Let j(n) = 7*n**3 + 60*n**2 + 65*n + 12. Let k(w) = -6*b(w) - 39*j(w). Determine o so that k(o) = 0.
-7, -1, -2/7
Let z = -461 - -463. Let x(i) be the third derivative of -1/72*i**8 + 0*i**5 + z*i**2 + 0*i + 0 + 0*i**4 + 1/90*i**6 + 1/63*i**7 + 0*i**3. Factor x(n).
-2*n**3*(n - 1)*(7*n + 2)/3
Let f = -15257 - -106807/7. Let -f*b**3 + 8/7*b + 2/7*b**2 - 2/7 = 0. What is b?
-1, 1/4, 1
Factor -128*j**3 - 5*j**4 - 4142*j - 478*j - 2630*j**2 - 2205 - 92*j**3.
-5*(j + 1)**2*(j + 21)**2
Let o(h) be the second derivative of h**7/840 + h**6/240 - h**4/48 - h**3/24 + 13*h**2/2 - 28*h. Let c(i) be the first derivative of o(i). Factor c(a).
(a - 1)*(a + 1)**3/4
Suppose -6*r + 3 = -7*r. Let u be -12*((-39)/12 - r). Factor 3*i**5 + 6*i**2 - 2*i**4 - i**5 - 2*i**u - 4*i**2.
2*i**2*(i - 1)**2*(i + 1)
Let t(k) be the second derivative of -2*k**6/15 + 28*k**5/25 - 16*k**4/5 + 32*k**3/15 + 32*k**2/5 - 86*k. What is z in t(z) = 0?
-2/5, 2
Let b(c) be the third derivative of -c**9/3024 + c**7/840 + 11*c**3/6 - 7*c**2. Let v(a) be the first derivative of b(a). Factor v(f).
-f**3*(f - 1)*(f + 1)
Let g(l) be the third derivative of 0*l + 23/135*l**5 + 25/27*l**3 + 1/945*l**7 + 25*l**2 + 5/9*l**4 + 1/45*l**6 + 0. Find z, given that g(z) = 0.
-5, -1
Let l(c) = 52*c**3 + 154*c**2 - 118*c. Let n(b) = 7*b**3 + 22*b**2 - 17*b. Let a(z) = -6*l(z) + 44*n(z). Find s such that a(s) = 0.
0, 1, 10
Let q = -409942353/886288 - -5/68176. Let m = q - -463. Suppose 2/13*g**4 + m*g**3 - 2/13*g**5 - 4/13*g + 0 - 2/13*g**2 = 0. Calculate g.
-1, 0, 1, 2
Let h(a) be the first derivative of a**5/25 + 61*a**4/20 - 63*a**3/5 + 191*a**2/10 - 64*a/5 + 22. What is o in h(o) = 0?
-64, 1
Let m(q) be the second derivative of 3/4*q**3 - 3/28*q**7 + 2/5*q**6 + 3/2*q**2 + 0 + 0*q**5 - 5/4*q**4 + 9*q. Determine a, given that m(a) = 0.
-1, -1/3, 1, 2
Suppose 192*r - 172 + 98*r**3 + 3*r**4 - 110*r**3 + 8*r**2 - 20 - 44*r**2 = 0. Calculate r.
-4, 2, 4
Let i = -3/737 - 9536/11055. Let z = -4/15 - i. Factor 6/5*u**2 - z*u**3 - 3/5*u**4 + 0*u + 0.
-3*u**2*(u - 1)*(u + 2)/5
Let p(w) = w + 12. Let n be p(-8). Suppose 6 = n*u - 2*u. Factor 2/9 - 4/9*m**u + 0*m**2 + 4/9*m - 2/9*m**4.
-2*(m - 1)*(m + 1)**3/9
Let m(i) = -10*i**3 + 375*i**2 - 2700*i + 4335. Let b(f) = 3*f**3 - 94*f**2 + 675*f - 1084. Let g(c) = -15*b(c) - 4*m(c). Find u, given that g(u) = 0.
-24, 3
Factor 1 + 23 + 25*u**2 - 52*u - 17*u**2.
4*(u - 6)*(2*u - 1)
Let u(y) = -5*y**3 - 30*y**2 - 30*y - 20. Suppose -a - 3*a - 16 = 0. Let t(m) = -5*m**3 - 29*m**2 - 31*m - 19. Let k(z) = a*u(z) + 5*t(z). Factor k(n).
-5*(n + 1)**2*(n + 3)
What is p in 0*p + 9*p**3 + 2*p - 5*p**4 - 7*p**2 + 83 - 161 + p**5 + 78 = 0?
0, 1, 2
Factor -57/4*j - 7/2 - 9/2*j**4 - 1/4*j**5 - 31/2*j**3 - 22*j**2.
