k**2 = 0. Calculate k.
0, 21
Let j(y) be the first derivative of -y**4/24 - 2*y**3/3 + 19*y**2/12 + 13*y + 432. What is i in j(i) = 0?
-13, -2, 3
Let f(j) = j**3 - 16*j**2 + 25*j + 46. Let q be f(14). Factor -10*u - 2*u**q - 14*u**3 + 231*u**2 - 485*u**2 + 232*u**2.
-2*u*(u + 1)**2*(u + 5)
Suppose 4*g - 2*d - 34 = 0, -6*d + 4*d = 2. Factor g*c - 64/7 - 2/7*c**3 - 8/7*c**2.
-2*(c - 2)**2*(c + 8)/7
Factor -2/9*l**3 - 2232 + 176*l + 10/9*l**2.
-2*(l - 18)**2*(l + 31)/9
Let b(j) be the first derivative of j**6/3 + 596*j**5/5 + 14390*j**4 + 544272*j**3 - 7990272*j**2 + 33958656*j - 3363. Factor b(k).
2*(k - 4)**2*(k + 102)**3
Suppose -17*x = -5*x - 36 + 12. Factor 35/2*n**x + 25/2 + 5/2*n**3 + 55/2*n.
5*(n + 1)**2*(n + 5)/2
Let u = -830773 - -830775. Factor -1/8*z**4 - 13/8*z**u + 3/2*z + 3/4*z**3 - 1/2.
-(z - 2)**2*(z - 1)**2/8
Let i = -99/8950 - -411997/26850. Factor 176*z**2 - 529/3 - i*z + 1/3*z**4 + 46/3*z**3.
(z - 1)*(z + 1)*(z + 23)**2/3
Let s be (17353/(-14))/67 - -35. Factor -9*k**3 + 147/4 + s*k**2 + 3/4*k**4 + 63*k.
3*(k - 7)**2*(k + 1)**2/4
Factor 496/9*p**2 + 164/3 + 986/9*p + 2/9*p**3.
2*(p + 1)**2*(p + 246)/9
Let q(h) be the first derivative of -h**5 - 50*h**4 - 910*h**3/3 - 620*h**2 - 525*h - 675. Factor q(o).
-5*(o + 1)**2*(o + 3)*(o + 35)
Let q be -5 + 11 + 0 + (2 - 0). Suppose -q = 4*t - 4*u, 28 = 3*t - 2*t + 5*u. Factor 11*i**5 - 6*i**5 + t*i**4 + 4*i**2 - 6*i**3 - 6*i**3.
i**2*(i - 1)*(i + 2)*(5*i - 2)
Suppose l = 5*l. Suppose 0 = -3*v - 6, r - 37 = -l*r + 3*v. Factor 4*d - 24*d**3 + 10*d**4 + 54*d**2 - r*d - 12*d**3 - d**5.
-d*(d - 3)**3*(d - 1)
Let n(d) be the first derivative of 3/7*d + 1/7*d**3 - 40 - 3/7*d**2. Factor n(s).
3*(s - 1)**2/7
Let f = 359944 - 359744. Determine k, given that 0*k**2 - 500 - f*k + 4/5*k**4 + 8*k**3 = 0.
-5, 5
Determine o so that 8/5*o**3 - 2/5*o**5 + 0*o + 8/5*o**2 - 2/5*o**4 + 0 = 0.
-2, -1, 0, 2
Suppose -30 + 0 = -6*p. Let z(b) = -b + 18. Let v be z(p). Suppose -7 - 3*o**2 - v + 2 + 21*o = 0. What is o?
1, 6
Let f(x) be the second derivative of 0 + 1/40*x**5 - 15*x + 0*x**2 - 11/6*x**3 - 3/16*x**4 - 1/720*x**6. Let o(j) be the second derivative of f(j). Factor o(y).
-(y - 3)**2/2
Let r(z) be the third derivative of -z**7/525 + z**6/100 + 11*z**5/150 - z**4/20 - 2*z**3/3 - 929*z**2 - 1. What is k in r(k) = 0?
-2, -1, 1, 5
Let n = -7087 - -7091. Let o be (1 - 3)*6/(-36). Factor -1/3*h**2 + 1/9*h**3 + 0 - 1/9*h + o*h**n.
h*(h - 1)*(h + 1)*(3*h + 1)/9
Let b(a) be the third derivative of 3*a**8/112 - 2*a**7/35 - 11*a**6/120 - a**5/30 + 12*a**2 - 76. Factor b(u).
u**2*(u - 2)*(3*u + 1)**2
Let a = 3 - -2. Let u be -1 + 33/3 - 2/4*14. What is q in -6*q**2 - 7*q + 24 + 0*q**3 - 5*q - 2*q**u + a*q**3 = 0?
