et u(o) = 4*o**4 + 32*o**2 - 24*o + 8. Let w(k) = 8*s(k) - u(k). Factor w(v).
4*v**2*(v - 4)*(v + 2)
Let n be (22 + -1)/(-7) + -1. Let t(k) = 10*k**2 + 10*k - 2. Let h(x) = x**3 + 12*x**2 + 11*x - 3. Let p(r) = n*h(r) + 6*t(r). Find s, given that p(s) = 0.
-1, 0, 4
Suppose 2*c = -3*v + 10, -2*v + 0 + 6 = c. Factor -3*o**3 + 2 + c*o**2 - o - o**3 + 6*o - o**5 - 3*o**4 - o**4.
-(o - 1)*(o + 1)**3*(o + 2)
Factor -3332*o**4 - 3*o - 7*o**2 + 6662*o**4 + 0*o**2 - 5*o**3 - 3331*o**4.
-o*(o + 1)**2*(o + 3)
Let c be 2/(-3 + 0 - -1). Let m be c*9/(-2)*(-2)/(-3). Factor -37*r**m - 7 + 32*r**3 + 2 + 5*r + 0 + 5*r**2.
-5*(r - 1)**2*(r + 1)
Let y = -58836 + 58872. Solve -193/4*w**2 - 1/4*w**4 - 13/2*w**3 - y - 78*w = 0.
-12, -1
Let t be ((-12)/135)/(1 - (-638)/(-594)). Factor 3/5*v**2 - 6/5*v**3 + t*v - 3/5.
-3*(v - 1)*(v + 1)*(2*v - 1)/5
Factor 51*n**3 + 5*n**4 - 740*n**2 + 79*n**3 + 463*n + 607*n - 465.
5*(n - 3)*(n - 1)**2*(n + 31)
Let j(z) = 22*z**2 + 10*z + 14*z + 5*z**3 - 2*z**3 - 4*z**3 + 36. Let k be j(23). Let 48*w - k - 4 - 81 - 4*w**2 = 0. What is w?
6
Let -552123 - 1045*j**2 - 1037*j**2 + 2079*j**2 + 2574*j = 0. What is j?
429
Let v(y) be the third derivative of y**4/24 - 31*y**3/6 - 13*y**2 + 2. Let j be v(31). Factor j*r**2 - 5/3*r**5 - 4/3*r**3 + 0*r + 4*r**4 + 0.
-r**3*(r - 2)*(5*r - 2)/3
Let p be 2 - ((-3818)/(-1738) + 21/(-77)). Let u = p - -772/237. Factor 4/3*y**4 + 0*y + 0*y**3 + 0 + 0*y**2 - u*y**5.
-2*y**4*(5*y - 2)/3
Determine l, given that -1/4*l**4 + 416 + 29/2*l**3 - 78*l**2 - 8*l = 0.
-2, 4, 52
Let c(k) = 7*k**2 - 23*k + 43. Let y(q) = -24*q + 11*q**2 - 2747 - 3*q**2 + 2793. Let i(l) = -6*c(l) + 5*y(l). Suppose i(b) = 0. What is b?
2, 7
Let r(c) be the third derivative of -5 - 25/24*c**4 - 40/9*c**3 + 1/36*c**5 + 13*c**2 + 0*c. Factor r(t).
5*(t - 16)*(t + 1)/3
Let k be (-2)/4 + (-2)/(-4) - -5. Suppose -6*s = -k*l - 2*s + 27, 0 = 4*s + 12. Factor -512/7 - 23328/7*b**l - 15552/7*b**2 - 13122/7*b**4 - 4608/7*b.
-2*(9*b + 4)**4/7
Factor 149187 - 16*r + 143*r - 447*r - 5*r**2 + 8*r**2 - 1018*r.
3*(r - 223)**2
Let z be 19 - ((198/(-15))/(-3) - -14). Factor -12/5*k**3 + 3/5*k**4 - 12/5*k + z + 18/5*k**2.
3*(k - 1)**4/5
Solve 34191/2*j**2 + 3/2*j**4 - 39458*j + 971/3*j**3 + 23762/3 = 0 for j.
-109, 2/9, 2
Factor 420*v + 9255*v**3 + 72*v**2 - 4630*v**3 - 4622*v**3.
3*v*(v + 10)*(v + 14)
Suppose -f + 92 = 22*f. Suppose -7*c + 22 = f*c. Factor -1/3*m**c + 0 - 5/3*m.
-m*(m + 5)/3
Suppose 48*g**3 + 168*g**2 - 22145258 - 1885*g + 2*g**4 + 317*g + 22145258 = 0. Calculate g.
-14, 0, 4
Let i(y) be the third derivative of 25/12*y**3 + 0*y + 0 - 15/32*y**4 - 1/48*y**5 + 94*y**2. Factor i(w).
