- 256. Let b(o) = 3*u(o) - 20*z(o). Determine h so that b(h) = 0.
-32, -2
Let z be (105/(-6))/(-7) + 9/18. Suppose z*x - 8 = -3*f + 5*x, -5*f + 4*x = -16. Solve f*m**2 + 0*m**4 + 0 + 0*m + 2/9*m**3 - 2/9*m**5 = 0 for m.
-1, 0, 1
Let p = 394/5 - 392/5. Let h(m) be the first derivative of 1/6*m**4 + 0*m + 8 - p*m**5 - 1/3*m**2 + 2/3*m**3. Find k, given that h(k) = 0.
-1, 0, 1/3, 1
Factor 0 + 25/3*b**2 + 5/3*b**3 + 20/3*b.
5*b*(b + 1)*(b + 4)/3
Factor -578/13 - 2/13*z**3 + 66/13*z**2 - 510/13*z.
-2*(z - 17)**2*(z + 1)/13
Factor 1075/8*p**4 + 2615/8*p**3 + 31*p + 2 + 1321/8*p**2 + 125/8*p**5.
(p + 4)**2*(5*p + 1)**3/8
Suppose 1693*w = 1692*w. Let n(a) be the third derivative of 1/420*a**7 + 0*a**6 + w*a**5 + 0*a**3 + 0*a + 0*a**4 + 0 - 8*a**2. What is v in n(v) = 0?
0
Let p(a) = -3*a**4 + 39*a**3 - 75*a**2 + 69*a - 18. Let k(v) = 3*v**4 - 38*v**3 + 76*v**2 - 70*v + 19. Let x(z) = 6*k(z) + 5*p(z). Factor x(n).
3*(n - 8)*(n - 1)**3
Suppose -h + 4*i = 0, 1 = -3*i + 4. Let w = -10 + 13. Factor 5*d**3 - 2*d**w + d**2 + 0*d**2 + d**h - 5*d**3.
d**2*(d - 1)**2
Suppose -5 - 7 = 6*b. Let s be (-15)/(-30) - 7/b. Suppose s*x**3 + 8*x**5 - 20*x**4 + 9*x**2 - x**2 + 0*x**2 = 0. What is x?
-1/2, 0, 1, 2
Let f(z) be the second derivative of 1/70*z**6 - 1/21*z**3 + 0*z**2 - 18*z - 1/28*z**4 + 1/140*z**5 + 0 + 1/294*z**7. Factor f(d).
d*(d - 1)*(d + 1)**2*(d + 2)/7
Determine j so that 12037 - 29*j + 18487 + 4*j**2 + 11092 + 845*j = 0.
-102
Let t = 742/15 - 125/3. Suppose 0 - t*y**2 + 3*y**3 - 18/5*y = 0. What is y?
-2/5, 0, 3
Find h, given that -2 + 2/5*h**2 - 8/5*h = 0.
-1, 5
Let q(x) = x**3 - 10*x**2 - 11*x + 3. Let f be q(11). Let l = f - 0. Factor 2*w**3 - w**3 - 2*w**l - 2*w**2 + 0*w**3.
-w**2*(w + 2)
Factor 35*h**2 - 20*h**2 + 24 - 8*h**2 - 117*h - 22*h**2.
-3*(h + 8)*(5*h - 1)
Suppose j + 2*g - 6*g - 16 = 0, 0 = 3*g + 9. Factor 6*h**2 - 8*h**3 + 8*h + 4*h**4 - 10*h**4 - 4*h + j*h**2.
-2*h*(h - 1)*(h + 2)*(3*h + 1)
Suppose 8 = -9*p + 35. Let f be (2/(-12))/(2 - 3). Find l, given that 1/3*l**p - f*l + 1/6*l**2 + 0 = 0.
-1, 0, 1/2
Let z be 24/4 - (6 - 0). Let y(q) be the third derivative of z*q - q**2 - 1/480*q**6 + 1/120*q**5 + 0*q**3 - 1/96*q**4 + 0. Determine d so that y(d) = 0.
0, 1
Suppose 2*p + 2*p - 76 = 0. Let j = p - 7. Solve -5*d**2 + 8 + j*d + 9*d**2 + 0*d = 0 for d.
-2, -1
Suppose -5*v - 3*r = 6, 2*v - 2*r - 4 = -v. Let a(m) be the second derivative of 0*m**2 + v*m**3 + 12*m + 0 - 1/210*m**6 - 1/70*m**5 + 0*m**4. Factor a(i).
-i**3*(i + 2)/7
Let t(s) = -s**4 - s**3 + s - 1. Let k be (-10)/(-40) + 18/(-8). Let v(f) = 5*f**4 + 5*f**3 - 3*f + 3. Let x(z) = k*v(z) - 6*t(z). What is g in x(g) = 0?
