j(p) be the first derivative of -1/15*p**5 + 0*p**3 + 4 + 0*p - 6*p**2 + 1/2*p**4. Let z(f) be the second derivative of j(f). Factor z(a).
-4*a*(a - 3)
Let i(t) be the third derivative of t**6/480 + 123*t**5/80 - 185*t**4/48 + 214*t**2 + 3. Factor i(v).
v*(v - 1)*(v + 370)/4
Let a = -28/41 - -377/492. Let c(l) be the third derivative of 0*l - 1/3*l**3 + 1/60*l**6 + 1/30*l**5 - a*l**4 + 0 + 25*l**2. Suppose c(o) = 0. What is o?
-1, 1
Let b(m) be the third derivative of m**8/504 + 49*m**7/45 - 23*m**6/6 + m**2 + 60*m + 1. Factor b(j).
2*j**3*(j - 2)*(j + 345)/3
Let l(d) be the second derivative of d**6/15 - 4*d**5/5 + 7*d**4/6 + 146*d + 1. Factor l(z).
2*z**2*(z - 7)*(z - 1)
Let c(k) be the second derivative of -5*k**4/12 - 70*k**3/3 - 480*k**2 + 1133*k. Find w such that c(w) = 0.
-16, -12
Find o such that -2672/17*o - 2/17*o**3 + 5280/17 + 346/17*o**2 = 0.
4, 165
Let z be 9372/36 + 9*2/(-3). Let c = 255 - z. Suppose 0 - 2/3*d - c*d**2 = 0. What is d?
-1, 0
Determine l so that 185*l - 5476 + 5476 - 2*l**2 - 159*l = 0.
0, 13
Solve 98/23 + 96/23*z - 2/23*z**2 = 0 for z.
-1, 49
Suppose -978*d**2 + 2206*d - 200 - 1044*d**2 - 754*d**2 - 1025 + 1056*d**3 + 874*d - 144*d**4 = 0. What is d?
7/6, 5/2
Let o(q) be the first derivative of 5*q**3/9 - 530*q**2/3 - 2140*q/3 - 1126. Factor o(n).
5*(n - 214)*(n + 2)/3
Let c(g) be the third derivative of -g**7/1155 - 133*g**6/660 - 2*g**5/5 - 16*g**2 - 3. Factor c(x).
-2*x**2*(x + 1)*(x + 132)/11
Let y(a) = -a**2 - 310*a - 16444. Let b be y(-68). Factor 156*z**4 + 345*z**2 + 723/2*z**3 + b + 114*z + 24*z**5.
3*(z + 2)**3*(4*z + 1)**2/2
Let d(a) be the third derivative of -a**6/96 + 13*a**5/8 + 135*a**4/32 - 395*a**3/12 + 3457*a**2. Find s such that d(s) = 0.
-2, 1, 79
Let s = 26 - 10. Suppose -12*g + 10*g + 4*v = -34, -45 = -5*g + 2*v. Factor -g*o**2 + s + 9*o**2 + 26*o**2 + 64*o.
4*(o + 2)*(7*o + 2)
Let a(n) be the first derivative of 5*n**4/4 + 365*n**3/3 + 1355*n**2/2 - 1725*n + 8958. Factor a(h).
5*(h - 1)*(h + 5)*(h + 69)
Let q = 986 - 338. Let b = q - 4532/7. Factor 6/7*u**2 - b*u - 2/7*u**3 + 0.
-2*u*(u - 2)*(u - 1)/7
Let z(s) be the first derivative of 232 + 169/8*s**4 + 26/3*s**3 + s**2 + 0*s. Solve z(a) = 0 for a.
-2/13, 0
Suppose -6*q = -0*q - 1092. Determine n so that q*n**2 - 78*n**2 - 92*n**2 + 4*n + 4*n + 4*n**3 = 0.
-2, -1, 0
Let c(v) be the third derivative of v**7/630 + v**6/12 - 43*v**5/45 + 19*v**4/12 + 35*v**3/2 - 2039*v**2. Find f, given that c(f) = 0.
-35, -1, 3
Let w(x) be the first derivative of 1/3*x**6 - 2*x**3 + 1/2*x**4 + 0*x - 11 - 2*x**2 + 6/5*x**5. Suppose w(n) = 0. What is n?
-2, -1, 0, 1
Let y(u) = u**3 - 5*u**2 + 2*u - 6. Let a = -86 + 91. Let x be y(a). Find p such that -9*p**2 - 12 - 10*p**x + 6*p**3 + 3*p**4 + 10*p**4 - 24*p = 0.
