r o(j).
-4*(j - 2)*(j + 1)
Suppose 2357*r - b - 6 = 2360*r, b = -2*r - 6. Let f(v) be the second derivative of r - 26*v + 31/12*v**3 + 1/6*v**4 - 2*v**2. Suppose f(o) = 0. Calculate o.
-8, 1/4
Let c(u) be the second derivative of -u**5/20 - 241*u**4/12 - 40*u**3 + 15526*u. Factor c(q).
-q*(q + 1)*(q + 240)
Suppose -4*y - 85 + 69 = 0. Let b(i) = 125*i**2 + 545*i + 475. Let u(c) = 9*c**2 + 39*c + 34. Let l(t) = y*b(t) + 55*u(t). Factor l(r).
-5*(r + 1)*(r + 6)
Let n(h) be the second derivative of -3*h**5/8 + 70*h**4/3 - 415*h**3/3 - 340*h**2 + 4545*h. Find d, given that n(d) = 0.
-2/3, 4, 34
Let p(u) = u**2 + 6*u - 5. Let q be p(-6). Let b be (18/105)/((-3)/q). Factor 0 + 0*n + 0*n**3 + b*n**4 - 2/7*n**2.
2*n**2*(n - 1)*(n + 1)/7
Let w(l) be the third derivative of l**7/350 - l**6/200 - l**5/100 + l**4/40 + 548*l**2. Find o such that w(o) = 0.
-1, 0, 1
Let y be ((-16)/10 - 0)/(-2). Let k be -5 + -1 - (-56)/(-35)*-4. Factor 0*p**3 + 2/5*p**4 + 0*p - y*p**2 + k.
2*(p - 1)**2*(p + 1)**2/5
Let o = 270 - -44. Let l = o + -312. Let 0*f - 1/7*f**4 - 2/7*f**3 + 0 + 3/7*f**l = 0. Calculate f.
-3, 0, 1
Let n = 10 + -7. Suppose -2*h + 3*j = 3*h - 75, n*h + 4*j - 16 = 0. Factor -h*q**2 - 3*q**2 - 12 - 27*q - 3*q**2 - 3*q**3.
-3*(q + 1)**2*(q + 4)
Let b(i) be the second derivative of i**4/6 + 121*i**3/3 + 120*i**2 + 1948*i. Solve b(o) = 0 for o.
-120, -1
Suppose 3*t = 12, 48*u - 47*u + 2*t = -1791. Let z = u + 1802. Suppose 76/3*i**2 - 320/3*i - 4/3*i**z - 400/3 = 0. Calculate i.
-1, 10
Factor -1217 - 15*k + 2527 - 1238 - 3*k**2.
-3*(k - 3)*(k + 8)
Let 293*t**3 + 15226*t**4 - 6867*t - 23120 - 45*t**3 - 3012*t**2 - 15230*t**4 - 19517*t = 0. What is t?
-5, -1, 34
Find l, given that -35*l + 49*l - l**3 - 4*l**3 - 35*l**2 + 10*l**2 - 24*l + 40 = 0.
-4, -2, 1
Let c = 8836 + -8836. Let g(j) be the first derivative of 0*j**2 + c*j**4 - 10/57*j**3 + 8/19*j + 2/95*j**5 + 11. Solve g(v) = 0 for v.
-2, -1, 1, 2
Determine n, given that 154*n**5 + 116*n**2 + 136*n**2 + 70*n**3 - 22*n**2 - 78*n**5 - 146*n - 226*n**4 - 4 = 0.
-1, -1/38, 1, 2
Let v(t) be the third derivative of -t**6/200 - 3*t**5/100 + 13*t**4/40 + 3*t**3/2 - 1363*t**2. Suppose v(o) = 0. What is o?
-5, -1, 3
Let l = -87409/5 + 360571/20. Find x, given that l + 3/4*x**2 + 81/2*x = 0.
-27
Let w be 308/49*(21/6 - 0). Let s be ((-231)/(-121) - 2)*w/(-4). What is u in 1/6*u - 5/6*u**3 - s*u**2 + 1/6 - 1/3*u**4 = 0?
-1, 1/2
Determine r so that r**3 - 29495*r**2 - 29416*r**2 - 115*r - 58 + 58855*r**2 = 0.
-1, 58
Let p = 812 + -820. Let b be (-40028)/(-140) + 1*p/40. Factor b + 2/7*f**4 - 62/7*f**3 - 2600/7*f + 660/7*f**2.
2*(f - 10)**3*(f - 1)/7
Let -75/2*t**2 + 0 + 54*t**4 - 375/4*t**3 - 27/4*t**5 + 0*t = 0. Calculate t.