-1, 0
Suppose 20*l + 7*l = 108. Let x(c) be the second derivative of -3/40*c**5 - 1/8*c**l + 3/8*c**2 + 7*c + 1/8*c**3 + 1/56*c**7 + 1/40*c**6 + 0. Factor x(t).
3*(t - 1)**2*(t + 1)**3/4
Suppose 0 = -3*o - 3, -14 = -4*d - 5*o + 5. Let y(b) be the third derivative of -5*b**2 + 0*b**3 - 1/8*b**4 + 1/40*b**d + 0*b**5 + 0 + 0*b. Factor y(s).
3*s*(s - 1)*(s + 1)
Let d(z) = z**3 - 6*z**2 + 4. Suppose -4*y - 3*l + 32 = l, 0 = 2*l - 4. Let b be d(y). Factor -2*h - 10 - h**b + 0*h + 11 + 2*h**3.
-(h - 1)**3*(h + 1)
Let g(d) be the first derivative of -d**4/3 - 4*d**3/3 - 2*d**2 - 4*d + 15. Let v(k) be the first derivative of g(k). Factor v(x).
-4*(x + 1)**2
Let h(d) be the third derivative of 0*d - 1/2184*d**8 - 33*d**2 + 1/390*d**6 - 1/195*d**5 + 1/1365*d**7 - 1/156*d**4 + 1/39*d**3 + 0. Factor h(o).
-2*(o - 1)**3*(o + 1)**2/13
Let v(d) be the second derivative of d**7/70 - 3*d**6/50 - 27*d**5/100 - d**4/4 + 383*d. Factor v(h).
3*h**2*(h - 5)*(h + 1)**2/5
Let a be (-2 - 30/6)/(-2 + 1). Let p = -7 + a. Determine h, given that p - 6*h**2 - 35/4*h**3 - h = 0.
-2/5, -2/7, 0
Let c(t) = -t**4 - 9*t**2 + 11*t - 1. Let v(b) = -b**2 + b. Suppose 2*p = -2*p + 16. Let a(q) = p*c(q) - 44*v(q). Factor a(w).
-4*(w - 1)**2*(w + 1)**2
Factor 22/5*q**2 + 2/5*q**5 + 8/5 - 24/5*q - 2/5*q**3 - 6/5*q**4.
2*(q - 2)*(q - 1)**3*(q + 2)/5
Find v, given that 116/5*v - 24 + 8/5*v**2 - 4/5*v**3 = 0.
-5, 1, 6
Let c be (-3)/(-12)*-1 + 1248/1152. Let -5/6*t + c*t**3 - 5/6*t**2 + 5/6*t**4 + 0 = 0. What is t?
-1, 0, 1
Let d(q) be the third derivative of 37*q**5/15 - 38*q**4/3 + 8*q**3/3 + 123*q**2. Factor d(z).
4*(z - 2)*(37*z - 2)
Let x(h) be the second derivative of 0 - 3/2*h**2 - 5/4*h**3 - 3/40*h**5 - 13*h - 1/2*h**4. Find j such that x(j) = 0.
-2, -1
Let t(r) = 8*r**3 + 43*r**2 - 3*r + 6. Let d(s) = 15*s**3 + 85*s**2 - 5*s + 10. Let l(m) = -3*d(m) + 5*t(m). Factor l(o).
-5*o**2*(o + 8)
Let w(r) = -10*r**2 - 16*r. Let h = 43 - 46. Let t(l) = 8*l**2 + 17*l. Let p(y) = h*w(y) - 4*t(y). Suppose p(k) = 0. Calculate k.
-10, 0
Let u be (-84)/(-90) + 18/45. Factor -4/9 + 20/9*y - u*y**2 - 4*y**3.
-4*(y + 1)*(3*y - 1)**2/9
Suppose 0 = -4*a - 3*y - 543, a + 137 - 15 = 2*y. Let g = 135 + a. Factor -3/7*h**g + 36/7*h**2 + 192/7 - 144/7*h.
-3*(h - 4)**3/7
Let t(j) be the second derivative of j**4/12 - j**3 + 4*j**2 + 11*j. Let u be t(4). Determine d so that -d**3 + 0*d - d**4 + d**2 + 8*d - 7*d + u*d**4 = 0.
-1, 0, 1
Suppose 3*k + 3*m - m = -81, 5*k - 4*m = -135. Let d = -12 - k. Determine r, given that 2 - 8*r**2 + 32*r**2 - d*r**3 - 8 - 3*r = 0.
-2/5, 1
Suppose 9*r = -4*r + 130. Let w be (4/2)/(r + -9). Let 0 + 2/3*a + 6*a**4 - 10/3*a**w + 2*a**3 = 0. Calculate a.
-1, 0, 1/3
Let c = 89378/55855 + -2/11171. Determine a so that 6/5*a**3 - c*a + 4/5*a**2 - a**4 + 0 + 1/5*a**5 = 0.
