2*d**3 - d**2 = 0?
-2, -1, 1
Solve 0*m - 26*m**3 + 1/2*m**5 + 0 - 18*m**2 - 15/2*m**4 = 0 for m.
-2, -1, 0, 18
Factor 8*g**5 - 3*g**5 + g**4 + g**5 + 6*g**4 + 2*g**4 + 3*g**3.
3*g**3*(g + 1)*(2*g + 1)
Let c(x) be the second derivative of 3*x**5/5 + 5*x**4/4 + x**3/2 - 6*x + 2. Factor c(g).
3*g*(g + 1)*(4*g + 1)
Let x(v) = -v**2 - 4*v + 14. Let j be x(-6). Let g be j*(-4 - -2) + 12. Let -4*s - 14*s**2 + 8 + 6*s**2 - 4*s**3 + g*s = 0. Calculate s.
-2, -1, 1
Let a(j) = -j**3 + 6*j**2 + j - 3. Let v be a(6). Find n, given that 10*n + 14*n**2 + v*n**3 - 19*n**2 - 8*n**3 = 0.
-2, 0, 1
Let o be ((-18)/(-10)*-1)/((-16)/80). Let y(m) be the second derivative of 9/2*m**2 + m**3 + 0 + 1/12*m**4 + o*m. Suppose y(a) = 0. Calculate a.
-3
Let c(k) be the first derivative of -k**6/6 + 3*k**5/5 + k**4/2 - 2*k**3 - k**2/2 + 3*k + 82. Factor c(n).
-(n - 3)*(n - 1)**2*(n + 1)**2
Let f(u) be the first derivative of -u**6/60 + u**4/12 + u**2 - 8. Let g(w) be the second derivative of f(w). Let g(z) = 0. Calculate z.
-1, 0, 1
Let u = 116 + -119. Let v be (u/(-2))/(0 + (-12)/(-16)). Determine j so that 1/5*j + 4/5*j**v + 3/5*j**3 + 0 = 0.
-1, -1/3, 0
Let h(d) be the first derivative of 2/3*d**3 + 4/3*d**2 + 1 + 8/9*d. Determine j, given that h(j) = 0.
-2/3
Let a(l) be the third derivative of l**6/300 + l**5/10 + 9*l**4/20 + 13*l**3/15 - 2*l**2 - 5*l. Suppose a(t) = 0. What is t?
-13, -1
Suppose -5060 + 2165 - 4818 = -857*n. Determine o, given that -13365/8*o**4 + n*o**2 + 6 + 702*o**3 + 2187/2*o**5 - 48*o = 0.
-1/4, 2/9, 2/3
Let q(z) = -27*z**5 + 4*z**4 + 16*z**3 + 2*z**2 - 5*z - 2. Let j(g) = -33*g**5 + 5*g**4 + 17*g**3 + g**2 - 4*g - 1. Let i(f) = 4*j(f) - 5*q(f). Factor i(l).
3*(l - 2)*(l - 1)*(l + 1)**3
Let f(k) = k + 11. Let r be f(-11). Factor -c**5 + 7*c**4 - 12*c**4 + r*c**3 + 5*c**2 - 4*c**5 + 5*c**3.
-5*c**2*(c - 1)*(c + 1)**2
Let g be (-10)/(-4) + 1 + (130 - 123). Factor g*m**2 - 12*m - 3/2*m**3 - 24.
-3*(m - 4)**2*(m + 1)/2
Let x(k) be the second derivative of -k**9/3024 - k**8/840 + k**7/840 + k**6/180 + 23*k**3/6 - 17*k. Let p(w) be the second derivative of x(w). Factor p(a).
-a**2*(a - 1)*(a + 1)*(a + 2)
Let r = 56 - 54. Let w = -252 - -2272/9. What is v in 0*v**3 - 2/9*v + w*v**4 + 2/9*v**5 - 4/9*v**r + 0 = 0?
-1, 0, 1
Let y(x) = x**3 + 15*x**2 - 65*x - 973. Let w be y(-15). Factor -2*v**3 + 0 - 2/3*v**5 + 2/3*v**2 + w*v**4 + 0*v.
-2*v**2*(v - 1)**3/3
Let g(k) be the first derivative of k**6/50 + k**5/25 - k**4/12 - k**3/15 - 15*k + 17. Let p(n) be the first derivative of g(n). Let p(c) = 0. What is c?
-2, -1/3, 0, 1
Factor 162*p - 6*p**3 - 729/2 - 1/2*p**4 + 9*p**2.
