r + q = 0.
0, 1
Let i be 6/(-51) - (-2886)/1989. Factor -16/3*a**2 - i*a**3 + 0 - 4*a.
-4*a*(a + 1)*(a + 3)/3
Let y(i) be the second derivative of i**6/10 + 21*i**5/10 - 3*i**4 - 76*i**3 + 336*i**2 - i - 1878. Factor y(m).
3*(m - 2)**2*(m + 4)*(m + 14)
Determine s, given that 2/3*s**4 - 336*s + 0 + 1016/3*s**2 - 260/3*s**3 = 0.
0, 2, 126
Let c be 8/(-12)*1 + 253/(-3). Let h = 176 + c. Factor 0*k - h - 6*k - 2*k**2 + 87.
-2*(k + 1)*(k + 2)
Let d(m) be the third derivative of m**5/100 - 519*m**4/40 - 52*m**3 + 895*m**2 + m. Factor d(r).
3*(r - 520)*(r + 1)/5
Suppose 456*g + 9 = -17 + 26. Factor g*k + 4/5 + 1/5*k**3 - 3/5*k**2.
(k - 2)**2*(k + 1)/5
Let d be 12*(-5)/10 - 2*-2. Let u be (-12)/(-9) + d/(-3)*1. Solve -30*p**u - 25*p + 34*p - 5*p**3 - 34*p = 0.
-5, -1, 0
Let k(h) be the third derivative of h**8/42 + 142*h**7/105 + 9*h**6/10 - 284*h**5/15 - 70*h**4/3 - 3712*h**2. Let k(c) = 0. What is c?
-35, -2, -1/2, 0, 2
Find f, given that -f**2 + 15*f - 73 - 78*f - 120 - 41*f - 11 = 0.
-102, -2
Suppose 3*c - 6*c + 12 = 0. Let x(r) = r**2 - 5*r - 125. Let b be x(-10). What is z in -13*z - 3*z**4 + b*z**2 - c*z**2 + 31*z = 0?
-2, -1, 0, 3
Suppose -5*a = -3*w - 295, 9*w = 5*a - 135 - 130. Solve -18/5*i**5 + a*i**3 + 28/5*i - 78/5*i**4 - 178/5*i**2 + 0 = 0 for i.
-7, 0, 1/3, 2
Let o(d) = -7*d**4 - 22*d**3 - 36*d**2 - 9*d + 3. Let b = 365 + -359. Let r(l) = l**4 - l**3 - 2*l**2 - 1. Let i(f) = b*r(f) + 2*o(f). Factor i(y).
-2*y*(y + 3)**2*(4*y + 1)
Factor 4*c**2 + 190*c + 2346 + 950 + 716 + 888 + 538*c.
4*(c + 7)*(c + 175)
Determine g so that 540/11*g**2 + 144722/11 + 1/11*g**3 + 73437/11*g = 0.
-269, -2
Let d(s) be the third derivative of 1/720*s**6 + 3*s**3 - 2*s**2 - 179*s + 0*s**4 + 0 - 1/40*s**5. Factor d(t).
(t - 6)**2*(t + 3)/6
Let n be 13/(390/72) - 4/10. Let -25*l**n - 11*l**2 + 108*l + 4*l**3 - l**3 = 0. Calculate l.
0, 6
Factor 288/7 - 162/7*f + 22/7*f**2.
2*(f - 3)*(11*f - 48)/7
Let o(u) be the first derivative of 2*u**3/45 + 7*u**2/3 + 156*u/5 + 4027. Suppose o(d) = 0. Calculate d.
-26, -9
Let c = -1675/2 - -18455/22. Let m(i) be the first derivative of -22 + 2/11*i**3 + 24/11*i - c*i**2. Factor m(u).
6*(u - 4)*(u - 1)/11
Suppose -a - 706 - 490 = -5*g, 5 = -5*a. Find h such that 18*h**3 - 242*h**2 - g*h**2 + 473*h**2 - 24*h + 12*h**4 + 2*h**5 = 0.
-3, -2, 0, 1
Let u(x) be the third derivative of 0*x + 0*x**4 + 4/945*x**7 + 18 + 1/108*x**6 + x**2 + 0*x**3 + 1/270*x**5. Factor u(q).
2*q**2*(q + 1)*(4*q + 1)/9
Let c = -4782 + 4785. Let o(p) be the first derivative of -8 + 4/7*p - 3/7*p**2 + 2/21*p**c. Factor o(t).
2*(t - 2)*(t - 1)/7
Factor -272*j**2 + 4*j**3 + 90*j + 74*j + 117*j + 247*j.
4*j*(j - 66)*(j - 2)
Let u(c) be the first derivative of -12*c + 1/2*c**3 + 3 + 1/12*c**4 + c**2. Let x(g) be the first derivative of u(g). Determine j so that x(j) = 0.
