the third derivative of p(a). Factor o(t).
5*(t + 2)**2
Suppose 0 = 11*r - 14*r + 444. Let k = r - 1330/9. Determine i, given that 2/9*i**5 + 2/3*i**3 + 0*i + k*i**2 + 0 + 2/3*i**4 = 0.
-1, 0
Suppose -q - 3*w - 167 = 0, q + 112 = 2*w - 65. Let j = q - -173. Factor -15/2*p**4 + j*p + 0 + 0*p**2 + 3/2*p**3.
-3*p**3*(5*p - 1)/2
Let o(r) be the second derivative of r**6/120 + r**5/40 - r**4/16 - r**3/3 - r**2/2 - r + 69. Solve o(x) = 0 for x.
-2, -1, 2
Suppose 6912/7 + 3744/7*u - 78/7*u**3 + 219/7*u**2 + 3/7*u**4 = 0. Calculate u.
-3, 16
Let f be 8229/1477 - (0 + (-8)/(-14)). Let m(s) be the first derivative of -9 + 2*s**4 + 0*s**3 + 0*s - 36/5*s**f + 0*s**2. Factor m(i).
-4*i**3*(9*i - 2)
Factor 2/7*k**5 + 10/7*k**3 - 4/7*k**2 + 0*k - 8/7*k**4 + 0.
2*k**2*(k - 2)*(k - 1)**2/7
Let p = -419/155 + 90/31. Let -2/5*r**3 + p*r + 0*r**4 + 0*r**2 + 1/5*r**5 + 0 = 0. What is r?
-1, 0, 1
Let u(b) be the second derivative of 0 + 11/8*b**4 - 27*b**2 - 3*b**3 + 15*b + 3/20*b**5 - 1/20*b**6. Determine n so that u(n) = 0.
-2, 3
Factor -84*d + 2039 - 2*d**2 + 2*d**2 + d**2 + 4850 + 250*d.
(d + 83)**2
Suppose 3*n = -n + 8. Suppose -2*m = -3*i - 7, -4*i = 5*m - n*m - 2. Factor -5*a + a**3 - 1 + 0 + 4*a**3 + 6 - 5*a**m.
5*(a - 1)**2*(a + 1)
Let s be -3*(16/(-12) - 0). What is j in 7*j - s*j**4 + 5*j**3 - 4*j**5 + 7*j**3 + j + 20*j**2 + 0*j**3 = 0?
-1, 0, 2
Suppose 0 = 2*u + 4*x - 28, 0 = u + x - 31 + 22. Factor 2/9*o**3 + 2/9*o**2 - 2/9*o**u + 0 - 2/9*o.
-2*o*(o - 1)**2*(o + 1)/9
Suppose 13*m + 124 = 11*m. Let g = m + 65. Find y, given that 1/2 - 7/2*y - 9/2*y**g + 15/2*y**2 = 0.
1/3, 1
Let c(r) = -r - 4. Let g be c(-6). Let h = 6 - 0. Factor 4*j**2 - 5 + 4*j + 5 - h*j**g.
-2*j*(j - 2)
Solve -68/7*l - 60/7*l**3 + 0 + 132/7*l**2 - 4/7*l**4 = 0.
-17, 0, 1
Let w(i) = 44*i**2 - 84*i - 96. Let m(k) = -16*k**2 + 28*k + 32. Let t(d) = -8*m(d) - 3*w(d). Find g, given that t(g) = 0.
-1, 8
Let o(l) = -l**3 - l**2 - l - 1. Let k(t) = 135*t**5 + 5130*t**4 - 97*t**3 - 3467*t**2 - 1532*t - 197. Let u(q) = -k(q) + 7*o(q). Find j, given that u(j) = 0.
-38, -1/3, 1
Factor 2*o**3 - 91 + 62 - 2*o - 26*o**2 + 55.
2*(o - 13)*(o - 1)*(o + 1)
Factor 0*f**2 - 1441 + 2693 + 58*f - 1376 + 2*f**2.
2*(f - 2)*(f + 31)
Let m(h) be the third derivative of h**7/105 + 2*h**6/15 + 3*h**5/5 + 4*h**4/3 + 5*h**3/3 + 547*h**2. Factor m(w).
2*(w + 1)**3*(w + 5)
Let t = -33 - -28. Let v be t/(-15) - (-25)/105. Factor v*d**3 + 8/7*d**2 - 8/7 - 4/7*d.
4*(d - 1)*(d + 1)*(d + 2)/7
Suppose 0 = -3*u + 2*t + 1, -5*u - t = -3*t - 7. Suppose -4*l - 3*l**4 - 7*l**5 - l**2 - 5*l**u + 16*l**5 + 4*l = 0. What is l?
-1/3, 0, 1
Let s(f) be the first derivative of -5*f**6/6 + 5*f**4 + 10*f**3/3 - 15*f**2/2 - 10*f + 9. Factor s(r).
