(-32)/(-3)). Factor -13*a**4 + 9*a**5 - 12*a**2 - 11*a**4 + 12*a**2 + m*a**3.
3*a**3*(a - 2)*(3*a - 2)
Suppose -16*j - 3*j = -95. Suppose 4*u = 2*k + 12, -6*k = j*u - 4*k - 6. Find t, given that 1/2*t**u + 1/2 + t = 0.
-1
Let o be 7720/16 - (3 + (2 - 4)). Let n = o + -477. Determine j, given that 0 + 3*j**4 + 3/2*j**5 + n*j - 3*j**2 - 6*j**3 = 0.
-3, -1, 0, 1
Let f(n) = 10*n + 2. Let r be f(-3). Let z = 35 + r. Factor -z*q**2 + 6 - q**2 + q**2 + 4*q + 5*q**2.
-2*(q - 3)*(q + 1)
Let m(p) be the first derivative of 1/24*p**3 - 1/48*p**6 + 5/96*p**4 - 4 - 5*p + 0*p**2 - 1/80*p**5. Let u(c) be the first derivative of m(c). Factor u(g).
-g*(g - 1)*(g + 1)*(5*g + 2)/8
Let a(z) be the second derivative of z**5/20 + 5*z**4/2 + 50*z**3 - 25*z**2 - 13*z. Let u(k) be the first derivative of a(k). Solve u(n) = 0 for n.
-10
Let l(f) be the second derivative of -f**4/8 - 23*f**3/4 - 153*f**2/2 + 862*f - 2. Factor l(m).
-3*(m + 6)*(m + 17)/2
Solve 66/7 - 9*q**3 - 197/7*q + 195/7*q**2 - 1/7*q**4 = 0 for q.
-66, 1
Let w(s) be the third derivative of -s**8/168 - s**7/35 + s**6/60 + s**5/10 - 4*s**2 + 441. Find j such that w(j) = 0.
-3, -1, 0, 1
Suppose -3*i = -5*k - 0*i + 801, -5*k + i + 807 = 0. Factor -5 - 7 + k*h**2 - 3*h + 17*h - 164*h**2.
-2*(h - 6)*(h - 1)
Let v(y) = -y**3 - 9*y**2 - 6*y + 19. Let t be v(-8). Let d(l) = -l**3 + 2*l**2 + 4*l. Let u be d(t). Factor -4*h**3 - h**3 - 4*h + 12*h**2 + 13*h**3 + 8*h**u.
4*h*(h + 1)*(4*h - 1)
Let y(x) be the second derivative of x**6/15 - 23*x**5/10 + 51*x**4/2 - 241*x**3/3 + 110*x**2 + 5598*x. Factor y(i).
2*(i - 11)*(i - 10)*(i - 1)**2
Let g(y) = -y**3 + 11*y + 24. Let f be g(-2). Let s(k) be the first derivative of 8/27*k**3 - f + 2*k - 7/6*k**2 - 1/36*k**4. Factor s(h).
-(h - 3)**2*(h - 2)/9
Let o(i) be the third derivative of i**7/2100 + 79*i**6/600 + 6697*i**5/600 + 1501*i**4/10 + 4332*i**3/5 - 12*i**2 - 205. Determine t, given that o(t) = 0.
-76, -3
Let g(c) = 8*c**3 + 402*c**2 + 390*c - 797. Let r(q) = -58*q**3 - 2814*q**2 - 2728*q + 5578. Let w(k) = -44*g(k) - 6*r(k). Let w(h) = 0. Calculate h.
-200, -2, 1
Let r be (5 - 174/30)/(26/(-65)). Let y(l) be the first derivative of 0*l + 3*l**r + 3/4*l**4 + 29 - 3*l**3. Determine f, given that y(f) = 0.
0, 1, 2
Let o(y) be the third derivative of -85*y**6/3 + y**5/12 - 430*y**2 - 2. Determine k, given that o(k) = 0.
0, 1/680
Let z(b) be the second derivative of 0*b**2 + 0 - 77*b - 1/3*b**4 - 4/3*b**3. Factor z(c).
-4*c*(c + 2)
Suppose 30*j - 360 = -90*j. Let a(z) be the second derivative of 2/5*z**j - 18*z + 0*z**2 - 1/20*z**4 + 0. Find h such that a(h) = 0.
0, 4
Suppose -51*y = 34*y - 6885. Suppose 5*w + 22*w = y. Determine j so that -1/6*j**w + 2/3*j - 2/3*j**2 + 0 + 1/6*j**4 = 0.
-2, 0, 1, 2
Let o(a) be the first derivative of -4/3*a**3 - 43 + 3/5*a**4 + 4/25*a**5 - 6/5*a**2 + 16/5*a. Factor o(v).