-1/3, 0, 10/3, 5
Suppose 115*o**4 - 2*o**3 - 4 - 114*o**4 + 4 + 11*o**3 - 10*o**2 = 0. What is o?
-10, 0, 1
Let v = 141881/21 + -46827/7. Find z such that 4/3*z**2 + 2500/3 - v*z = 0.
25
Let j(f) = -f**3 + 4*f**2 - 6*f + 7. Suppose v = -6 + 8. Let n be j(v). Factor 6*a**2 + 2*a**4 + 3*a**3 + 2*a + a**n + 2*a**3.
2*a*(a + 1)**3
Let b(m) be the third derivative of 23*m**2 - 1/6*m**4 + 0*m + 2/3*m**3 + 1/60*m**5 + 0. Factor b(a).
(a - 2)**2
Let j be (64596/(-66))/7 - 7. Let r = j - -147. What is a in 0 - r*a - 2/11*a**2 = 0?
-1, 0
Let y(l) = -15*l**2 - 210*l - 680. Let x(u) = -13*u**2 - 216*u - 679. Let r(j) = 5*x(j) - 4*y(j). Find z, given that r(z) = 0.
-45, -3
Let c be 1*(-10)/(-55) - 2314/385. Let p = c + 32/5. Let 6/7 - 2/7*b**2 + p*b = 0. Calculate b.
-1, 3
Find h such that 18*h**3 + 309*h + 5*h**3 - 354*h + 575 - 28*h**3 - 1110*h + 585*h**2 = 0.
1, 115
Let p be (4/(-10))/((-2)/10). Let r = 3/21263 - -21239/170104. Factor -1/4*n + r*n**p + 0.
n*(n - 2)/8
Let a be 23 + 2*(-8)/(0 - -4). Suppose -46*w + 81 = -a*w. Find y such that -16/5*y + 0 - 2/5*y**4 + 4/5*y**w + 8/5*y**2 = 0.
-2, 0, 2
Determine o so that 5/4*o**4 + 0 - 35/4*o**3 - 10*o + 35/2*o**2 = 0.
0, 1, 2, 4
Let i(y) = -380*y - 7575. Let a be i(-20). Let r(w) be the first derivative of -a - 4/3*w**3 + 32*w - 14*w**2. Factor r(x).
-4*(x - 1)*(x + 8)
Let k(t) be the third derivative of 0*t + 5/7*t**3 - 1/56*t**4 - 1/14*t**5 + 1/280*t**6 + 0 - 168*t**2. Factor k(b).
3*(b - 10)*(b - 1)*(b + 1)/7
Let n(g) = -276*g + 2208. Let a be n(8). Let d(m) be the second derivative of a - 1/60*m**6 + 4*m + 1/24*m**5 + 0*m**2 + 0*m**3 - 1/36*m**4. Factor d(r).
-r**2*(r - 1)*(3*r - 2)/6
Let -r**4 - 15*r**2 - 70 - 78*r**2 - 1180 - 91*r**2 - 41*r**2 + 875*r + 25*r**3 = 0. What is r?
5, 10
Let y(q) be the third derivative of 0*q**3 + 11*q + 0 + 1/132*q**4 + 2*q**2 + 1/330*q**5. Factor y(k).
2*k*(k + 1)/11
Let c(r) = r**5 - r**4 + r**3 - r**2 + 2*r + 1. Let m(f) = -3*f**5 + 7*f**4 + 34*f**3 + 2*f**2 - 4*f - 2. Let k(g) = -2*c(g) - m(g). Find j such that k(j) = 0.
-4, 0, 9
Suppose 16*z = 5*q + 14*z + 439, q - 4*z = -95. Let d be 19/8 + -11 + q/(-8). Determine s, given that -3/4*s**2 - 3/2 + 21/4*s**3 + d*s**4 - 21/4*s = 0.
-2, -1, -1/3, 1
Let t(b) be the third derivative of b**6/480 + 3*b**5/80 - 5*b**4/4 - 16*b**3/3 + 43*b**2 + 5*b. Factor t(j).
(j - 8)*(j + 1)*(j + 16)/4
Let v(s) = 3*s**2 - 27*s + 170. Let a(t) = -2*t**2 + 26*t - 171. Let r(p) = -4*a(p) - 3*v(p). Factor r(x).
-(x - 6)*(x + 29)
Factor 109955 - 1052*m**2 - 67564*m - m**3 - 3*m**3 + 102313.
-4*(m - 3)*(m + 133)**2
Let n(s) = 5*s**3 + 170*s**2 + 2*s + 71. Let y be n(-34). Suppose -4*b = -y*b - 5*w + 8, -4*b + 5*w = 2. Determine g so that -1/4*g**b + 0*g + 0 = 0.