-5*(r - 2)*(r - 1)*(r + 1)**3
Suppose 10*x = -4*h, -10*x + 5*x = h - 5. Factor 1/2 + 1/4*a**x + 3/4*a.
(a + 1)*(a + 2)/4
Let a(x) be the second derivative of -x**3/2 - 3*x. Let b be a(-1). Factor 2*h**5 - b*h**5 - 4*h**4 + h**3 + 5*h**4 + h**2 - 2*h**4.
-h**2*(h - 1)*(h + 1)**2
Let h(d) be the first derivative of 2/21*d**3 + 3/7*d**2 + 0*d + 20. Factor h(j).
2*j*(j + 3)/7
Let m(n) = 12*n**3 + 22*n**2 - 38*n + 12. Let z(v) = 11*v**3 + 22*v**2 - 38*v + 11. Let c(k) = 3*m(k) - 4*z(k). Factor c(i).
-2*(i - 1)*(i + 4)*(4*i - 1)
Let h = 16735 + -16735. Factor 0*z**2 - 1/3*z**4 + 0 - 1/3*z**3 + h*z.
-z**3*(z + 1)/3
Solve -122*q**4 + 214*q**2 - 59*q**3 - 15*q**3 + 10*q**5 + 42*q - 20*q**5 - 92*q**4 + 42*q = 0.
-21, -1, -2/5, 0, 1
Find q, given that 8/7*q**2 - 24/7 - 4/7*q**3 + 20/7*q = 0.
-2, 1, 3
Factor 120*d**3 - 3*d**4 + 222*d + 162*d + 85 + 378*d**2 - 25 + 69.
-3*(d - 43)*(d + 1)**3
Let c be 3/(-6) - 3/(-2). Determine k so that -c - 8*k**2 + 3 + 70*k - 76*k = 0.
-1, 1/4
Factor 3 + 21/8*u - 3/8*u**2.
-3*(u - 8)*(u + 1)/8
Let y(m) = -m**2 + 4. Let n(o) = -3*o**2 - 24*o - 6. Let j(s) = n(s) - 5*y(s). Factor j(p).
2*(p - 13)*(p + 1)
Let r(g) be the third derivative of -g**5/270 - g**4/27 - g**3/9 - 44*g**2 + 4*g. Factor r(q).
-2*(q + 1)*(q + 3)/9
Suppose i = 6*i - 5*w - 30, -4*i + 20 = -3*w. Solve 9*t**2 + t**2 + 36 - 6*t**i + 24*t = 0.
-3
Let g = 213/836 + -1/209. Let i(u) be the first derivative of -g*u**2 + 7/18*u**3 + 0*u - 6 + 1/30*u**5 - 5/24*u**4. Factor i(k).
k*(k - 3)*(k - 1)**2/6
Let s(z) be the second derivative of z**5/15 + 8*z**4/9 + 14*z**3/9 - z - 20. Determine u so that s(u) = 0.
-7, -1, 0
Let v(j) = -16*j**3 - 15*j**2 + 6*j + 11. Let y(c) = 225*c**3 + 210*c**2 - 85*c - 155. Let q be (51/(-4))/((-9)/60). Let n(d) = q*v(d) + 6*y(d). Factor n(l).
-5*(l + 1)**2*(2*l - 1)
Let h(v) be the first derivative of -2*v**4/15 - 158*v**3/45 - 76*v**2/3 + 40*v/3 - 187. Factor h(u).
-2*(u + 10)**2*(4*u - 1)/15
Suppose 3*y = 3*f - 45, -3*f = f + 3*y - 74. Suppose -2*r - 3*h - 3 = r, 3*r = 2*h + f. Factor -3/4*b**r - 3/4*b**2 + 0 + 0*b.
-3*b**2*(b + 1)/4
Find u, given that 44/3*u**2 + 2/3*u**5 + 12*u**3 + 14/3*u**4 + 26/3*u + 2 = 0.
-3, -1
Let i = 38 - 34. Solve i*r**4 - 60*r**3 + 4*r**3 - 80*r**2 - 3*r**4 - 32*r - 13*r**4 = 0 for r.
-2, -2/3, 0
Let t be 1 - 39/9 - 1/(-3). Let w be 20/5 - 2/t. Factor 8/3 - w*l**2 - 8*l.
-2*(l + 2)*(7*l - 2)/3
Factor 3*g + 0 - g**2 - 1/4*g**3.
-g*(g - 2)*(g + 6)/4
Suppose -6*j + 312 = 282. Suppose 2*z + 2*z + 4*q - 28 = 0, -2*z + 29 = j*q. Factor 0 + z*x**3 - 2/3*x**4 + 0*x - 4/3*x**2.
-2*x**2*(x - 2)*(x - 1)/3
Let x(t) = 2*t**3 - 2*t**2 + 33*t - 60. Let q(c) = -c**3 + c**2 - 34*c + 60. Let y(a) = -7*q(a) - 6*x(a). Suppose y(n) = 0. Calculate n.
