*d**2 + 8/3*d**3 - 1/6*d**b + 0 - 4*d. Determine z so that n(z) = 0.
4
Let l(p) = 3*p**3 + 3*p - 2. Let h(n) = 58*n**3 - 256*n**2 + 1026*n - 756. Let f(a) = h(a) - 18*l(a). Factor f(c).
4*(c - 60)*(c - 3)*(c - 1)
Suppose -11*h + 32 = 5*h. Let l = 16 - 10. Solve 5 + 0*x - 3 - 2*x**2 + h*x - l*x**3 + 4*x**3 = 0.
-1, 1
Let i(n) be the third derivative of -n**8/1512 + 2*n**7/105 - n**6/60 - 12*n**5/5 - 12*n**4 + 4708*n**2. Factor i(z).
-2*z*(z - 12)**2*(z + 3)**2/9
Determine o, given that 2/13*o**2 - 352/13 + 10/13*o = 0.
-16, 11
Factor -2*t**5 - 5*t - 16 - 4*t**2 + t**5 - t**5 - t + 8*t**3 + 20.
-2*(t - 1)**3*(t + 1)*(t + 2)
Factor 3/2*l**2 + 2*l + 1/4*l**3 + 0.
l*(l + 2)*(l + 4)/4
Let r(z) be the second derivative of 5*z**4/12 - 1625*z**3/6 + 810*z**2 - 2*z - 3044. Factor r(w).
5*(w - 324)*(w - 1)
Let m be (211 + -211)*((-2 - -1) + 2). Let 5*s**4 + 0*s - 2*s**3 - 6*s**4 - 143*s**2 + 144*s**2 + 2*s + m*s**3 = 0. What is s?
-2, -1, 0, 1
Suppose -16*o - 15 = -13*o. Let i be (o/4)/(10/(-6)). Factor -3/4 + 0*m + i*m**2.
3*(m - 1)*(m + 1)/4
Suppose 3*r - 12 = -3*t, -t - 6*r = -2*r - 4. Suppose 5*d = -t + 14. Factor -4*x**4 - 3*x**2 - 2*x**5 - 6*x**4 - x**d + 2*x**4 - 10*x**3.
-2*x**2*(x + 1)**2*(x + 2)
Let y be 3903/(-5) - (8 - 570/75). Let g = y + 2344/3. Let 0*i + 0 - 1/3*i**5 + g*i**3 - 2/3*i**4 + 2/3*i**2 = 0. Calculate i.
-2, -1, 0, 1
Let i = -68751 - -756269/11. Factor -2/11*a**3 + 0 + i*a**2 - 6/11*a.
-2*a*(a - 3)*(a - 1)/11
Let y(q) be the third derivative of -3*q**8/28 - 20*q**7/21 - 19*q**6/10 + 8*q**4/3 - 260*q**2 - 2*q + 4. Let y(s) = 0. Calculate s.
-4, -1, 0, 4/9
Let i(f) be the first derivative of -3/2*f**4 - 14/3*f**3 + 1/6*f**6 + 1/5*f**5 + 8 - 3*f - 11/2*f**2. Find y, given that i(y) = 0.
-1, 3
Let a(m) be the second derivative of 2*m**7/21 - 11*m**5/5 + 6*m**4 - 16*m**3/3 - m + 708. Factor a(k).
4*k*(k - 2)*(k - 1)**2*(k + 4)
Let x = -37109/25 + 37604/25. Factor -x + 42/5*l - 3/5*l**2.
-3*(l - 11)*(l - 3)/5
Suppose 28*r - 29*r + 51 = 0. Find i, given that -r*i**4 + 40*i**3 + 4 + 406*i + 47*i**2 - 209*i - 237*i = 0.
-1, 2/17, 2/3, 1
Let y(f) be the third derivative of f**7/1680 - f**6/90 + f**5/12 - f**4/3 - 13*f**3/3 + 71*f**2. Let v(c) be the first derivative of y(c). Factor v(n).
(n - 4)*(n - 2)**2/2
Factor -170/7*a - 62/7*a**3 - 2/7*a**4 - 174/7*a**2 - 8.
-2*(a + 1)**3*(a + 28)/7
Let t be -27*(40/70)/((-1404)/182). What is n in 0 - 36/5*n**t - 3/5*n**5 + 12/5*n**4 + 6/5*n**3 - 27/5*n = 0?
-1, 0, 3
Factor 0 - 51/2*w**3 + 1/2*w**5 + 0*w**4 - 24*w + 49*w**2.
w*(w - 6)*(w - 1)**2*(w + 8)/2
Let s(n) be the second derivative of -n**4/8 + 11*n**3/4 - 21*n**2 - 979*n. Let s(t) = 0. What is t?
4, 7
Let c(x) be the first derivative of -16/9*x**3 - 2/3*x - 7/12*x**4 - 59 - 11/6*x**2. Factor c(h).