-2, 2
Let m(q) be the third derivative of q**5/570 - 29*q**4/38 - 175*q**3/57 - q**2 + 10. Let m(t) = 0. What is t?
-1, 175
Let r be 1/2*(-73 + 71) + 6/2. Factor 5/6*n**3 - 25/6*n**r + 20/3 + 5/3*n.
5*(n - 4)*(n - 2)*(n + 1)/6
Let y = 7 - 7. Let z = 1/16174 - -32339/145566. Factor -2/9*s**2 + z + y*s.
-2*(s - 1)*(s + 1)/9
Suppose 2*n + 5*k = -14, -3*n + 14 = -5*k - 15. Determine y so that -16*y + 324*y**3 - 304*y**n + 3*y**5 - 7*y**5 = 0.
-2, -1, 0, 1, 2
Let v(z) be the first derivative of 0*z - 127 + 2/3*z**3 + 2*z**2. Factor v(c).
2*c*(c + 2)
Let n be (12 - 59) + (48 - 150/210). Suppose 7 + 1 = 4*w. What is o in 0 + 2/7*o**3 + 0*o - 4/7*o**w + 4/7*o**4 - n*o**5 = 0?
-1, 0, 1, 2
Let r be 7 + -2 - 4/(-12)*-39. Let d be 2 + (-14 - r) + (-11)/(-2). Determine v, given that d*v**2 - 3/2*v - 3/2*v**4 + 0 + 3/2*v**3 = 0.
-1, 0, 1
Let o = 2711 + -5227/2. Let l(q) be the first derivative of -9 - 125/4*q**4 + 275/3*q**3 + 45*q - o*q**2. Determine v so that l(v) = 0.
3/5, 1
Suppose 10766 - 1841 = 17*u. Let z = -523 + u. Find v such that 1/2*v**z - 2*v - 2 + 1/2*v**3 = 0.
-2, -1, 2
Suppose -n = -5*z - 30, -5*n - z + 240 = 4*z. What is b in 29*b**2 - 512*b + 339*b**2 - 48*b - n*b**3 - 83*b**2 + 320 = 0?
1, 8/3
Let n = 618514 - 618510. Factor 4/3 - 4/3*s**n - 8/3*s**3 + 0*s**2 + 8/3*s.
-4*(s - 1)*(s + 1)**3/3
Let c be 2*10/(-4) + 40937/7839. Solve 0*p**2 - 256/9*p + 16/9*p**3 - c*p**4 + 512/9 = 0.
-4, 4
Let s(y) be the first derivative of -3 - 4/11*y**3 + 5/22*y**4 + 0*y**2 + 16/55*y**5 - 1/11*y**6 + 0*y. Determine u, given that s(u) = 0.
-1, 0, 2/3, 3
Let a(j) be the second derivative of -56*j + 55/4*j**4 - 120*j**3 + 160*j**2 + 0 - 1/2*j**5. Factor a(l).
-5*(l - 8)**2*(2*l - 1)
Let o = 253 + -151. Factor 4*r**4 + 8 - o + 9*r - 34 + 24*r**2 - 137*r + 28*r**3.
4*(r - 2)*(r + 1)*(r + 4)**2
Determine c, given that -730212*c**2 + 183 + 675*c + 1147 + 730217*c**2 = 0.
-133, -2
Let b(i) = -i**3 + 2*i**2 + 2*i + 7. Let g be b(3). Suppose u + 6 = g*u. Factor 3*z**4 + 8*z + 6*z**3 - 2*z**2 - z**u - 14*z.
3*z*(z - 1)*(z + 1)*(z + 2)
Let o(d) = -16*d**2 - 2776*d + 8412. Let s(m) = -51*m**2 - 8325*m + 25239. Let v(h) = 13*o(h) - 4*s(h). Find x such that v(x) = 0.
-700, 3
Let d(j) be the third derivative of -j**8/24 + 2*j**7/35 + 2*j**6/15 - j**5/5 - j**4/12 + 3*j**2 + 139. Suppose d(v) = 0. What is v?
-1, -1/7, 0, 1
Let k(n) be the first derivative of 2*n**5/75 + n**4/5 - 16*n**3/45 - 32*n**2/5 - 256*n/15 - 2427. Solve k(z) = 0.
-4, -2, 4
Let b(s) be the second derivative of s**6/15 - 9*s**5/5 + 83*s**4/6 - 22*s**3 - 39*s - 1. Determine z so that b(z) = 0.
0, 1, 6, 11
Let i(u) = -176*u - 2992. Let p be i(-17). Let d(w) be the second derivative of 1/50*w**6 + p*w**4 - 2/5*w**3 + 0*w**2 + 13*w + 9/100*w**5 + 0. Factor d(g).
