7*q**4 + 0 - 1/90*q**5 - 1/27*q**3. Find k, given that g(k) = 0.
-1, 0
Let k = -1523 + 1527. Let x(a) be the first derivative of 8*a**4 + 0*a**2 + 16/3*a**3 + 14 + 0*a + k*a**5 + 2/3*a**6. Solve x(g) = 0 for g.
-2, -1, 0
Let n(w) be the second derivative of -w**6/40 - 27*w**5/80 - 3*w**4/2 - 2*w**3 - 2*w + 25. Suppose n(v) = 0. Calculate v.
-4, -1, 0
Suppose -85 - 5 = -5*z. Let a be (8/42)/(z/63). Let -a*f + 2/9*f**2 + 0 = 0. Calculate f.
0, 3
Let t(b) be the second derivative of -2*b**6/15 - 14*b**5/5 + 68*b**4/3 - 48*b**3 + 322*b. Factor t(k).
-4*k*(k - 2)**2*(k + 18)
Let r(m) be the first derivative of 10 + 0*m**3 - 2/5*m**5 + 1/3*m**4 + 2/15*m**6 + 0*m**2 + 10*m. Let h(n) be the first derivative of r(n). Factor h(d).
4*d**2*(d - 1)**2
Let w = -4085 + 4087. Factor -2/9*p**w - 2/9*p + 4/9.
-2*(p - 1)*(p + 2)/9
Let z(v) be the third derivative of v**8/672 + 2*v**7/105 + 5*v**6/48 + 19*v**5/60 + 7*v**4/12 + 2*v**3/3 + 3*v**2 + 41. Factor z(g).
(g + 1)**2*(g + 2)**3/2
Suppose 0*a - 2/3*a**4 + 2/9 + 16/9*a**3 - 4/3*a**2 = 0. Calculate a.
-1/3, 1
Factor -22*x**2 + 3*x**4 - 4*x**4 - 42*x**3 - 3*x**4 - 71*x**2 - 48*x + 7*x**4.
3*x*(x - 16)*(x + 1)**2
Let z(w) = 4*w**4 - 68*w**3 - 64*w**2. Let a(k) = -2*k**4 + 45*k**3 + 43*k**2. Let n(h) = 8*a(h) + 5*z(h). Factor n(b).
4*b**2*(b + 2)*(b + 3)
Suppose 0 = g - 4*g - 69. Let o = g - -49/2. Let 3/4*v**3 - o + 0*v**2 - 9/4*v = 0. What is v?
-1, 2
Factor -17/4*u**2 - u**3 - 4*u - 3/4.
-(u + 1)*(u + 3)*(4*u + 1)/4
Let m(g) be the third derivative of 0 + 1/1680*g**8 + 0*g**4 - 1/200*g**6 + 0*g**7 + 0*g - 1/150*g**5 + 0*g**3 + 9*g**2. Factor m(l).
l**2*(l - 2)*(l + 1)**2/5
Let t be (-20)/2*7/((-70)/4). Let -111*v**2 + 14*v**3 - t - 31*v**3 + 33*v**2 - 22*v**4 - 53*v**3 - 34*v = 0. Calculate v.
-1, -2/11
Let n be (5 - 2 - -2)*(15 - 2190/150). Factor -15 - 5/2*w**n - 25/2*w.
-5*(w + 2)*(w + 3)/2
Let o(k) be the first derivative of -k**3/8 - 371*k**2/16 + 31*k/2 - 94. Factor o(s).
-(s + 124)*(3*s - 1)/8
Solve 0 - 2*n**4 - 6/7*n**2 + 3/7*n**5 + 17/7*n**3 + 0*n = 0 for n.
0, 2/3, 1, 3
Let m(w) = 3*w**5 - 28*w**4 - 288*w**3 - 1024*w**2 - 1276*w + 4. Let x(l) = -l**5 - l**4 - l - 1. Let q(s) = m(s) + 4*x(s). Factor q(j).
-j*(j + 4)**3*(j + 20)
Suppose 8*g + 139*g - 735 = 0. Let x(k) be the first derivative of 0*k**3 + 0*k**g + k**4 - k**2 - 5 + 0*k - 1/3*k**6. Let x(f) = 0. Calculate f.
-1, 0, 1
Suppose -16 = -2*r - 3*n + 28, 0 = -r + 4*n + 22. Suppose -16*d = -10 - r. Determine p so that 8/13*p**3 - 12/13*p**d - 2/13*p**4 + 8/13*p - 2/13 = 0.
1
Let l = -111 + 110. Let t be ((-42)/(-24) + l)/((-3)/(-1)). Suppose 1/2*s**2 - 1/4*s**3 - 1/2 + t*s = 0. Calculate s.
