 o such that 4*o**2 - w*o**2 - o**2 - 3*o = 0.
-1, 0
Let z(l) be the first derivative of l**5/30 - 7*l**4/18 + 2*l**3/3 + 17*l - 8. Let f(x) be the first derivative of z(x). Let f(g) = 0. What is g?
0, 1, 6
Let c(q) = q**3 + 14*q**2 - 22*q - 15. Let n be c(-17). Let w = n - -3564/7. Solve w*k**2 - 10/7*k + 2/7 = 0 for k.
1/4, 1
Suppose 21 - 11 = -h. Let p(u) = -u**2 - 9*u + 10. Let v be p(h). Factor 1/2*z**2 + v - 1/2*z**3 + z.
-z*(z - 2)*(z + 1)/2
Let s(f) = -f**5 + f**4 + f**3 - f**2 - f. Let l(z) = -5*z**5 - 36*z**4 - 84*z**3 - 62*z**2 - z + 10. Let d(p) = -l(p) + 2*s(p). Suppose d(t) = 0. Calculate t.
-10, -1, 1/3
Let q(s) = -9*s - 1. Suppose k = 4*h, -2*k - 5*h - 7 = -5*k. Suppose k*j - 7 = 9. Let i(o) = -o**2 + 10*o. Let z(p) = j*i(p) + 6*q(p). Factor z(b).
-2*(b + 3)*(2*b + 1)
Let h(x) be the third derivative of x**6/1380 - x**5/345 - 2*x**4/69 + 11*x**2. Factor h(a).
2*a*(a - 4)*(a + 2)/23
Let g = 6897 - 6895. Solve -4/7*x**g + 0 + 2/7*x**5 - 2/7*x + 0*x**3 + 4/7*x**4 = 0.
-1, 0, 1
Let r = -1/363 + 146/9075. Let x(m) be the third derivative of 0*m + 0 - r*m**5 + 2/15*m**3 - 8*m**2 + 0*m**4. Suppose x(n) = 0. What is n?
-1, 1
Factor d + 1/2 + 0*d**2 - d**3 - 1/2*d**4.
-(d - 1)*(d + 1)**3/2
Let i(v) = 13*v - 48. Let f be i(4). Factor -6*s - 69 + 2*s**f + 2*s**3 - 19*s**2 - 11 - 98*s - 17*s**2.
2*(s - 5)*(s + 2)**3
Suppose -202 = -4*b + 5*u - 185, -3*u + 3 = 2*b. Factor 0*w**2 + 1/2*w**4 - 3/2*w**b + 0 + 2*w.
w*(w - 2)**2*(w + 1)/2
Factor 14/3*n**2 + 8/3*n**3 - 124/3*n + 10.
2*(n - 3)*(n + 5)*(4*n - 1)/3
Let l(g) be the first derivative of -7*g**5/180 + g**4/18 + g**3/6 + 2*g**2 - 7. Let j(d) be the second derivative of l(d). Factor j(w).
-(w - 1)*(7*w + 3)/3
Let u(l) be the first derivative of 0*l**2 + 1/48*l**4 - 1/120*l**5 + 1/3*l**3 + 1/720*l**6 + 1 + 0*l. Let y(i) be the third derivative of u(i). Factor y(s).
(s - 1)**2/2
Let o(v) be the first derivative of 11 + 4*v + 9*v**2 + 14/3*v**3. Find m such that o(m) = 0.
-1, -2/7
Let a(w) = 5*w**5 - 11*w**4 + 15*w**3 - 7*w**2 - 2. Let d(u) = u - 137*u**2 + 1 - 139*u**2 - u**5 + 275*u**2. Let b(o) = -3*a(o) - 6*d(o). Factor b(s).
-3*s*(s - 1)**3*(3*s - 2)
Factor 2/5*h - 2/5*h**3 + 4/5*h**2 - 4/5.
-2*(h - 2)*(h - 1)*(h + 1)/5
Let y(i) be the third derivative of -i**5/60 + i**4/6 + 2*i**3 + 3*i**2 + 2*i. Suppose y(h) = 0. What is h?
-2, 6
Let b(i) be the first derivative of i**5/5 + i**4/6 - 32*i**3/27 - 16*i**2/9 - 69. Factor b(m).
m*(m - 2)*(3*m + 4)**2/9
Let j(n) = -n**2 + 133*n + 363. Let c(y) = 132*y + 360. Let t(p) = -5*c(p) + 4*j(p). Find q, given that t(q) = 0.
-29, -3
Let q(d) = 14*d**2 - 96*d + 115. Let f(n) = 5*n**2 - 32*n + 39. Let t(r) = -11*f(r) + 4*q(r). Factor t(h).
(h - 31)*(h - 1)
Let i(l) be the third derivative of 4/3*l**4 + 8/3*l**3 + 0 + 1/30*l**6 + 1/3*l**5 + 0*l - 10*l**2. Solve i(h) = 0.