-2, -1
Let w(n) be the third derivative of -n**7/70 - 79*n**6/40 + n**5/20 + 79*n**4/8 + 1796*n**2. Factor w(s).
-3*s*(s - 1)*(s + 1)*(s + 79)
Let a(u) = u**3 + 157*u**2 - 155*u - 3. Let f be a(1). Determine b so that f*b**2 + 1/3*b**3 - 1/3*b + 0 = 0.
-1, 0, 1
Let s(f) = -2*f**2 + 74*f + 78. Let g be s(38). Factor 160 + 60*v**g - 7*v**3 - 68*v - 98*v + 2*v**3 + 12*v - 26*v.
-5*(v - 8)*(v - 2)**2
Let k(n) be the second derivative of n**4/108 + 157*n**3/18 + 235*n**2/9 - 3220*n. Find i such that k(i) = 0.
-470, -1
Let q(t) be the first derivative of 20*t + 1/5*t**5 + 24 - 61/2*t**2 + 21*t**3 - 23/4*t**4. Factor q(y).
(y - 20)*(y - 1)**3
Suppose -45 = 5*j + a, -5*j + 17 = 4*a + 62. Let l be (16/(-32))/(j/8 + 1). Factor 38*n + n**2 + 8*n**3 - l*n**2 + 36*n**2 - 12 + 5*n**2.
2*(n + 2)*(n + 3)*(4*n - 1)
Factor 311/3*g - 155/3 + 1/3*g**3 - 157/3*g**2.
(g - 155)*(g - 1)**2/3
Suppose 128/3 - 480*f + 1350*f**2 = 0. What is f?
8/45
Let k(v) = -1102*v - 6609. Let f be k(-6). What is r in 8/17*r - 10/17*r**f + 6/17*r**4 + 0 + 2/17*r**5 - 6/17*r**2 = 0?
-4, -1, 0, 1
Let l(w) = 8*w**2 - 18*w + 24. Let m(o) = -2*o - 29 - 2*o**2 - 28 + o**2 + 54. Let k(y) = -l(y) - 5*m(y). Let k(t) = 0. Calculate t.
1/3, 9
Let w(o) be the first derivative of -28*o**6/3 + 783*o**5/5 - 2009*o**4/2 + 8888*o**3/3 - 3504*o**2 - 128*o + 10673. What is i in w(i) = 0?
-1/56, 2, 4
Let w = 0 - 28. Let v = w - -109. Suppose 10*m - v*m**3 + 132*m**4 + 6*m**3 - 24*m**2 + 2*m - 45*m**5 = 0. Calculate m.
-2/5, 0, 1/3, 1, 2
Let x = -10324/93 - -3524/31. Factor 1/3*m**3 + x - 10/3*m + 1/3*m**2.
(m - 2)*(m - 1)*(m + 4)/3
Let u = -77207/4 - -19302. Let k(b) be the first derivative of -1/8*b**4 + 1/30*b**3 + u*b**2 - 1/50*b**5 - 33 + 0*b. Factor k(h).
-h*(h - 1)*(h + 1)*(h + 5)/10
Determine p, given that 130 - 910*p**2 + 745*p**3 + 9293*p - 18589*p + 30*p**4 + 9301*p = 0.
-26, -1/3, 1/2, 1
Determine k, given that 2*k**2 - 4106700 + 2*k**2 - 9*k**2 + 2*k**2 + 18*k + 7002*k = 0.
1170
Let p(v) be the second derivative of 5*v**7/168 - 7*v**6/24 + 11*v**5/16 - 25*v**4/48 - 164*v + 1. Factor p(h).
5*h**2*(h - 5)*(h - 1)**2/4
Let b = 27/17705 + 566479/53115. Let j = 61/5 + -143/15. Determine u so that j + b*u + 14/3*u**2 = 0.
-2, -2/7
Suppose -256*o = -155*o - 158*o + 798. Let y(i) be the second derivative of 3 - o*i - 6/11*i**2 - 1/66*i**4 - 5/33*i**3. Determine n so that y(n) = 0.
-3, -2
Let c(y) be the second derivative of -y**5/45 + y**4/18 + 29*y**2/2 + 19*y. Let g(r) be the first derivative of c(r). Factor g(h).
-4*h*(h - 1)/3
Factor 57*m - 35*m**2 + 13/3*m**3 + 1/3*m**4 + 0.
m*(m - 3)**2*(m + 19)/3
Suppose 4*l = -5*k + 367, -61*k = -60*k - 4*l - 59. Factor -40*i**2 - 39*i**2 - 3*i**3 + k*i**2 - 6*i + 36 + 5*i**3.