-1, 1, 2
Let r(h) = h. Let n(g) = g**3 + 3*g**2 + 4*g + 1. Let l = 30 - 33. Let s(u) = l*r(u) + 3*n(u). Let s(c) = 0. Calculate c.
-1
Let g(k) be the third derivative of k**8/2240 + k**7/210 + k**6/60 + 2*k**5/15 - 4*k**2. Let b(f) be the third derivative of g(f). What is q in b(q) = 0?
-2, -2/3
Let w be 2*(-1 + 2)/2. Suppose -h - 13 = -4*i, -w = -3*i - 2*h + 17. Determine q so that -q**2 + 4*q**4 + i*q**2 - 7*q**2 - 8*q**2 + 8*q = 0.
-2, 0, 1
Let q(f) = f - 7. Let y be q(25). Factor -y*g**2 + 6*g**2 + 6*g**4 - 3 - 9*g**3 + 6*g**2 + 9*g + 3*g**2.
3*(g - 1)**2*(g + 1)*(2*g - 1)
Let a(l) be the third derivative of -5/8*l**4 - 5/1008*l**8 - 7/36*l**6 + 0 + 4/9*l**5 + 1/21*l**7 - 15*l**2 + 5/9*l**3 + 0*l. Let a(o) = 0. Calculate o.
1, 2
Let q(w) = w**3 - 7*w**2 + 5*w - 33. Let z be q(7). Suppose 0 = 2*c + 4*n + 16, 3*c - 6*c + 4*n = -26. Suppose -1/2*h + 0 - z*h**c = 0. Calculate h.
-1/4, 0
Suppose -2*a - 34*u + 30*u = 4, -10 = -4*a + u. Solve 6*m - 36/5*m**a - 3/5*m**4 - 9/5 + 18/5*m**3 = 0.
1, 3
Factor -98/3*z**3 + 184*z - 80/3 - 308*z**2.
-2*(z + 10)*(7*z - 2)**2/3
Let w = -41 - -43. Factor -21*s**5 - 4*s**2 + 36*s**4 - 6*s**3 - s**2 - s**w - 3*s**3.
-3*s**2*(s - 1)**2*(7*s + 2)
Suppose -3*k - 21 = -2*q, -6*k = -k - 5. Suppose -q*y = -13*y + 3. Factor -1/2*a**4 - 1/2 + 0*a + 0*a**y + a**2.
-(a - 1)**2*(a + 1)**2/2
Let s = 12 + -2. Let g = -4 + s. Solve 0*w - 2*w**2 + 6*w - g + 2*w = 0.
1, 3
Factor 42 + 5*u**2 - 39 - 52*u - 9*u**2 - 163.
-4*(u + 5)*(u + 8)
Let x(l) be the first derivative of -4/5*l**5 + 4/3*l**3 - l**4 - 5 + 0*l + 2*l**2. What is q in x(q) = 0?
-1, 0, 1
Let g(h) be the second derivative of -h**4/6 + 4*h**3/3 + 32*h**2 + 4*h + 13. Suppose g(k) = 0. Calculate k.
-4, 8
Factor 9/4 - 2*u - 1/4*u**2.
-(u - 1)*(u + 9)/4
Let o(u) be the second derivative of -1/3*u**2 + 4/27*u**3 + 0 + 12*u - 1/54*u**4. Factor o(d).
-2*(d - 3)*(d - 1)/9
Let v(b) be the second derivative of 1/2*b**2 - 7*b - 2*b**5 - 5/3*b**3 + 8/15*b**6 + 0 + 11/4*b**4. Factor v(h).
(h - 1)**2*(4*h - 1)**2
Let r(d) be the first derivative of 2*d - 3 + 0*d**3 - 1/10*d**6 + 3/20*d**5 + 0*d**2 + 0*d**4. Let g(i) be the first derivative of r(i). Factor g(o).
-3*o**3*(o - 1)
Let q(w) = -3*w**2 - 53*w - 45. Let p(c) = 2*c**2 + 50*c + 44. Let s(d) = -5*p(d) - 4*q(d). Find x such that s(x) = 0.
-1, 20
Let g be (3 - 2)/((-2)/(-18)). Suppose 0 = 4*a + 3*k - 23, -5*a + 3*a = -k - g. Factor a + 3*o**2 - 4*o**2 - 4.
-(o - 1)*(o + 1)
Let n(h) be the second derivative of -h**7/112 + h**6/8 - 87*h**5/160 + h**4 - 3*h**3/4 + 75*h. Find i, given that n(i) = 0.
0, 1, 2, 6
Let m be (-6)/(-4)*(1560/90 - 14). Factor -5/2*l**4 - 5/2 + 0*l + 0*l**3 + m*l**2.
-5*(l - 1)**2*(l + 1)**2/2
Let y(f) = f**2 + 5*f + 4. Let s(r) = -r**2 - 5*r - 4. Let c be s(-5). Let u be y(c). Factor 0*h**2 + u + 2/7*h**3 + 0*h.