-2, -1
Let s = 3524 - 3521. Let -3/4*i**4 + 0 + 2*i**s + 1/2*i - 7/4*i**2 = 0. Calculate i.
0, 2/3, 1
Let x(n) = -n**3 - n**2 - 5*n. Let w(f) = -24*f**3 - 9*f**2 - 18*f + 2. Let p(j) = 3*w(j) - 21*x(j). Factor p(q).
-3*(q - 1)*(q + 1)*(17*q + 2)
Let y(t) = -25*t**3 - 15*t**2 + 65*t - 40. Suppose -21*k + 5 = -20*k. Let i(l) = -l**4 - 2*l**3 - l**2 + l. Let x(v) = k*i(v) - y(v). Factor x(f).
-5*(f - 2)**2*(f - 1)*(f + 2)
Let t = -822 - -829. Let p(g) be the third derivative of -3/100*g**6 + 0*g + 7/50*g**5 - 4/15*g**4 + t*g**2 + 4/15*g**3 + 0. Factor p(y).
-2*(y - 1)*(3*y - 2)**2/5
Let j(o) be the second derivative of 0*o**4 + 1/130*o**5 - 1/39*o**3 + 0*o**2 - 7*o + 0. Solve j(g) = 0 for g.
-1, 0, 1
Let a(w) = -w**3 - 21*w**2 + 2. Let l be a(-21). Factor -3*q**3 - 10*q**2 + 0*q**3 + 34*q**l.
-3*q**2*(q - 8)
Let j(w) be the first derivative of -1/5*w**4 + 2/25*w**5 + 0*w**3 + 0*w**2 + 1/15*w**6 + 0*w - 33. Factor j(f).
2*f**3*(f - 1)*(f + 2)/5
Let h(u) be the third derivative of 11*u**7/420 - 31*u**6/240 + 2*u**5/15 + u**4/12 - u**2 - 86*u. Solve h(d) = 0 for d.
-2/11, 0, 1, 2
Factor 1/2*c**2 - 83 + 81/2*c.
(c - 2)*(c + 83)/2
Suppose -9*r + 42 = 12*r. Let a(o) be the second derivative of r*o**3 - 1/3*o**4 + 0 + 0*o**2 + 3*o. Suppose a(p) = 0. What is p?
0, 3
Let o = -3 + 8. Let w = 7 + o. Factor w*a - 12 + 3*a**2 + 8*a + 4*a + 12*a**2.
3*(a + 2)*(5*a - 2)
Find p such that -4*p**3 - 54 + 5*p - 52*p**2 + 10 + 8*p**3 + 87*p = 0.
1, 11
Factor -2*i**3 + 0*i - 8/9*i**2 + 0 - 4/3*i**4 - 2/9*i**5.
-2*i**2*(i + 1)**2*(i + 4)/9
Let z(m) = -m**3 + 45*m**2 + 40*m + 280. Let a be z(46). Factor -6/5*f + 0 - 2/5*f**a - 2*f**3 - 14/5*f**2.
-2*f*(f + 1)**2*(f + 3)/5
Let z(a) = a**4 - a**2 - 1. Let i(r) = r**4 - 95*r**3 + 179*r**2 - 85*r + 4. Let q(l) = -i(l) - 4*z(l). Find u, given that q(u) = 0.
0, 1, 17
Suppose 96/13 + 10/13*t**4 - 72/13*t**3 + 100/13*t - 6*t**2 = 0. What is t?
-1, 6/5, 8
Let f(l) be the first derivative of l**6/36 + 3*l**5/10 + 5*l**4/4 + 23*l**3/9 + 11*l**2/4 + 3*l/2 - 180. Solve f(j) = 0 for j.
-3, -1
Factor 76*c**2 - 56*c + 4*c**4 - 11*c**5 + 16 - 12*c**3 - 38*c**3 + 9*c**5 + 12*c**4.
-2*(c - 2)**3*(c - 1)**2
Let c(m) be the second derivative of -8*m**2 - 2/3*m**3 + 0 - 11*m + 13/6*m**4 - 3/10*m**5. Suppose c(d) = 0. Calculate d.
-2/3, 1, 4
What is h in -80/3 - 2/3*h**2 - 44/3*h = 0?
-20, -2
Let s(n) = -n**2 - n - 6. Let x be s(-3). Let f = -9 - x. Factor -12*q**f - 9*q**3 + 24*q - 34*q**2 - 4*q + 8.
-(q + 2)*(3*q - 2)*(7*q + 2)
Let k(d) = -d**3 - d**2 - d. Let w(l) = 19*l**3 - 9*l**2 - l. Let p be ((-2)/(-3))/((-18)/27). Let q(n) = p*w(n) - 3*k(n). Solve q(a) = 0.