4*(v - 1)**2*(v + 1)*(v + 4)/5
Let c(b) = 3*b + 50. Let z be c(-10). Suppose z = -5*q, 2*q + 2 = -2*f + 4. Factor f*n**4 - 2*n**4 - n**5 + 2*n**5 + n**2 - 9*n**3 + 4*n**2.
n**2*(n - 1)**2*(n + 5)
Let h(g) be the second derivative of g**5/50 - 7*g**4/45 + g**3/15 + 12*g**2/5 - 2*g - 1204. Determine p so that h(p) = 0.
-4/3, 3
Let d be (-12)/(-18) + 60/18. Factor -l**4 - 28*l**3 - 293*l + 429*l + 648*l - 504*l**2 - l**d + 88*l**3.
-2*l*(l - 14)**2*(l - 2)
Suppose s + 0*s = -1. Let f be (4 + (s - -1))*2. Factor -18*w + 5*w**2 + f*w + 5*w.
5*w*(w - 1)
Let j(t) be the third derivative of -1/540*t**5 + 0*t + 1/54*t**3 + 11*t**2 + 0 + 0*t**4. Factor j(v).
-(v - 1)*(v + 1)/9
Factor 9 + 11770*y**2 + 6050*y**3 - 1311/2*y.
(y + 2)*(110*y - 3)**2/2
Let t be ((-4)/(-1290))/(-11 - (-885795)/80525). Let u = 2/129 + t. Find d such that -5*d - u - 1/2*d**2 = 0.
-5
Suppose -27 = 2*q + 39. Let d = q + 37. Solve 29*p**2 - 26*p**2 - d*p - 2*p = 0 for p.
0, 2
Let y(t) be the second derivative of 23*t**4/54 + t**3/9 - 210*t. Factor y(n).
2*n*(23*n + 3)/9
Let n(d) be the first derivative of -2*d**3/9 - 256*d**2/3 + 514*d/3 - 6522. What is h in n(h) = 0?
-257, 1
Let y(c) be the third derivative of -14/15*c**3 - 13/60*c**4 + 1/150*c**5 + 0 - 22*c + 3*c**2. Let y(o) = 0. Calculate o.
-1, 14
Let d(i) = 10*i**3 + i**2 - 5*i + 9. Let u be d(6). Suppose -5*o + 8700 = -o. Factor 12*a**4 + 8*a**3 + 4*a**5 + o - u.
4*a**3*(a + 1)*(a + 2)
Let u be (-50)/(-60)*1*6/15. Let r = 3727 - 3725. Factor 0 + 1/6*x**3 + u*x**r + 1/6*x.
x*(x + 1)**2/6
Let h(z) be the third derivative of 7*z**5/20 + 39*z**4/8 + 10*z**3 + 8*z**2 + 74*z + 3. Solve h(c) = 0.
-5, -4/7
Suppose 16*m - 1477 = -1301. Suppose 5*j + 1 = v, -m*v = 5*j - 6*v - 5. Factor j + 1/3*s**2 - 1/9*s**3 + 0*s.
-s**2*(s - 3)/9
Suppose -4*i + 10 = 2*c, 10 = 2*c - 4*c. Let m be (-438)/(-60) + (0 - i/(-25)). Factor -5/2*u**4 + 5/2*u**2 + 0 - 15/2*u + m*u**3.
-5*u*(u - 3)*(u - 1)*(u + 1)/2
Determine y, given that -164829*y**2 + 1533099 - 3068*y + 164830*y**2 + 820057 = 0.
1534
Let h(o) be the first derivative of 3*o**5/5 - 957*o**4/2 + 103657*o**3 - 907236*o**2 + 2696112*o - 2856. Suppose h(x) = 0. Calculate x.
3, 316
Determine x so that 76/5 - 152/5*x**3 - 1/5*x**5 + 2/5*x**2 - 78/5*x**4 + 153/5*x = 0.
-76, -1, 1
Let j(y) be the first derivative of -21*y**5/20 + 843*y**4/8 - 572*y**3 + 228*y**2 + 3543. Let j(v) = 0. Calculate v.
0, 2/7, 4, 76
Let x(l) = 10*l + 16. Let m be x(-4). Let f = m - -27. Factor 15*d**2 - f*d + 9 - 18*d**2 - 3.
-3*(d - 1)*(d + 2)
Let h be (62 + -58)*3/4. Let 28*k**4 - 81*k**2 + 13*k**h - 29*k**4 + 5*k**3 = 0. Calculate k.
