1, 36
Let b(w) be the first derivative of w**3/12 + 595*w**2/2 + 354025*w - 10449. Suppose b(n) = 0. Calculate n.
-1190
Let v(l) be the second derivative of 19/10*l**3 + 11/20*l**4 + 3/100*l**5 + 3 + 2*l + 27/10*l**2. Factor v(p).
3*(p + 1)**2*(p + 9)/5
Let a = -139 + 209. Let z be (-310)/a + 5*1/1. Factor 2/7*c**5 + 0*c**4 + 0*c**2 + 0 - z*c**3 + 2/7*c.
2*c*(c - 1)**2*(c + 1)**2/7
Let a(t) be the third derivative of t**6/120 + 107*t**5/60 - 55*t**4/3 + 74*t**3 + 2149*t**2 + t. Determine j so that a(j) = 0.
-111, 2
Let k(r) = 10 - 31 + 30*r - 97 - 11 - 77. Let s be k(7). Factor 0*m + 2/9*m**3 + 2/9*m**s + 0 - 2/9*m**5 - 2/9*m**2.
-2*m**2*(m - 1)**2*(m + 1)/9
Let m be (-516)/(-4773)*(-74)/(-4). Determine x, given that 8/7 - 34/7*x + 8/7*x**m = 0.
1/4, 4
Let m(v) be the third derivative of 16*v**2 - 5/3*v**5 + 0 - 11/24*v**6 + 0*v + 5/3*v**3 - 35/24*v**4. Factor m(o).
-5*(o + 1)**2*(11*o - 2)
Let v(x) = 45*x**2 + 44*x - 157. Let j(m) = -56*m**2 - 43*m + 158. Let i(g) = 4*j(g) + 5*v(g). Factor i(a).
(a - 3)*(a + 51)
Let s(f) be the third derivative of f**6/600 + f**5/75 - f**4/8 - 3*f**3/5 + 1595*f**2. What is z in s(z) = 0?
-6, -1, 3
Let x = 40753 - 3423313/84. Let r = x + 31/21. Factor r*z**2 + 9/2*z + 15/4.
3*(z + 1)*(z + 5)/4
Let z(o) = -o**3 + 8*o**2 - 9*o + 19. Let u be z(7). Suppose u*p + 3*h = 25, 6*h - 2*h = 4*p - 20. Factor 73*n**3 - 4*n**5 + 3*n**p - 75*n**3 - 3*n**4.
-n**3*(n + 1)*(n + 2)
Let w(z) be the second derivative of 10/3*z**3 + 0*z**2 - 10/3*z**4 + 48*z + 0 + 1/4*z**5 + 1/2*z**6. Find g, given that w(g) = 0.
-2, 0, 2/3, 1
Determine i so that -6052 - 63*i**3 + 3*i**4 - 207*i**2 - 213*i - 5988 + 11968 = 0.
-1, 24
Let l(a) = a**3 + 4*a**2 - 2. Let u be l(-3). Find g, given that -8*g**3 + g**2 + 28*g**3 + u*g**2 - 8*g**4 - 20*g**5 = 0.
-1, -2/5, 0, 1
Let a(s) be the third derivative of 2*s**2 + 64/27*s**4 + 30 - 1/945*s**7 + 0*s - 16/45*s**5 - 256/27*s**3 + 4/135*s**6. Factor a(z).
-2*(z - 4)**4/9
Let r(t) be the third derivative of 3*t**6/20 + 106*t**5/5 + 421*t**4/12 + 70*t**3/3 - 1790*t**2. Factor r(v).
2*(v + 70)*(3*v + 1)**2
Solve -7*i**5 + 18293 + i**4 + 8*i**4 - 13*i**2 + 15*i**3 + 3*i**5 - 15*i - 18293 = 0 for i.
-1, 0, 5/4, 3
Let d be 3*8*8/((-2016)/(-243)) + 0. Factor -34/7*p**2 + d + 2/7*p**3 + 18*p.
2*(p - 9)**2*(p + 1)/7
Find y, given that 42*y**3 + 91*y**2 - 141*y**2 + y**4 + 89*y**2 + 2*y**4 = 0.
-13, -1, 0
Let v be (-144)/(-10) - 12/(-20). Let m be (15 - v)*2/4. Factor 4/7*h - 4/7*h**5 + 8/7*h**2 - 8/7*h**4 + m + 0*h**3.
-4*h*(h - 1)*(h + 1)**3/7
Let q(p) be the second derivative of -p**4/84 + 2*p**3/21 + 48*p**2/7 + 150*p + 6. Factor q(x).
-(x - 12)*(x + 8)/7
Suppose -493 = 5*y - 2*k + k, 0 = -y + 4*k - 110. Let a = 134 + y. Factor 2 + 6 - a*u + 3*u**2 - 8.