-1, 0, 2
Let -23*h**4 - 14*h**4 + 41*h**4 = 0. Calculate h.
0
Let d = -2836/5 + 569. Let n(c) = c + 28. Let o be n(-24). Factor 7/5*u + u**3 - 2/5 - 1/5*u**o - d*u**2.
-(u - 2)*(u - 1)**3/5
Let i(g) be the second derivative of -9/20*g**5 + 1/2*g**4 + 6*g**3 - 12*g**2 - 12*g - 2. Factor i(d).
-3*(d - 2)*(d + 2)*(3*d - 2)
Let c(p) be the first derivative of 0*p**2 + p**5 + 12 + 0*p + 0*p**3 - 5/6*p**6 + 0*p**4. Factor c(t).
-5*t**4*(t - 1)
Let n = 70 - 94. Let b be 26 + n - 1*(1 - 0). Let 0*f + b - 1/4*f**3 - 3/4*f**2 = 0. Calculate f.
-2, 1
Let p(g) be the third derivative of 0*g**4 + 0*g - 1/300*g**6 - 3*g**2 + 1/150*g**5 + 0 + 0*g**3. What is u in p(u) = 0?
0, 1
Determine t so that 765*t**2 + 490*t**2 + 45*t + 12120*t**3 - 70 - 12300*t**3 = 0.
-1/4, 2/9, 7
Determine f so that 2/7*f**2 - 20/7 + 18/7*f = 0.
-10, 1
Let q(i) = -5*i**2 + 12*i - 12. Let c(h) = 11*h**2 - 24*h + 24. Let v = 17 + -19. Let m(j) = v*c(j) - 5*q(j). Determine x so that m(x) = 0.
2
Let w(s) = -2*s**4 + 8*s**3 - 20*s**2 - 12*s + 42. Let p(b) = 4*b**4 - 17*b**3 + 41*b**2 + 23*b - 83. Let y(d) = -6*p(d) - 11*w(d). Factor y(f).
-2*(f - 3)**2*(f - 2)*(f + 1)
Let b(i) = -723*i + 362. Let s(r) = 5*r**2 + 3614*r - 1811. Let u(y) = -11*b(y) - 2*s(y). Suppose u(g) = 0. What is g?
1/2, 72
Let m(g) = -5*g**2 - 503*g + 202. Let z be m(-101). Factor z + 7/6*c**2 + 2*c.
c*(7*c + 12)/6
Let l(p) be the second derivative of -p**5/50 - p**4/5 + 7*p**3/15 + p + 53. Suppose l(r) = 0. Calculate r.
-7, 0, 1
Factor 14/11 + 16/11*z + 2/11*z**2.
2*(z + 1)*(z + 7)/11
Let d(v) be the third derivative of -v**7/840 - v**6/80 - 11*v**5/240 - v**4/16 - 3*v**2 + 16*v. Factor d(u).
-u*(u + 1)*(u + 2)*(u + 3)/4
Let o(z) be the third derivative of z**6/480 - 65*z**2. Find s, given that o(s) = 0.
0
Let o = -1774 - -1777. Factor -6/7*h**2 + 0 + 4/7*h + 0*h**o + 2/7*h**4.
2*h*(h - 1)**2*(h + 2)/7
Let m = 91 + -91. Let u(p) be the first derivative of -1/3*p**3 + 1/2*p**4 + m*p + 12 + 1/5*p**5 - p**2. Factor u(b).
b*(b - 1)*(b + 1)*(b + 2)
Factor 132 + 18 - 6 - 72*r + 4*r**2 + 115 + 65.
4*(r - 9)**2
Let c = -59/3 + 67/3. Let x(w) be the second derivative of -6*w + c*w**3 + 1/10*w**5 + 5/6*w**4 + 0 + 4*w**2. Suppose x(b) = 0. Calculate b.
-2, -1
Factor 6*j - 1/4*j**3 + 3/4*j**2 - 20.
-(j - 4)**2*(j + 5)/4
Let q(f) be the third derivative of -1/42*f**7 + 0*f + 5/8*f**4 + 23*f**2 - 1/12*f**5 + 0 - 1/8*f**6 + 5/3*f**3. Suppose q(j) = 0. Calculate j.
-2, -1, 1
Factor -17/4*b + 2 + 5/2*b**2 - 1/4*b**3.
-(b - 8)*(b - 1)**2/4
Factor 4*f + 2/5*f**2 - 78/5.
2*(f - 3)*(f + 13)/5
Let d be ((-231)/(-84))/(2*(-1)/(-8)). What is s in 46 - 4 + 5*s**2 + 38 - 29*s - d*s = 0?
4
Let x(m) = 7*m**2 + 25*m + 45. Let t be ((-15)/(-6))/(2/(-4)). Let p(n) = -4*n**2 - 13*n - 22. Let h(k) = t*p(k) - 3*x(k). Factor h(d).
-(d 