-1/4, 0, 1
Solve 471*n**4 - 473*n**4 - 20*n**3 - 26*n**2 - 8*n**3 = 0 for n.
-13, -1, 0
Let y = 251 - 66. Let p be (-4)/(-26) - y/(-65). Determine z, given that -3/2*z + 0*z**2 + 3/2*z**p + 0 = 0.
-1, 0, 1
Let m(j) = -163*j + 5 - 31*j + 4 - 3. Let p be m(-15). Factor 128*i - 1912*i**2 - 2484*i**3 - 182*i - 32 - 378*i + p*i**5 - 1090*i**4 + 3034*i**4.
4*(i - 1)*(i + 1)*(9*i + 2)**3
Suppose 33*n - 29*n = -108. Let c be (n/(-63))/(6/(-14) + 1). Find a, given that -1/8 + 7/8*a**2 + 0*a + c*a**3 = 0.
-1, -1/2, 1/3
Let t(c) be the first derivative of c**6/720 - c**5/120 + c**4/48 - 11*c**3/3 - 2. Let m(h) be the third derivative of t(h). Determine z, given that m(z) = 0.
1
Let a be 1/2*(-11 + 14 - 3). Let y(h) be the first derivative of a*h - 7 + 1/22*h**4 + 2/11*h**2 - 2/11*h**3. Find w such that y(w) = 0.
0, 1, 2
Suppose -t - 55 = 5*p - 138, 3*p = t + 45. Let m be 0 + (p/(-5) - -5). Determine i, given that 6/5*i**4 + 3/5*i**5 - m*i**3 - 12/5*i**2 + 12/5*i + 0 = 0.
-2, 0, 1
Let b(v) be the second derivative of v**7/42 + v**6/10 - v**5/20 - v**4/4 - 38*v. Determine p so that b(p) = 0.
-3, -1, 0, 1
Suppose 4/5*n**3 - 68/5*n**2 + 0 + 24*n = 0. What is n?
0, 2, 15
Let f = -30 - -30. Solve -1 - 8 + f + 12*r**2 + 3 - 21*r = 0 for r.
-1/4, 2
Let f = -1097 + 47159/43. Let h = f - -189/215. Factor -6/5*i - h*i**2 - 3/5.
-3*(i + 1)**2/5
Factor -2/15*z**3 - 12/5 + 2*z + 8/15*z**2.
-2*(z - 6)*(z - 1)*(z + 3)/15
Let f = -315 + 11341/36. Let o(z) be the third derivative of -1/9*z**4 + 8*z**2 - f*z**5 - 2/9*z**3 + 0*z - 1/360*z**6 + 0. Factor o(i).
-(i + 1)*(i + 2)**2/3
Let c(p) be the first derivative of p**6/60 + 19*p**5/50 - 33*p**4/20 + 2*p**3/15 + 22*p**2/5 - 493. Suppose c(s) = 0. Calculate s.
-22, -1, 0, 2
Let d(n) be the third derivative of -n**6/240 + n**5/4 - 99*n**4/16 + 242*n**3/3 + 621*n**2. Let d(o) = 0. What is o?
8, 11
Let c = -4 + 10. Let w be (2/(-3))/((-2)/c). Factor -h**4 - 3*h**5 - w*h**4 + 6*h**5.
3*h**4*(h - 1)
Let 3/5*p**2 + 9/5*p**3 + 0 - 6/5*p = 0. Calculate p.
-1, 0, 2/3
Suppose 5*p = 9*p - 4, -5*o + 3*p = -117. Let h = o - 22. What is k in 14/9*k**3 + 2/3*k - 4/9 + 8/3*k**h = 0?
-1, 2/7
Suppose -5*i + 11 = m, -4*i = 2*m - m - 9. Let -7*r + 3*r + 5*r**3 + 10*r**2 - i*r**2 - 9*r**3 = 0. Calculate r.
0, 1
Suppose 507 + 2661 = 4*t. Factor 32 + t*s**2 + 72*s**2 + 631*s**4 - 43*s**3 + 1987*s**3 - 7921*s**4 - 352*s.
-2*(5*s + 2)*(9*s - 2)**3
Let f(q) be the third derivative of 0 + 5/12*q**3 - 1/48*q**5 - 8*q**2 + 0*q + 5/96*q**4. Factor f(b).
-5*(b - 2)*(b + 1)/4
Suppose -15*g = -21*g - 24. Let w be ((-192)/(-15) - 4) + g. Factor -8/5 - 2/5*v**4 - 26/5*v**2 - 12/5*v**3 - w*v.
-2*(v + 1)**2*(v + 2)**2/5
Let p be (-68)/(-222) + (-12)/18. Let h = -1/37 - p. Factor -2/3*m**3 + 0*m**2 + 0 - h*m**4 + 0*m.
-m**3*(m + 2)/3