-(j + 1)**4*(j + 14)/4
Suppose -59 - 145 = -4*l. Let o = -51 + l. Solve -2/3*y**2 + 4/3*y + o = 0.
0, 2
Let f(n) be the second derivative of -n**5/50 - n**4/15 + 4*n**3/15 + 8*n**2/5 + 54*n. Factor f(a).
-2*(a - 2)*(a + 2)**2/5
Let z(q) be the first derivative of 0*q**2 + 1/4*q**4 + q + 2 + q**3. Let x(d) be the first derivative of z(d). Factor x(p).
3*p*(p + 2)
Find g, given that 76 - 120*g - 2 - 26 - 6*g**3 + 51*g**2 = 0.
1/2, 4
Let r = -157769/3 - -52595. Factor 8/3*k - r - 1/3*k**2.
-(k - 4)**2/3
Let p be -4*2/352*28. Let f = p - -43/33. Factor f - 13/3*s + 28/3*s**3 + 13/3*s**2.
(s + 1)*(4*s - 1)*(7*s - 2)/3
Let j = 15 - 19. Let k be -3 - j/((-16)/(-20)). Factor -3*s**k - 1 - 5 + 6.
-3*s**2
Let l(w) be the third derivative of -21*w**5/100 - w**4/5 + w**3/2 + 3*w**2 + w. Factor l(k).
-3*(3*k - 1)*(7*k + 5)/5
Let k = -133 - -799/6. Let s(p) be the first derivative of 0*p + 0*p**3 - 2 - 1/12*p**4 + k*p**2. Find f such that s(f) = 0.
-1, 0, 1
Let o be (1 + -4 - -5)*111/333. Find g such that -14/3*g**3 + 16/3*g + 10/3*g**4 - o*g**2 - 8/3 - 2/3*g**5 = 0.
-1, 1, 2
Let v(w) be the first derivative of -w**4 - 4*w**3/9 + 8*w**2 + 16*w/3 - 680. Determine d so that v(d) = 0.
-2, -1/3, 2
Suppose -4*h + x + 21 = 0, 13 = 4*h - 4*x - 23. Suppose 0*u - c + 13 = h*u, -31 = -4*u + 5*c. Determine s so that u - s**3 + 7 - 11 = 0.
0
Factor 1/2*t**5 - 1/2*t**3 + 0 - 2*t**2 + 2*t**4 + 0*t.
t**2*(t - 1)*(t + 1)*(t + 4)/2
Let f(a) be the first derivative of -2*a**3/9 + 370*a**2/3 - 68450*a/3 + 271. Suppose f(u) = 0. What is u?
185
Let v(g) be the second derivative of -g**7/2520 + g**6/120 - 3*g**5/40 + g**4 - 15*g. Let s(t) be the third derivative of v(t). Factor s(x).
-(x - 3)**2
Suppose -2*f + 4*f + 19 = 5*d, -19 = -3*f - 2*d. Let t = -70 + 72. Factor -l**4 + 2*l**4 + l**4 + t*l**f.
2*l**3*(l + 1)
What is u in -18 - 4*u**3 + 35 + 9*u**2 - 29 + u**3 = 0?
-1, 2
Let b be (16/(-18))/((-62)/279). Let a(p) be the second derivative of 1/18*p**b - 10*p + 0 - 1/3*p**2 + 0*p**3. Factor a(d).
2*(d - 1)*(d + 1)/3
Let l be (-4 + 5)*(10 + 0). Factor -5*d + 3*d + 7*d - l + 5*d**2.
5*(d - 1)*(d + 2)
Factor 56*w**2 + 0*w - 51*w**2 - 5*w.
5*w*(w - 1)
Determine b, given that 5*b - 23*b - 2*b**2 + 2*b**2 + 44 - 2*b**2 = 0.
-11, 2
Let u be (-361)/(-7581)*(4 + -2 - -12). Let z be (-3)/(-1*(2 - 1)). Factor -u*o**4 - 13/6*o**2 - 1/6 + o + 2*o**z.
-(o - 1)**2*(2*o - 1)**2/6
Let u(j) be the first derivative of -1/4*j**2 - 6/5*j**5 + 25/12*j**3 - 9 - 1/4*j + 1/8*j**4. What is q in u(q) = 0?
-1, -1/6, 1/4, 1
Let b(t) = -6*t**3 + 21*t**2 + 24*t - 36. Let g(w) = -7*w**3 + 23*w**2 + 24*w - 36. Let c(l) = 4*b(l) - 3*g(l). Factor c(q).
-3*(q - 6)*(q - 1)*(q + 2)
Let r(c) be the second derivative of -c**7/210 - c**6/45 - c**5/30 + 11*c**3/6 + 28*c. Let p(k) be the second derivative of r(k). Factor p(y).