-5*(w - 1)*(w + 10)/4
Let i be (19/(-28) - -1)*(3 + -39 - 23408/(-627)). Factor 30/7*w + i*w**2 + 75/7.
3*(w + 5)**2/7
Suppose 139*m - 133*m - 18 = 0. Solve 80*z**2 + 1145*z**m - 641*z**3 - 1372*z**5 + 4*z + 82*z**4 + 702*z**4 = 0 for z.
-1/7, 0, 1
Suppose 5*x = -2*o + 4, 2*o = 16*x - 20*x + 2. Let -8*j**2 + 4 + x*j**2 - 4*j + 7*j**2 = 0. Calculate j.
2
Let c = 5245 - 5241. Let w(q) be the second derivative of 0 + 4/3*q**2 - 37/18*q**c - 8/9*q**3 - 20*q - 17/15*q**5 - 1/5*q**6. What is z in w(z) = 0?
-2, -1, 2/9
Let t(u) be the third derivative of -u**9/52920 + u**8/23520 + 17*u**5/15 + u**2 + 20. Let w(s) be the third derivative of t(s). Factor w(j).
-2*j**2*(4*j - 3)/7
Suppose -3*a = -8*a + 185. Determine x, given that a*x**2 + 12 - 15*x**2 - 20*x**2 - 10*x = 0.
2, 3
Suppose -2*y - 92 = -p - 251, 0 = -2*p - 6. Factor -y*a - 2*a - 72*a**2 + 10*a**4 - 32 - 28*a**3 - 14*a**4.
-4*(a + 1)*(a + 2)**3
Let h be (-105)/(-110) - ((-2120)/(-176) - 12). Suppose -8/11 - 2/11*b**3 - h*b**2 - 16/11*b = 0. What is b?
-2, -1
Let l(z) be the first derivative of 3/10*z**5 - 4/3*z**4 - 2*z + 9 + z**3 + 2*z**2. Let x(s) be the first derivative of l(s). Determine u so that x(u) = 0.
-1/3, 1, 2
Suppose -124*j + 1/4*j**2 + 0 = 0. Calculate j.
0, 496
Determine z so that 3*z**2 + 121*z + 73*z + 16*z + 474*z + 49152 + 84*z = 0.
-128
Suppose -10 = 3*t + 4*m, 3*t - 3*m = -m + 14. Solve -113 + 98 - a**2 + 48*a - 8*a**t = 0 for a.
1/3, 5
Let q(m) be the third derivative of -5*m**2 + 1/4*m**6 + 5/4*m**5 + 5/3*m**4 - 1/42*m**7 + 0*m**3 + 8*m + 0. Factor q(y).
-5*y*(y - 8)*(y + 1)**2
Let x(u) = 2*u**2 - 8*u - 3. Let o be x(4). Let d be 10 - (2/o)/((-2)/9). Determine p, given that -3*p**2 - 9 - d + 16 = 0.
0
Suppose -401 = -18*v + 175. Let t be 128/10 + v/(-40). Factor -21/4*u**2 + 6*u + t + 3/4*u**3.
3*(u - 4)**2*(u + 1)/4
Let c(h) = 22*h**4 - 115*h**3 - 443*h**2 - 176*h + 129. Let k(y) = 3*y**3 + y**2 + 1. Let n(p) = -c(p) + k(p). Suppose n(g) = 0. What is g?
-2, -1, 4/11, 8
Let p(y) = 13*y**3 + 144*y**2 + 810*y + 1345. Let h(o) = 19*o**3 + 216*o**2 + 1215*o + 2018. Let w(z) = 5*h(z) - 7*p(z). Determine d, given that w(d) = 0.
-15/2, -3
Let k be (-6)/90 - 5405/(-705). Suppose 6*i = 2*i + 12. Solve k*g + 38/5*g**2 - 12/5 + 8/5*g**i = 0.
-3, -2, 1/4
Let w(g) = -3*g**2 - 36*g - 102. Let n = 234 - 227. Let o(a) = -4*a**2 - 36*a - 105. Let p(y) = n*w(y) - 6*o(y). What is j in p(j) = 0?
-2, 14
Suppose -38*d + 40*d = 10. Suppose -3*x = -3*l + 6, -2*l = -l - d*x - 2. Factor 33*r**l - 16*r**2 + 10*r - 6 - 13*r**2.
2*(r + 3)*(2*r - 1)
Let t be 0/((-3)/1*(-5)/(-3)). Let m be 1/(-2)*(-1 - t). Find q, given that -25/2 - m*q**2 - 5*q = 0.
-5
Let u be (0/(8 - 0))/(-8 - -6). Let n(b) be the third derivative of -1/6*b**3 - 1/20*b**5 + u - 1/6*b**4 + 0*b + 7*b**2. Determine y, given that n(y) = 0.