2*h**3/7
Let a = -118 - -121. Let s(k) be the third derivative of 0*k**6 + 1/21*k**a + 0*k - 1/105*k**5 + 0 + 1/735*k**7 + 0*k**4 - k**2. Factor s(l).
2*(l - 1)**2*(l + 1)**2/7
Suppose -120*r + 117*r + 6 = 0. Let f be (r - 4/(-1))/(165/10). Let -4/11*l**2 - 2/11*l + f + 2/11*l**3 = 0. Calculate l.
-1, 1, 2
Let r(p) be the first derivative of p**6/30 + p**5/9 + p**4/9 + 5*p**2/2 - 10. Let a(k) be the second derivative of r(k). Determine m so that a(m) = 0.
-1, -2/3, 0
Let r(q) = -15*q**2 + 6275*q + 283475. Let z(d) = 4*d**2 - 1793*d - 80993. Let y(s) = -7*r(s) - 25*z(s). Find p, given that y(p) = 0.
-90
Suppose 1 + 19 = 10*o. Let -c - o*c**2 - c**5 + c**4 + 2*c**5 - 3*c**4 + 4*c**4 = 0. What is c?
-1, 0, 1
Let 0 + 5/3*j**2 - 5/3*j**4 + 4/3*j - j**3 - 1/3*j**5 = 0. What is j?
-4, -1, 0, 1
Let l(j) = j**3 + 5*j**2 + 4*j - 3. Suppose -5*y - 16 = -1. Let m be l(y). Suppose 0*c**2 + 0*c + 0 - 2/9*c**m = 0. Calculate c.
0
Let c(u) be the third derivative of -u**5/75 + 5*u**4/6 - 16*u**3/5 - 3*u**2 + 25*u. Determine x, given that c(x) = 0.
1, 24
Let j(l) be the third derivative of -l**8/141120 - l**7/17640 + 3*l**5/20 + 9*l**2. Let k(r) be the third derivative of j(r). Factor k(y).
-y*(y + 2)/7
Let k(y) be the first derivative of 0*y**3 + 9/50*y**5 + 1 - y + 0*y**2 + 1/15*y**4. Let c(b) be the first derivative of k(b). Determine l so that c(l) = 0.
-2/9, 0
Let j(u) be the first derivative of 3*u**5/20 - 27*u**4/4 + 143*u**3/2 + 513*u**2/2 + 1083*u/4 + 721. Determine x so that j(x) = 0.
-1, 19
Let i = -13/9 + 187/117. Suppose -5*f + 6*o + 27 = 2*o, 4*f - 3*o - 21 = 0. Factor 0*d - i*d**2 + 0 - 2/13*d**f.
-2*d**2*(d + 1)/13
Factor 2/3*f**4 - 2/3*f**3 - 40/3*f + 0 - 32/3*f**2.
2*f*(f - 5)*(f + 2)**2/3
Let x(d) be the first derivative of 35 + 2/27*d**3 + 2*d - 2/3*d**2. Suppose x(g) = 0. What is g?
3
Let d(r) be the first derivative of r**5/55 - r**4/44 - 2*r**3/33 + 99. Factor d(q).
q**2*(q - 2)*(q + 1)/11
Let p(l) = -l**3 + 3*l**2 + 4*l - 8. Let w be p(3). Let x be w + -1 - (-275)/(-100). Find j, given that -x*j**2 - 1/2 - 3/4*j = 0.
-2, -1
Suppose 27 = 4*q + l - 0*l, 5*l = 2*q - 19. Suppose 0 = q*f - 8*f + 10. Suppose -3*m - 6*m**4 + f*m**4 + 3*m = 0. Calculate m.
0
Let u(d) be the second derivative of -d**4/18 + 10*d**3/9 - 16*d**2/3 + 8*d + 2. Solve u(v) = 0 for v.
2, 8
Let w(s) be the third derivative of -s**6/30 - 4*s**5/5 - 29*s**4/6 + 28*s**3 + 207*s**2 + 1. Factor w(t).
-4*(t - 1)*(t + 6)*(t + 7)
Let l = 1021/6 - 417/2. Let x = l - -39. Determine m so that -x*m**5 + 0 + 0*m**3 - 2/3*m**4 + 0*m + 0*m**2 = 0.
-1, 0
Let z = 8 + 25. Suppose -z = -13*t + 19. Factor t + 4/3*x**3 - 4*x**2 - 4/3*x.
4*(x - 3)*(x - 1)*(x + 1)/3
What is t in -6*t**2 + 43*t**2 - 138*t**3 - 3*t**2 + 2*t**2 - 21*t**5 + 24*t + 99*t**4 = 0?