3*u*(u - 12)
Let x = -498/317 + 6022/2219. Factor -66/7*k + 20/7 - x*k**3 - 54/7*k**2.
-2*(k + 2)*(k + 5)*(4*k - 1)/7
Let m(v) = -9*v**2 - v + 3. Let y(j) = -4*j**2 - j + 2. Let g = -2 + -5. Suppose -1859*i + 1874*i - 45 = 0. Let s(x) = g*y(x) + i*m(x). What is q in s(q) = 0?
-5, 1
Let t be (-1335336)/(-157794) - (-8)/(-2). Let r = t + -2/2023. Factor -36/13 + r*b - 6/13*b**2.
-2*(b - 9)*(3*b - 2)/13
What is g in 2/9*g**4 + 0*g + 156800/9*g**2 + 1120/9*g**3 + 0 = 0?
-280, 0
Let i be 2/(-4)*672/(-28). Let f be 0/((-6)/(10 - i)). Factor 0 - p**2 + f*p + 1/3*p**3.
p**2*(p - 3)/3
Let u = 14810/31 + -103639/217. Solve 2/7*j + 3/7*j**3 + 0 - 5/7*j**2 + 1/7*j**4 - u*j**5 = 0 for j.
-2, 0, 1
Suppose -145*d = -150*d + 1460. Let g = -289 + d. Let -4/3*v**2 + 6*v**g + 2*v**5 + 0 + 0*v - 20/3*v**4 = 0. Calculate v.
0, 1/3, 1, 2
Let z(s) be the first derivative of -s**5/10 + 169*s**4/8 - 167*s**3/6 - 169*s**2/4 + 84*s - 1951. Let z(r) = 0. Calculate r.
-1, 1, 168
Suppose 17*w = 41 + 27. Let 20*g - 20*g**2 + w*g - 289*g**3 + 285*g**3 = 0. What is g?
-6, 0, 1
Let f(v) = 5*v**3 - 2268*v**2 - 64*v. Let t(m) = 10*m**3 - 4535*m**2 - 120*m. Let a(b) = -15*f(b) + 8*t(b). Determine n so that a(n) = 0.
0, 452
Let q(y) = -y**2 + 36*y + 40. Let b be q(37). Factor -12 + 0*g**3 + 9*g**2 - 9*g**3 + 6*g**b.
-3*(g - 2)**2*(g + 1)
Let f(r) be the first derivative of -2*r**6/3 + 76*r**5/5 - 79*r**4 + 532*r**3/3 - 200*r**2 + 112*r + 1572. Factor f(n).
-4*(n - 14)*(n - 2)*(n - 1)**3
Let k(c) = c**3 + 22*c**2 - c - 17. Let t be k(-22). Suppose 0 = 4*y - 3*n - 9, y + 2 = t*n - 0*n. Solve -7*a + 2*a**2 + a - 2*a**y - 8*a**2 + 2*a = 0 for a.
-2, -1, 0
Let d(b) be the second derivative of 3*b**5/140 + 481*b**4/28 + 137*b**3/2 + 1437*b**2/14 - 26*b + 23. Factor d(o).
3*(o + 1)**2*(o + 479)/7
Let f be (5/7 - 9*(-285)/(-945))*-2. Suppose 0*y**2 + 0 + 0*y - 3/2*y**f + 3*y**3 = 0. What is y?
0, 2
Suppose 64948*b - 144 = -5*s + 64946*b, -123 = -4*s + b. Solve s + 5/4*r**2 - 25/2*r = 0 for r.
4, 6
Suppose 1973*h = 2030*h. Determine q, given that 156/7*q**2 + 120/7*q**3 + h - 48/7*q - 291/7*q**4 + 9*q**5 = 0.
-2/3, 0, 2/7, 1, 4
Suppose 69*z + 769 = 2141*z - 3518 + 143. Factor 0 + 5/2*r**3 + 0*r**4 - 5/4*r - 5/4*r**5 + 0*r**z.
-5*r*(r - 1)**2*(r + 1)**2/4
Let l(r) = 50706*r - 354940. Let m be l(7). Suppose 6/7*i**5 + 0 + 2*i**3 + 0*i + 8/7*i**m - 4*i**4 = 0. What is i?
-1/3, 0, 1, 4
Suppose -4*g + 0*g = 384. Let s be 13/(52/g)*(-1 + 0). Suppose -24 + s - 6*k**2 - 2*k**3 - 3*k - k**3 = 0. What is k?
-1, 0
Let o(i) be the second derivative of -i**5/80 - 61*i**4/16 + 139*i**3/6 - 93*i**2/2 + 2207*i. Factor o(a).
-(a - 2)*(a - 1)*(a + 186)/4
Let d(m) = 10*m**2 + 206*m - 608. Let k(w) = 17*w**2 + 412*w - 1214. Let i(y) = -7*d(y) + 4*k(y). Suppose i(t) = 0. Calculate t.