-(h + 1)**2*(7*h + 2)/3
Let x be 64*(28/(-8) - -4). Let v = x - 30. Determine u, given that -2*u**5 + 6*u + 2 - 2*u**4 + 4*u**v - 2*u**5 + 2*u**5 - 4*u**3 - 4*u**4 = 0.
-1, 1
Let b be ((-10)/(-6))/((-8)/(-24)). Factor b*i**4 - 2*i**5 + 2*i**2 - 3*i**4 + 0*i**3 + 4*i**4 - 6*i**3.
-2*i**2*(i - 1)**3
Let w be (0 - -5) + 355/(-213). Let s(i) be the first derivative of -11 - 25/9*i**3 + 5/3*i + w*i**2. Determine p, given that s(p) = 0.
-1/5, 1
Let f(r) be the third derivative of -r**8/6720 + r**7/560 + r**6/60 - 2*r**5/15 + 2*r**2 + 40*r. Let k(w) be the third derivative of f(w). Factor k(j).
-3*(j - 4)*(j + 1)
Factor 109*b**3 + 53*b**3 - 1238*b**2 - 1984 - 7895*b**2 - 767*b**2 - 8896*b.
2*(b - 62)*(9*b + 4)**2
Let y(z) be the first derivative of z**4/14 + 6*z**3/7 - 3*z**2 + 22*z/7 - 468. Factor y(f).
2*(f - 1)**2*(f + 11)/7
Let j = -55974 - -55976. Factor 16 + 52/5*l**j - 128/5*l - 4/5*l**3.
-4*(l - 10)*(l - 2)*(l - 1)/5
Let n(m) be the third derivative of m**6/720 - m**5/120 - 143*m**4/48 + 3887*m**3/36 - 3325*m**2. Factor n(w).
(w - 13)**2*(w + 23)/6
Let p(h) = -213 + 27*h - 220 + 382. Let b be p(2). Solve 0 - 6*s**4 + 0*s + 6*s**2 - 3/2*s**b + 3/2*s**5 = 0.
-1, 0, 1, 4
Let f(x) be the first derivative of -1/2*x**6 + 0*x**2 + 9/4*x**4 - 95 - 6/5*x**5 + 0*x**3 + 0*x. Solve f(b) = 0.
-3, 0, 1
Let k(o) be the second derivative of 0 + 21/4*o**2 + 1/24*o**4 + 5/6*o**3 + 118*o. Suppose k(f) = 0. What is f?
-7, -3
Let n = 111 + -99. Let s = 41/3 - n. Factor 10/3*j**3 + s*j**4 - 10/3*j - 5/3 + 0*j**2.
5*(j - 1)*(j + 1)**3/3
Let j(q) = -q**2 - 5*q + 55. Let g(d) = -d**2 - 2*d + 57. Let l(s) = 4*g(s) - 3*j(s). Let a be l(12). Find x such that 4/3 - 10/9*x**2 + 46/9*x - 8/9*x**a = 0.
-3, -1/4, 2
Let x = 7 + -5. Determine p so that 2761*p**4 - 2765*p**4 + 5*p**2 - 1 + 3*p**x - 4*p**3 + 1 = 0.
-2, 0, 1
Suppose -2*n = -4*i - 129 - 141, 3*n - i - 380 = 0. Let j = n - 121. Factor a**4 + 26*a**3 - 30*a**3 + a**j.
2*a**3*(a - 2)
Determine o so that 0 + 0*o - 2/3*o**3 + 340*o**2 = 0.
0, 510
Factor 288/5*w**2 + 4368/5*w + 16562/5.
2*(12*w + 91)**2/5
Suppose 406*w + 24 = 410*w. Determine i, given that -9*i + 20*i**3 + 10*i**2 - 163 + 163 - 10*i**4 - w*i - 5*i**5 = 0.
-3, -1, 0, 1
Let d(v) be the third derivative of -1/360*v**6 + 1/180*v**5 - 102*v**2 + 0*v + 0*v**4 + 0*v**3 - 1. Solve d(q) = 0.
0, 1
Suppose -4*n - 2 = 3*o, -4*n = -3*o - 0*n + 14. Factor -127*p**2 + 2*p**3 - o*p + 129*p**2 - 2*p**4 + 0*p**4.
-2*p*(p - 1)**2*(p + 1)
Let l(g) = 3*g**2 - 15*g - 195. Let u be l(-6). Solve 9/5*a**u - 3/5*a + 0 - 6/5*a**2 = 0 for a.
-1/3, 0, 1
Determine u, given that 2*u**3 - 98 - 247*u**2 + 2*u - 190 - 108 + 43*u**2 + 596*u = 0.
1, 2, 99
Determine u, given that -94*u**2 + 19*u**2 - 639 - 622 - 170*u + 5*u**3 + 1261 = 0.