-3, 2
Let r be 27/(-15)*(-400)/240. Find s, given that -12/7*s**r + 20/7*s**2 - 8/7*s + 0 = 0.
0, 2/3, 1
Let q(t) be the third derivative of t**7/490 + t**6/20 + 17*t**5/35 + 65*t**4/28 + 75*t**3/14 + 5*t**2 - 37. Factor q(z).
3*(z + 1)*(z + 3)*(z + 5)**2/7
Let a = -622 - -1247/2. Find d, given that a + 3/4*d**3 - 3/2*d**2 - 3/4*d = 0.
-1, 1, 2
Solve 1 + 14*l**3 + l**5 + 3*l - 18*l**3 + 300*l**2 - 4 + 1 - 298*l**2 = 0 for l.
-2, -1, 1
Let g be ((-17950)/17591)/((-8)/14) + (-2)/7. Suppose g*t**2 + t + 1/2*t**3 + 0 = 0. What is t?
-2, -1, 0
Let n(v) be the second derivative of v**6/50 - 9*v**5/100 + v**4/20 + 3*v**3/10 - 3*v**2/5 - 141*v + 1. Determine z so that n(z) = 0.
-1, 1, 2
Suppose -2*h**2 + 68/3*h + 16 - 8*h**3 + 2/3*h**4 = 0. What is h?
-1, 2, 12
Let -7 + 2*z**3 - 13 + 20*z + 20 - 27*z**3 + 5*z**5 = 0. What is z?
-2, -1, 0, 1, 2
Factor 3/4*l - 1/4*l**3 + 1/2 + 0*l**2.
-(l - 2)*(l + 1)**2/4
Let r(t) = -t + 5. Let n be r(-4). Let v(m) = 11*m + 24. Let c be v(-2). Factor 3*p**5 + 0*p**5 - 6*p + n*p**2 + c*p**3 - 9*p**4 + p**3 + 0*p.
3*p*(p - 2)*(p - 1)**2*(p + 1)
Factor 0 + 42/5*x**3 + 0*x**2 + 0*x + 2/5*x**4.
2*x**3*(x + 21)/5
Let d(w) be the second derivative of -1/56*w**7 + 0*w**2 - 9/80*w**5 + 0 + 14*w + 0*w**3 + 1/16*w**4 + 3/40*w**6. Solve d(i) = 0.
0, 1
Factor -8/5 + 74/5*x + 19/5*x**2.
(x + 4)*(19*x - 2)/5
Let g(i) be the second derivative of 0*i**3 - 1/15*i**6 - 1 + 0*i**5 + 1/6*i**4 + 0*i**2 - 24*i. Find k, given that g(k) = 0.
-1, 0, 1
Let k(j) be the first derivative of -2*j**3 + 9*j + 42 - 32 + j**3 - 3*j**2. Factor k(p).
-3*(p - 1)*(p + 3)
Factor -10*f**2 + 4*f**5 - 14*f + 10*f**3 + 5 + 9*f + 5*f**4 - 9*f**5.
-5*(f - 1)**3*(f + 1)**2
Factor -8/7 - 15/7*d**3 - 50/7*d + 73/7*d**2.
-(d - 4)*(d - 1)*(15*d + 2)/7
Let j be 1/2 + (-321)/(-42) - (-2118)/(-353). Factor -j*x + 3/7*x**2 - 18/7.
3*(x - 6)*(x + 1)/7
Let i(l) be the third derivative of l**7/70 - l**6/20 - l**5/20 + l**4/4 + 2*l**2 + 21. Factor i(k).
3*k*(k - 2)*(k - 1)*(k + 1)
Factor -3*u + 32*u**2 + u**5 + u**3 - 19*u - 8 + 5*u**4 - 49*u**2.
(u - 2)*(u + 1)**3*(u + 4)
Let r = 74 + -76. Let c be -12*(1 + (128/(-42) - r)). What is a in 0 + c*a + 6/7*a**2 + 2/7*a**3 = 0?
-2, -1, 0
Factor 24/11*b + 2/11 + 60/11*b**2 + 18/11*b**4 + 56/11*b**3.
2*(b + 1)**3*(9*b + 1)/11
Let d = 10 + -14. Let i be -2 - d - (1 - 2). Solve 2*t**4 + 3*t**2 - 6*t**2 + 2*t**i - 2*t**5 + t**2 = 0.
-1, 0, 1
Suppose -141*g = -137*g - 16. Let n(o) be the second derivative of 0*o**2 + 4/9*o**g + 4*o - 7/5*o**6 - 4/9*o**3 + 59/30*o**5 + 0. Solve n(w) = 0 for w.
-2/7, 0, 2/9, 1
Let v(w) be the third derivative of -w**8/112 + 19*w**7/175 - 37*w**6/100 + 11*w**5/25 + 7*w**4/40 - w**3 - 46*w**2. Find q such that v(q) = 0.
-2/5, 1, 5
Let n = -10 - -10. Suppose 3*u - 6 + n = 0. Factor 9 - 3*q