2*(i - 3)**2*(i + 2)
Let b(o) = -o**3 - 3*o**2 - 10*o - 12. Let z be b(-3). Let l be 104/12 - z/(-24)*-8. What is c in 0*c - 2/3*c**2 + l = 0?
-2, 2
Determine u, given that -17496/5*u**2 + 2916/5*u**3 + 3/5*u**5 + 0 + 0*u - 162/5*u**4 = 0.
0, 18
Let u(y) be the second derivative of 2 + 0*y**2 - 1/2*y**4 - 3*y**3 + 1/2*y**5 - 1/15*y**6 + 6*y. Factor u(t).
-2*t*(t - 3)**2*(t + 1)
Let a(u) = u**3 + 48*u**2 + 1. Let w(t) = 25*t**4 - 15*t**3 - 340*t**2 + 40*t - 5. Let o(h) = 5*a(h) + w(h). Factor o(c).
5*c*(c - 2)*(c + 2)*(5*c - 2)
Factor 7*h**4 - 4/7 - 4*h**3 - 45/7*h**2 + 4*h.
(h - 1)*(h + 1)*(7*h - 2)**2/7
Let s(z) = -6*z - 1. Let x be s(-1). Let r = x - 1. Find l, given that l**4 - 4*l**4 - 4*l + 4*l**2 + 0*l + r*l**3 - l**4 = 0.
-1, 0, 1
Let d be (8/(-12))/((-5)/15). Factor -11*k - 37*k - 2*k**d - 30 + 16*k.
-2*(k + 1)*(k + 15)
Suppose 40*p + 3*n = 43*p + 9, 3*p = -4*n + 33. Factor -28/5*g**2 + 0*g + 0 - 2/5*g**p.
-2*g**2*(g + 14)/5
Suppose o - 4 = 3*r, 2*r = -17*o + 12*o + 88. Suppose -19*u + 27*u - o = 0. Solve -2/3*n**u + 1/3*n**4 - 1/3*n - 1/3*n**5 + 2/3*n**3 + 1/3 = 0 for n.
-1, 1
Suppose 0 = 5*r + 2905 - 2925. Factor -47*g**2 - 726 - 84 + 588*g**4 + 582*g**r + 75*g**3 - 1175*g**4 - 1035*g - 98*g**2.
-5*(g - 9)**2*(g + 1)*(g + 2)
Let t(j) = -j**4 + 2*j**2 + 3. Let q(a) = -a**4 - 9*a**3 + 4*a**2 + 39*a - 9. Let z(y) = 5*q(y) - 15*t(y). Factor z(d).
5*(d - 3)**2*(d + 2)*(2*d - 1)
Let m(z) = 34*z**4 - 121*z**3 - 624*z**2 - 848*z - 343. Let x(u) = 8*u**4 - 30*u**3 - 156*u**2 - 212*u - 86. Let n(c) = 2*m(c) - 9*x(c). Factor n(b).
-4*(b - 11)*(b + 1)**2*(b + 2)
Let b(w) be the first derivative of -7 - 56*w**2 - 65 - 16*w - 14 + 27*w**4 - 52*w**3. Factor b(g).
4*(g - 2)*(3*g + 1)*(9*g + 2)
Suppose 24*m**3 - 17 - 47*m**4 - 17 - 13 + 47 + 13*m**5 = 0. What is m?
0, 8/13, 3
Let a(j) = j**2 + 3*j. Let u(l) = -6*l + 10. Let r(q) = -q + 2. Let n(t) = 5*r(t) - u(t). Let p(v) = -4*a(v) + 4*n(v). Factor p(i).
-4*i*(i + 2)
Let d(m) be the second derivative of m**5/30 + m**4/18 - 14*m**3/9 - 8*m**2 - 2*m + 1839. Factor d(x).
2*(x - 4)*(x + 2)*(x + 3)/3
Let n(a) = -3*a**3 - 967*a**2 - 1950*a - 951. Let k(l) = l**3 + 483*l**2 + 973*l + 477. Let s(y) = -15*k(y) - 6*n(y). Let s(p) = 0. What is p?
-1, 483
Let q(x) be the first derivative of -5/4*x**4 + 20*x - 190 - 20/3*x**3 + 5/2*x**2. Factor q(g).
-5*(g - 1)*(g + 1)*(g + 4)
Let c = -14511 + 14516. Let z(a) be the first derivative of -5/3*a**3 - 5/2*a**2 - 29 + c*a + 5/4*a**4. Find k, given that z(k) = 0.
-1, 1
Let 54 - 27*v**3 + 5*v - 23*v**2 - 19 - 12*v**2 + 6*v**3 + 16*v**3 = 0. What is v?
-7, -1, 1
Let x(d) be the second derivative of -3*d**5/190 + 89*d**4/114 - 425*d**3/57 - 3757*d**2/19 + 1