0, 9
Suppose 4*r = -r + 35. Suppose 0 = 10*g - r*g - 87. Factor -8*n**4 + 41*n**3 + 11*n**3 - 4 - n - 60*n**2 - 8*n**4 + g*n.
-4*(n - 1)**3*(4*n - 1)
Let w(u) be the first derivative of u**4/4 - 4*u**3/3 - 127*u**2/2 + 130*u - 1512. Factor w(s).
(s - 13)*(s - 1)*(s + 10)
Suppose -1504*r = -1490*r. Factor -3/5*v**3 + 12/5*v + r*v**2 + 0.
-3*v*(v - 2)*(v + 2)/5
Let n(v) be the second derivative of -v**6/15 - 13*v**5/5 + 14*v**4/3 + 26*v**3/3 - 27*v**2 + 233*v. Factor n(a).
-2*(a - 1)**2*(a + 1)*(a + 27)
Find r, given that 3*r - 8666906*r**2 + 3*r + 135 + 8666905*r**2 = 0.
-9, 15
Let m = 3508 - 3506. Let j(q) be the third derivative of -18*q**m + 0*q + 0 - 1/12*q**5 + 5/12*q**4 + 0*q**3. Factor j(w).
-5*w*(w - 2)
Let w(c) = -7*c**4 - c**2 + c + 1. Let p(z) = -26*z**4 - 58*z**3 - 1354*z**2 - 4370*z + 14584. Let f(d) = p(d) - 4*w(d). Factor f(q).
2*(q - 45)*(q - 2)*(q + 9)**2
Let a(c) be the first derivative of -1/9*c**6 - 2/3*c**2 - 101 + 0*c + 1/18*c**4 - 38/27*c**3 + 22/45*c**5. Suppose a(r) = 0. What is r?
-1, -1/3, 0, 2, 3
Let g(w) be the first derivative of 4*w**5/5 - 29*w**4/2 - 236*w**3/3 - 141*w**2 - 108*w + 563. What is t in g(t) = 0?
-3/2, -1, 18
Let z = 556 + -554. Suppose 2*i = -z*m + 12, -m - 6 = 3*i - 6*i. Factor 0 + m*g**2 - 3/4*g**3 + 0*g.
-3*g**2*(g - 4)/4
Let u = 26793 - 26791. Let k(n) be the second derivative of 2/45*n**4 + 0 - 1/9*n**3 - 1/150*n**5 - 10*n + 2/15*n**u. Factor k(r).
-2*(r - 2)*(r - 1)**2/15
Factor 6*s**2 - 19213 - 56027 - 16060*s - 4*s**3 - 33660 - 482*s**2.
-4*(s + 9)*(s + 55)**2
Let q = -27/5689 + 5797/22756. Factor -1/2*t + 3/4*t**2 - q.
(t - 1)*(3*t + 1)/4
Let k be -7 - (12 - (-5 - -54)) - -1. Let f(s) be the third derivative of -1/140*s**5 + 0 - 1/8*s**4 - 3/7*s**3 + 0*s - k*s**2. Factor f(t).
-3*(t + 1)*(t + 6)/7
Solve 5465*t**3 + 5*t**2 - 25410 + 4983*t - 5462*t**3 - 281*t**2 = 0.
11, 70
Suppose -80/3 - 50/3*i**2 + 36*i - 1/6*i**4 + 3*i**3 = 0. Calculate i.
2, 4, 10
Let n(m) be the third derivative of m**6/240 + 11*m**5/24 + 107*m**4/48 + 53*m**3/12 + 1855*m**2. Factor n(s).
(s + 1)**2*(s + 53)/2
Let s = -1977 + 1987. Suppose -5*t + x = -18, 12*t - 3*x = s*t + 2. Let 0*k - 2*k**3 + 2*k**5 + 4/7*k**t - 4/7*k**2 + 0 = 0. What is k?
-1, -2/7, 0, 1
Let q(n) = n**3 + n**2 + 2*n + 1. Let i = 91 - 90. Let k(z) = 24*z**2 + 12*z - 16. Let f(h) = i*k(h) - 4*q(h). Factor f(a).
-4*(a - 5)*(a - 1)*(a + 1)
Factor 117305*i**5 - 2*i**2 - 117320*i**5 - 36*i**4 + 9*i + 14*i**2 - 18*i**3.
-3*i*(i + 1)**3*(5*i - 3)
Let j(p) be the first derivative of p**6/1980 + p**5/110 + 56*p**3/3 - 20. Let z(t) be the third derivative of j(t). Find k, given that z(k) = 0.
-6, 0
Let f = 1/202996 + 2841933/2232956. Suppose 16/11*q - 2/11*q**2 - f = 0. What is q?
1, 7
Let n(t) be the first derivative of -