3, 100
Let d(n) be the first derivative of n**6/10 - 69*n**5/25 + 141*n**4/10 + 86*n**3 + 1443*n**2/10 + 507*n/5 - 10379. Determine g so that d(g) = 0.
-1, 13
Let s(b) be the third derivative of b**5/20 - 81*b**4/8 - 261*b**3 - 3*b**2 - 748*b. Factor s(c).
3*(c - 87)*(c + 6)
Let t be (-3496)/(-253) + 4/22. Suppose -a - 5 = 0, 5*v + t - 4 = -4*a. What is q in 3/2*q**2 + 2*q**3 - v - 2*q + 1/2*q**4 = 0?
-2, -1, 1
Factor 3*k - 2*k - 180*k**2 + 4*k**5 - 98*k**4 + k**5 - 3*k**5 + 30 - 5*k**5 - 246*k**3.
-(k + 1)**3*(k + 30)*(3*k - 1)
Let s = -110 + 551/5. Let h be 522/1160*(-4)/(-3). Factor h*n - s*n**2 + 0.
-n*(n - 3)/5
Let p(g) be the second derivative of g**8/84 + g**7/15 + 49*g**6/450 + 11*g**3/6 + g**2/2 - 70*g. Let y(i) be the second derivative of p(i). Factor y(w).
4*w**2*(5*w + 7)**2/5
Factor 164/3 + 2/3*w**2 - 166/3*w.
2*(w - 82)*(w - 1)/3
Let h(c) be the third derivative of -c**6/15 - c**5/10 + c**4/12 + 239*c**2. Factor h(g).
-2*g*(g + 1)*(4*g - 1)
Let z = -219 + 229. Let i be 2/z + (-860)/(-200). Find t such that 0 - 3*t - 3/2*t**3 + i*t**2 = 0.
0, 1, 2
Let q be (-2)/(-3) + (52/12 - 6). Let k be (2/6)/((-6)/(-18)). Let l(r) = 8*r**2 - 38*r - 30. Let h(j) = -j**2 + j. Let u(d) = k*l(d) + q*h(d). Factor u(c).
3*(c - 5)*(3*c + 2)
Let i = 88432/3 - 29472. Factor -1/3*u**3 - i*u - 7/3*u**2 - 4.
-(u + 2)**2*(u + 3)/3
Suppose -10*v = -7*v. Suppose v = 4*f - 3*l - 4, 3*f + 3*l = 6*l. Factor 3*m**f - 3*m**2 - 87*m - 3*m**5 + 3*m**3 + 87*m.
-3*m**2*(m - 1)**2*(m + 1)
Let w(a) be the first derivative of -a**4/2 - a**3/3 + 5*a**2/2 + 5*a + 65. Let p(f) = f**3 - 3*f - 2. Let u(i) = -7*p(i) - 4*w(i). Solve u(g) = 0.
-3, -2, 1
Suppose 0 = -10*p - 59 + 239. Factor -18 + 6 - 14 - 3*r**2 - 1 + p*r.
-3*(r - 3)**2
Suppose -4*y - 15 = -5*r - 1, 4*y = -4. Suppose 5*u - r*h - 9 = -4*h, 6 = -2*h. Find k, given that 46/5*k**u + 74/5*k**2 - 36/5 - 6/5*k**4 - 14/5*k = 0.
-1, 2/3, 9
Let u = -52 + 55. Factor -5*y**2 + u*y**2 + 0*y**2 - 62*y + 24*y.
-2*y*(y + 19)
Let a be ((-115)/92)/(19 - (2 + 0)). Let n = 6241/204 - a. Determine x, given that -20*x**2 - 2/3 - 6*x - n*x**3 - 22*x**4 - 6*x**5 = 0.
-1, -1/3
Suppose 125*b - 21 = 54*b + 64*b. Let g(p) be the third derivative of -13*p**2 - 1/10*p**b + 0 + 0*p + 1/60*p**4 + 1/300*p**5. Factor g(s).
(s - 1)*(s + 3)/5
Let h(p) be the first derivative of -p**6/6 + 6*p**5/5 - 9*p**4/4 - 4*p**3/3 + 6*p**2 - 786. Factor h(b).
-b*(b - 3)*(b - 2)**2*(b + 1)
Let x(o) be the first derivative of -o**6/3 - 9*o**5 + 23*o**4/4 - 206. Factor x(t).
-t**3*(t + 23)*(2*t - 1)
Let z(k) be the first derivative of 0*k**3 - 1/4*k**5 + 0*k + 3/40*k**6 - 1/4*k**4 + 17/2*k**2 - 12. Let b(g) be the second derivative of z(g). Factor b(f).
3*f*(f -