0
Let l be 136/(-748) - 5768/(-22). Factor -l*d**2 - 8448*d - 8*d**3 + 6*d**3 + 3502 + 5210.
-2*(d - 1)*(d + 66)**2
Let -15/4*m**2 + 207/4*m + 135/2 = 0. What is m?
-6/5, 15
Solve 12 + 93/8*c**3 + 3/2*c**5 - 60*c + 183/4*c**2 - 87/8*c**4 = 0.
-2, 1/4, 1, 4
Determine w so that -9*w - w**2 - 34*w + 58 - 166 - 13*w = 0.
-54, -2
Let n(y) be the third derivative of -y**6/40 - 7*y**5/4 - 4*y**4 + 34*y**3 + 5495*y**2. Find q such that n(q) = 0.
-34, -2, 1
Suppose -6*b - 15*b - 1344 = 0. Let j be 512/b - 8/(-1). Determine x so that j - 35/4*x**2 - 10*x**3 - 5/2*x - 15/4*x**4 = 0.
-1, -2/3, 0
Let l(z) be the second derivative of 5*z**7/168 - 29*z**6/24 + 13*z**5/8 + 35*z**4/6 - 908*z + 1. Let l(u) = 0. Calculate u.
-1, 0, 2, 28
Let j(q) be the first derivative of 2/45*q**5 + 1/9*q**4 - 6 - 10/27*q**3 + 0*q - 2/3*q**2. Factor j(u).
2*u*(u - 2)*(u + 1)*(u + 3)/9
Let l(u) be the second derivative of -u**6/195 - 33*u**5/130 - 55*u**4/26 + 433*u**3/39 - 18*u**2 + 56*u - 9. Let l(s) = 0. What is s?
-26, -9, 1
Suppose 36*q - 1/4*q**3 + 0 - 7/4*q**2 = 0. Calculate q.
-16, 0, 9
Let a(m) = -25*m**2 - 2745*m - 2720. Let t(i) = -9*i**2 - 915*i - 906. Let r(w) = -4*a(w) + 11*t(w). What is z in r(z) = 0?
-914, -1
Let p = -30274 - -30286. What is f in p + 13/3*f**2 + 20*f - 10/3*f**3 + 1/3*f**4 = 0?
-1, 6
Let s be 35/(-5) - -1*23. Factor 228*r + 163*r + 3*r**3 - 47*r + s*r - 69*r**2 + 432.
3*(r - 12)**2*(r + 1)
Let o = -3262033/7 - -466023. Find k, given that -o*k + 32/7*k**2 + 0 - 2/7*k**3 = 0.
0, 8
Suppose 18*a = 42*a - 6768. Let w = a + -279. Find z such that 0*z**2 + 0 - 4/5*z + 4/5*z**w = 0.
-1, 0, 1
Let m be 4/14 + 4983/77. Suppose 6 = 68*w - m*w. Factor -4/7*o + 0 - 6/7*o**3 + 2/7*o**5 - 2/7*o**4 + 10/7*o**w.
2*o*(o - 1)**3*(o + 2)/7
Suppose -758*w = -700*w - 406. Let l(h) be the second derivative of 0*h**2 - 9*h + 2/21*h**w + 3/5*h**5 + 0 + 0*h**3 - 3*h**4 + 2/3*h**6. Factor l(q).
4*q**2*(q - 1)*(q + 3)**2
Let r = 253 + -241. Let l(i) = -1156*i**2 - 260*i - 4. Let p(n) = n + 1. Let j(h) = h**2 + 4*h + 2. Let x be j(-3). Let d(y) = r*p(y) + x*l(y). Factor d(v).
4*(17*v + 2)**2
Let n(c) be the third derivative of -c**5/60 - 25*c**4/24 - 14*c**3 - c**2 - 514. Factor n(u).
-(u + 4)*(u + 21)
Suppose 0 = 49*k - 4340 + 4242. Determine p, given that -2/7*p**4 + 10/7*p**3 + k*p + 26/7*p**2 + 0 = 0.
-1, 0, 7
Let x(o) be the third derivative of -o**6/360 - o**5/36 + o**4/9 + 8*o**3/3 + 4859*o**2 - 2*o. Factor x(b).
-(b - 3)*(b + 4)**2/3
Let p be (-24)/(5/10*1/1). Let y be 72/p + 2*58/56. Suppose -8/7*o - y*o**2 - 4/7 = 0. Calculate o.
-1
Let a(w) = -w**3 + 12*w**2 + 32*w - 28. Let t be a(12). Factor -21*z**2 + z**2 + t*z**5 - 351*z**5 + 15*z**4.
5*z**2*(z - 1)*(z + 2)**2
Let u(j) = j**3 + 51*j**2 - 51*j + 96. Let w be u(-52). Suppose -276 + 100 = -w*v. Determi