-4*y*(y + 1)**2
Let i(z) be the third derivative of z**8/504 + z**7/21 + 3*z**6/20 + 13*z**5/90 + 3*z**2 - 72. Factor i(f).
2*f**2*(f + 1)**2*(f + 13)/3
Factor -2/7*w**3 + 4 + 24/7*w**2 + 54/7*w.
-2*(w - 14)*(w + 1)**2/7
Let b(h) = -12*h**3 + 55*h**2 + 182*h + 146. Let y(f) = 5*f**3 - 27*f**2 - 90*f - 74. Let s(v) = 3*b(v) + 7*y(v). Let s(c) = 0. Calculate c.
-20, -2
Let a(y) = 4*y**3 - 4*y**2 - 8*y - 5. Let g(q) = -1. Let r be ((-8)/(-6) + -3)*24/(-8). Let w(f) = r*g(f) - a(f). Factor w(s).
-4*s*(s - 2)*(s + 1)
Let v(t) be the first derivative of -3*t**4/4 + 3*t**3 + 27*t**2/2 + 15*t + 64. What is w in v(w) = 0?
-1, 5
Let v(q) be the second derivative of -2*q**6/15 - q**5/5 + 4*q**4/3 + 8*q**3/3 - 479*q. Factor v(z).
-4*z*(z - 2)*(z + 1)*(z + 2)
Let a(w) = 3*w**3 - 3*w**2 - 6*w. Let m(j) = 3*j - 1. Let d be m(-1). Let f(k) = 2*k**3 - 3*k**2 - 5*k. Let u(h) = d*f(h) + 3*a(h). Solve u(b) = 0.
-2, -1, 0
Let u(a) = a**3 - 10*a**2 + a - 7. Let g be u(10). Factor -3*v**g - 3*v**3 + 3*v**3 - 3*v**2 + 9*v**2.
-3*v**2*(v - 2)
Factor 0 + 3/5*l**3 - 3/5*l + 1/5*l**4 - 1/5*l**2.
l*(l - 1)*(l + 1)*(l + 3)/5
Let j(x) = 12*x**2 + 11*x + 12. Let n be j(-1). Suppose -12*u = -n*u. Factor -2/3*l**4 + u*l - 5/6*l**3 - 1/6*l**5 + 0 - 1/3*l**2.
-l**2*(l + 1)**2*(l + 2)/6
Let r(v) be the first derivative of 3*v**6/5 - 14*v**5/25 - v**4/5 - 19. Factor r(d).
2*d**3*(d - 1)*(9*d + 2)/5
Suppose l + 3*x = -1, 0 = -4*l + 2*x - x + 9. Suppose l*u + 3 = 3*u. Factor -2*v**u - 2 + 3*v**3 + 2*v + 10*v**2 + 5*v**3.
2*(v + 1)**2*(3*v - 1)
Determine t so that -36/5 + 34/5*t + 2/5*t**2 = 0.
-18, 1
Let f be ((-57)/(-30) - 1)*-11*12/(-198). Factor 48/5*h - 12 - 3/5*h**2 - f*h**3.
-3*(h - 2)**2*(h + 5)/5
Let q(r) = -4*r - 14. Let y be q(-4). Suppose u - 2 = -0. Factor u*m + 13 - 3*m + m**3 + 0*m + m**y - 14.
(m - 1)*(m + 1)**2
Suppose -18*a = -10*a - 168. Let k be (-2)/6 - (-7)/a. Determine v so that 6/7*v**3 - 4/7*v**2 + k + 0*v - 2/7*v**4 = 0.
0, 1, 2
Let w = 392 - 389. Factor -24/13*t - 4/13*t**2 + 8/13*t**w + 18/13 + 2/13*t**4.
2*(t - 1)**2*(t + 3)**2/13
Factor -2924*q**3 + 2909*q**3 - 42*q**2 + 4*q + 5*q.
-3*q*(q + 3)*(5*q - 1)
Let l(y) be the first derivative of 0*y + 6/5*y**2 + 33/20*y**4 - 24/5*y**3 - 11. Factor l(z).
3*z*(z - 2)*(11*z - 2)/5
Let y(u) be the second derivative of u**5/4 - 35*u**3/6 - 15*u**2 - 87*u. Factor y(a).
5*(a - 3)*(a + 1)*(a + 2)
Let u be ((-4)/5)/((-2)/30). Suppose -4*g + u = -4. Factor 3*q + 2*q**2 - g - 5*q + 0*q.
2*(q - 2)*(q + 1)
Suppose -20 = -2*a - 4*o, 3 = -3*a - 2*o + 7*o. Solve 5*x**2 - 13*x**2 - 7 + a*x**2 - 1 + 12*x = 0.
1, 2
Let d(g) = 7*g**3 - 6*g + 4. Let r(c) = -3*c**3 + 3*c - 2. Let u(k) = -2*d(k) - 5*r(k). Find