-(p - 3)**2*(p + 9)**2/2
Let c(x) = 3*x**3 + 9 - 7*x**2 - x**2 + 3*x + 5*x**2. Let i(o) = -16*o**3 + 14*o**2 - 15*o - 45. Let y(w) = 33*c(w) + 6*i(w). Determine m so that y(m) = 0.
-1, 3
Let r(b) be the first derivative of 7*b**6/30 + b**5/3 - b**4/3 + 9*b**2/2 + 7. Let i(k) be the second derivative of r(k). Factor i(m).
4*m*(m + 1)*(7*m - 2)
Let g(d) be the second derivative of d**4/30 - 3*d**3/5 + 4*d**2 + 219*d. Solve g(s) = 0.
4, 5
Let a(x) be the third derivative of 0 + 0*x - 13*x**2 - 2/3*x**3 + 2/15*x**5 + 1/6*x**4. Suppose a(r) = 0. Calculate r.
-1, 1/2
Let d = -5726 + 5728. Factor 10/9*m**3 - 4/9*m**d + 4/9 - 10/9*m.
2*(m - 1)*(m + 1)*(5*m - 2)/9
Let r(n) = 4*n - 3. Let v be r(-5). Let y = v - -24. Factor -2*m + 9/4*m**3 + y - 3/4*m**2.
(m + 1)*(3*m - 2)**2/4
Factor -1/10*i**2 + 0 - 23/5*i.
-i*(i + 46)/10
Let s be 6 + 14695/(-2100) - -1. Let z(t) be the third derivative of 1/12*t**3 - 1/60*t**5 + 0*t**6 + s*t**7 + 0*t + 6*t**2 + 0*t**4 + 0. Factor z(j).
(j - 1)**2*(j + 1)**2/2
Let j(k) be the first derivative of 0*k + 7 - 10*k**2 + 5/3*k**3. Factor j(x).
5*x*(x - 4)
Suppose -6*f + 127 + 581 = 0. Let b = -469/4 + f. Factor -18*m**2 - 24*m - 6*m**3 - b*m**4 - 12.
-3*(m + 2)**4/4
Find u, given that 57/5*u**2 - 51/5*u - 6/5 = 0.
-2/19, 1
Let r(x) be the second derivative of 0 - 3/140*x**5 + 0*x**2 + 0*x**3 - 1/14*x**4 - 9*x. Factor r(w).
-3*w**2*(w + 2)/7
Let c = 352469/515940 - -3/17198. Let z = 14/15 - c. Find p, given that -z*p**2 - 4 - 2*p = 0.
-4
Suppose -12 = 4*t + 4*h - 44, -3*t - 5*h = -34. Let r(n) be the first derivative of 6 + 15/14*n**2 - 16/7*n**t + 27/28*n**4 + 6/7*n. Factor r(x).
3*(x - 1)**2*(9*x + 2)/7
Suppose 4*q - 8 = -4*c, -5*c - 16 + 20 = 2*q. Factor 1/7*f**4 - 2/7*f**5 + 0*f + c*f**2 + 1/7*f**3 + 0.
-f**3*(f - 1)*(2*f + 1)/7
Let n(i) be the second derivative of -20/3*i**3 - 3*i + 0 + 40*i**2 + 5/12*i**4. Let n(o) = 0. Calculate o.
4
Suppose 0*l - 1/9 + 4/9*l**5 + 5/3*l**4 + 10/9*l**2 + 20/9*l**3 = 0. Calculate l.
-1, 1/4
Let l(g) = 4*g**2 + 4*g - 4. Let k(m) = 7*m - 5. Let o(y) = -y**2 - 6*y + 5. Let z(n) = -2*k(n) - 3*o(n). Let h(i) = 6*l(i) - 4*z(i). Factor h(x).
4*(x + 1)*(3*x - 1)
Solve 0*q + 242/17*q**2 + 0 - 2/17*q**5 - 42/17*q**4 - 198/17*q**3 = 0.
-11, 0, 1
Let x(a) be the first derivative of a**4/3 - 12*a**3 + 162*a**2 - 4*a + 22. Let i(o) be the first derivative of x(o). Factor i(y).
4*(y - 9)**2
Let z = 12055 - 36163/3. Solve -2/3*g**4 + 4/3 - z*g**2 - 7/3*g - 1/3*g**5 + 8/3*g**3 = 0 for g.
-4, -1, 1
Let y(c) = 2*c - 3. Let d be y(4). Suppose 0 = -b + d*q + 28, -3 = b + 3*b + 3*q. Factor g**3 - 3*g**b + g**3 - 4*g**2 + 5*g**2.
-g**2*(g - 1)
Let o = 37/45 - -7