-1, -1/3
Let a(r) be the first derivative of 5*r**6/16 - 69*r**5/40 - 1035*r**4/32 - 109*r**3/8 + 255*r**2/4 + 99*r/2 - 1705. What is n in a(n) = 0?
-6, -1, -2/5, 1, 11
Let k = 156957 - 156954. Factor 1/6*n**4 - 8/3*n + 0 + 7/6*n**k + 4/3*n**2.
n*(n - 1)*(n + 4)**2/6
Factor -3*d**5 + 44718*d**2 + 16122*d**2 - 2*d**5 - 28860*d**3 - 192*d**4 - 623*d**4 + 45*d**4.
-5*d**2*(d - 2)*(d + 78)**2
Let u(s) be the first derivative of -5*s**4/8 + 5215*s**3/2 - 16317735*s**2/4 + 5673132535*s/2 + 1846. Determine p, given that u(p) = 0.
1043
Let x(p) be the first derivative of -9*p**5/5 - 411*p**4/4 - 78*p**3 + 822*p**2 + 1080*p + 201. Suppose x(q) = 0. What is q?
-45, -2, -2/3, 2
Let z(k) be the second derivative of -k**8/2520 + k**6/135 + 14*k**3 + 83*k. Let x(q) be the second derivative of z(q). Let x(w) = 0. Calculate w.
-2, 0, 2
Let n be ((-153)/(-60)*(1044/36 - 37))/((-32)/10). Factor -27/8 - n*j + 3/8*j**3 - 21/8*j**2.
3*(j - 9)*(j + 1)**2/8
Let y be ((-33)/(-6))/((-5)/3120*4). Let j = 2575/3 + y. Solve j*u**4 + 0 - 1/3*u**2 + 0*u**3 + 0*u = 0.
-1, 0, 1
Let h(f) = -f - 36. Let m be h(-35). Let a be (4900/63)/14 + m. Determine w so that -5/3*w**3 - 8/3*w - 4/9 - a*w**2 = 0.
-2, -2/5, -1/3
Let b(t) be the first derivative of -114/7*t - 1/7*t**3 - 9/2*t**2 + 179. Factor b(f).
-3*(f + 2)*(f + 19)/7
Suppose 18 - 102 = -21*x. Factor 4478*z**2 + 4 - 2*z - 4*z**4 - 4484*z**2 + 6*z**x + 2*z**3.
2*(z - 1)**2*(z + 1)*(z + 2)
Let a(s) = -2*s**2 + 25*s - 8. Let f be a(8). Factor -f*z**2 + 9*z + 50*z**3 - 5*z + 16*z + 4*z**5 + 22*z**3 + 0*z**2 - 32*z**4.
4*z*(z - 5)*(z - 1)**3
What is t in -2*t**2 - 14739*t**4 + 14743*t**4 - 13*t**2 - 16*t**3 + 72*t + 3*t**2 = 0?
-2, 0, 3
Let y(f) = -4*f**3 - 8*f**2 - 100*f + 216. Let t(a) = 5*a**3 + 9*a**2 + 99*a - 216. Let q(p) = 8*t(p) + 9*y(p). Find c such that q(c) = 0.
-6, 3
Suppose -12 = -2*p - p. Let c = 31 - 28. Factor c*q**3 + 2*q**2 - 2*q**2 + 3 - p*q - 3*q**2 + q.
3*(q - 1)**2*(q + 1)
Let i(d) be the first derivative of -6*d + 1/4*d**4 + 2/3*d**3 - 5/2*d**2 + 152. Suppose i(c) = 0. Calculate c.
-3, -1, 2
Let u be (22/(-55))/(20*(-10)/1125). Factor -6*v + u - 3/4*v**4 + 9/2*v**2 + 0*v**3.
-3*(v - 1)**3*(v + 3)/4
Let y be (-232)/87*3/(-2). Let d(v) = -v**2 + 9*v - 81. Let a(b) = 4*b - 40. Let n(i) = y*d(i) - 9*a(i). Let n(s) = 0. Calculate s.
-3, 3
Let i(k) be the first derivative of 2/7*k**3 + 0*k**2 - 8/7*k - 77 - 1/14*k**4. Let i(c) = 0. What is c?
-1, 2
Let d(n) = 9*n - 17. Let v be d(17). Factor -4*f**2 - 4*f**3 + 12 + 2*f**3 - v*f + 146*f.
-2*(f - 2)*(f + 1)*(f + 3)
Let d(u) = -3*u**4 + 17*u**3 - 22*u**2 - 52*u + 120. Let j(o) = 7*o**4 - 35*o**3 + 41*o**2 + 104*o - 240. Let t(l) = -9*d(l) - 4*j(l). Solve t(n) = 0.
-15, -2, 2
Let v = 95 - 88. Let h(u) be the second derivative of -1/