3*g*(g - 1)*(g + 2)**2/5
Let c(n) = n**3 - 36*n**2 + n - 27. Let z be c(36). Let q be (-52)/(-65) - 6/z. Factor -8/15*m + 0 - q*m**2.
-2*m*(m + 4)/15
Let 15*o - 9/5*o**4 - 1/5*o**5 + 6/5*o**3 + 27/5 + 62/5*o**2 = 0. Calculate o.
-9, -1, 3
Let n(r) = -238*r**2 - 729*r + 137. Let c(h) = 80*h**2 + 242*h - 46. Let t(a) = 7*c(a) + 2*n(a). Suppose t(g) = 0. What is g?
-3, 4/21
Let f = -539655/7 + 77094. Let c = 1 - 1. Suppose -f*x**2 + 3/7*x + c = 0. Calculate x.
0, 1
Let z = 61 - 57. Solve 6*t**3 - 4*t**4 - 3*t**3 - 3*t**3 + 8*t**2 + z*t**3 = 0.
-1, 0, 2
Suppose -5*h = -2*h - 2*i - 18, -5*h - 4*i + 52 = 0. Suppose 26 = 6*x + h. What is t in 10*t**2 - 20*t**x + 115*t - 20 + 15*t**2 - 10 = 0?
-2, 1/4, 3
Let r be (98/(-168) + (-3)/(-6))/(16/(-64)). Suppose r*i**2 + 7/3*i + 0 = 0. What is i?
-7, 0
Let n be (39 + (-78 - -39))*3/((-6)/2). Solve 10/13*w - 22/13*w**2 + n - 2/13*w**4 + 14/13*w**3 = 0 for w.
0, 1, 5
Determine i, given that 10 + 3/8*i**2 - 40*i**3 + 241/8*i - 1/2*i**4 = 0.
-80, -1/2, 1
Let a(c) be the third derivative of 0 + 0*c**4 + 36*c**2 + 0*c + 8/3*c**3 - 1/15*c**5. Find p such that a(p) = 0.
-2, 2
Let d = 2622 + -39329/15. Let y(n) be the second derivative of 29*n + d*n**3 + 0 + 1/50*n**5 - 1/15*n**4 + 0*n**2. Factor y(h).
2*h*(h - 1)**2/5
Let o be 466/10 - (2325 - 2288). Let 252/5*q - 312/5*q**2 - o + 39/5*q**3 - 21/5*q**5 + 18*q**4 = 0. Calculate q.
-2, 2/7, 1, 4
Let d(j) be the second derivative of -1/12*j**3 - 1/48*j**4 - 81*j + 0 + j**2. Suppose d(p) = 0. What is p?
-4, 2
Let r = -194 + 131. Let x = r + 66. Let s(t) = -5*t**3 - 4*t**2. Let g(p) = p**3 + p**2 + p. Let l(c) = x*s(c) + 12*g(c). Factor l(o).
-3*o*(o - 2)*(o + 2)
Let n(q) be the second derivative of -1/11*q**4 - 8/33*q**3 - 1/110*q**5 + 0*q**2 - 1 + 5*q. Suppose n(m) = 0. What is m?
-4, -2, 0
Suppose -4*d - 2*d - 60 = 0. Let v be (-5)/((-25)/d) - -8. Determine l, given that -2*l**2 + 5*l**2 - 7 - v*l + 10 = 0.
1
Let t(k) be the third derivative of -37/60*k**5 - 1/210*k**7 + 0*k + 204*k**2 + 11/120*k**6 - 3*k**3 + 15/8*k**4 + 0. Factor t(a).
-(a - 6)*(a - 3)*(a - 1)**2
Let q(l) = -240*l + 10324. Let z be q(43). Let v(y) be the second derivative of 0*y**2 + 0 - 36*y + 2/21*y**3 + 1/15*y**6 + 1/14*y**z - 6/35*y**5. Factor v(j).
2*j*(j - 1)**2*(7*j + 2)/7
Let b(z) = 18326825*z**2 + 138140*z + 220. Let x(d) = -1409757*d**2 - 10626*d - 17. Let o(g) = 3*b(g) + 40*x(g). Solve o(n) = 0 for n.
-2/531
Factor -117*f - 9*f**4 - 101*f - 189*f**2 + 84*f**3 + 272*f.
-3*f*(f - 6)*(f - 3)*(3*f - 1)
Let m be (-63540)/(-17775) + 20/790. Let 39/5*t + 3*t**2 - m = 0. Calculate t.
-3, 2/5
Suppose 4*b + 10 = -10. Let i be b*((-8)/52 + 32/1560). Solve -i + 2/3*a**2 + a = 0.
-2, 1/2
Let o(f) be the third derivative of f**7/1680 - f**6/240 + f**5/480 + f**4/