-2, 0, 17
Let m(r) be the second derivative of -r**7/504 - 13*r**6/216 - 2*r**5/3 - 5*r**4/2 + 14*r**3 - 26*r. Let b(z) be the second derivative of m(z). Factor b(n).
-5*(n + 1)*(n + 6)**2/3
Solve 492/5 + 2/5*j**2 + 494/5*j = 0.
-246, -1
Let o(d) = d**2 - d. Let v(q) = -2*q**2 + 32*q + 63. Let f(a) = -o(a) + v(a). Let i(k) = k**2 - 8*k - 16. Let r(z) = 4*f(z) + 15*i(z). Factor r(t).
3*(t + 2)**2
Suppose -61*a + 14*a**5 - a**2 - a**2 + 2*a**4 + 0*a**2 - 14*a**3 + 61*a = 0. What is a?
-1, -1/7, 0, 1
Let -168 + 3*u**4 - 5754710*u**3 + 9*u + 165*u**2 + 5754656*u**3 + 45*u = 0. Calculate u.
-1, 1, 4, 14
Let h = -380222/7 + 54601. Let j = 287 - h. Factor 8/7 + 4/7*o**5 + 64/7*o**2 + 8*o**3 + 36/7*o + j*o**4.
4*(o + 1)**4*(o + 2)/7
Suppose -1484 = -4*u + 4*d, -18*d = -3*u - 19*d + 1101. Suppose 17 = n - 5*b, -2*b - u = -2*n - 358. Factor 18*h**3 + 180*h**n + 3/5*h**4 + 0 + 600*h.
3*h*(h + 10)**3/5
Let v(i) = 6*i**2 + 27*i - 13. Let w be v(-5). Let j = 213/260 + -1/52. Factor j*y + 0 - 14/15*y**3 - 38/15*y**w.
-2*y*(y + 3)*(7*y - 2)/15
Let b(z) = -z**3 + 4*z**2 + z + 1. Let v(t) = 25*t**3 - 1470*t**2 + 69582*t + 19982. Let r(p) = 90*b(p) + 5*v(p). Factor r(c).
5*(c - 100)**2*(7*c + 2)
Suppose -55 = 26*r + 49. Let c be (-1 - 22/r) + 368/(-92). Factor 0*h**2 - 1/2*h**3 + c*h**4 + 0*h + 0.
h**3*(h - 1)/2
Let s(a) be the second derivative of -2*a**7/3 + 426*a**6/5 + 1771*a**5/5 + 1409*a**4/3 + 64*a**3 - 376*a**2 + 753*a. Suppose s(x) = 0. Calculate x.
-1, 2/7, 94
Let v(h) = -12*h**5 + 68*h**4 - 19*h**3 + 8*h**2 - 9. Let b(o) = -5*o**5 + 34*o**4 - 8*o**3 + 4*o**2 - 5. Let t(m) = 9*b(m) - 5*v(m). Factor t(y).
y**2*(y - 1)**2*(15*y - 4)
Factor -21739750*s**2 + 872*s + 348*s - 4*s**3 + 21738534*s**2.
-4*s*(s - 1)*(s + 305)
Let z = 43109/33502 - 5/4786. Factor 1/7 - 3*u**2 - 11/7*u**3 - z*u.
-(u + 1)**2*(11*u - 1)/7
Find r such that -327/2 - 1/2*r**3 - 439/2*r - 113/2*r**2 = 0.
-109, -3, -1
Suppose 54*g - 54 = 60*g. Let i(u) = -3*u**3 + 34*u**2 - 7*u - 15. Let n(d) = d**3 - 17*d**2 + 4*d + 8. Let c(r) = g*n(r) - 4*i(r). Factor c(s).
(s - 1)*(s + 6)*(3*s + 2)
Let q = 140714 + -6332861/45. Let d = 99/5 + q. Factor 128/9 - d*w + 2/9*w**2.
2*(w - 8)**2/9
Let n = -94 + 103. Suppose 2*u = 3*h - 25 + n, -3*u = 4*h + 7. Factor 3/7*g**h - 1/7*g**4 + 4/7*g - 4/7 - 2/7*g**3.
-(g - 1)**2*(g + 2)**2/7
Suppose 2468 = 727*r + 507*r. Suppose -1/4*w**r - 3/2 + 5/4*w = 0. What is w?
2, 3
Let a be ((-2)/(-8))/((-6)/(-72)). Suppose -a*z + 7*z = 16. Factor 0*f**2 + f**3 + 6*f**5 - 2*f**5 - f**2 - 5*f**5 + f**z.
-f**2*(f - 1)**2*(f + 1)
Suppose -19*w + 21*w = 160. Suppose -w = 59*n - 55*n. Let m(r) = 2*r**2 + 22*r + 20. Let j(t) = 15*t**2 + 155*t + 140. Let z(d) = n*m(d) + 3*j(d). Factor z(b).