-2, -1, 2
Let o = -121667/5 + 24334. Factor 0*p - 12/5*p**3 + 0*p**2 + o*p**4 + 0.
3*p**3*(p - 4)/5
Let l be ((-16)/6)/((-22)/33). Factor 125*a**3 - 100*a**4 - 22*a**5 + 53*a**l + 17*a**5 - 73*a**4.
-5*a**3*(a - 1)*(a + 25)
Suppose 8*n - 17 = 103. Suppose q + n = r + 12, 0 = -2*r - 4*q. Factor 7/5*m**3 + 4/5 - 12/5*m - 9/5*m**r.
(m - 2)*(m + 1)*(7*m - 2)/5
Let b(u) be the third derivative of u**6/24 - 25*u**5/6 + 55*u**4/3 + 320*u**3 - u**2 + 1421. Find r, given that b(r) = 0.
-2, 4, 48
Suppose -10*g = -22 + 2. Factor 43*z**3 - 48*z**3 - 40*z**2 + g - 40 + 95*z - 3 - 9.
-5*(z - 1)**2*(z + 10)
Let b = -61 + 60. Let q be (32/30)/(b - 20/(-18)). Factor -q - 3/5*m**2 + 24/5*m.
-3*(m - 4)**2/5
Let p(n) be the second derivative of -n**6/30 + 16*n**5/5 - 125*n**4/12 + 31*n**3/3 - 6162*n. Suppose p(s) = 0. What is s?
0, 1, 62
Suppose 26 = 5*g - 3*n, -g + 4*n - 4 = 1. Let s be (g + -5)/(1 + 0). Determine b, given that 1/5*b**s + 0 - 7/5*b = 0.
0, 7
Factor 35/9 + 1/9*z**4 + 34/9*z**3 - 4*z**2 - 34/9*z.
(z - 1)**2*(z + 1)*(z + 35)/9
Determine q, given that -83*q**2 - 5146*q + 88*q**2 + 2775*q - 2974*q = 0.
0, 1069
Let u = 2/287 + 227/8610. Let a(x) be the third derivative of 3/5*x**5 + 16*x**2 - u*x**6 - 9/2*x**4 + 18*x**3 + 0 + 0*x. Let a(w) = 0. What is w?
3
Determine d, given that -1488 + 6947*d**2 + 6945*d**2 + 76*d - 13888*d**2 = 0.
-31, 12
Let a(g) be the second derivative of -g**4/60 - 278*g**3/15 + 557*g**2/10 - 65*g + 8. Factor a(i).
-(i - 1)*(i + 557)/5
Let h(m) = -m**3 - 15*m**2 + 29*m - 81. Suppose -31 = 2*k + 3*v, -v + 4*v - 37 = 2*k. Let t be h(k). Solve 2/13*s**t + 0*s + 16/13*s**3 + 0 + 32/13*s**2 = 0.
-4, 0
Let h(g) be the third derivative of g**10/529200 - g**9/42336 + g**8/11760 - 29*g**5/12 + 7*g**2 - g. Let l(p) be the third derivative of h(p). Factor l(c).
2*c**2*(c - 3)*(c - 2)/7
Let x(u) be the third derivative of u**8/1596 - 3*u**7/133 + 4*u**6/15 - 161*u**5/114 + 71*u**4/19 - 260*u**3/57 + 2111*u**2. Find g such that x(g) = 0.
1/2, 2, 5, 13
Suppose 84*i - 279 = 17*i + 190. Let l(t) be the third derivative of 0 - 4/3*t**3 - 3/10*t**5 + 15*t**2 + 0*t - 1/30*t**6 + 1/35*t**i + t**4. Factor l(c).
2*(c - 1)**2*(c + 2)*(3*c - 2)
Let q be (-275)/(-77) + -4 - 48/(-14). Factor 12*f**4 - 48*f + 472*f**2 - 148*f**q - 143 - 113 - 32.
4*(f - 6)**2*(f - 1)*(3*f + 2)
Suppose 3*r - 10 = -2*y, 3*y + 12 = 5*r + 4*y. Suppose 4*x**2 + 2 + 25*x + 6*x**r - 5*x**2 + 18 = 0. Calculate x.
-4, -1
Suppose 48*u - 43*u - 47 = -4*c, 3*u - 5*c + 31 = 0. Let i(g) be the second derivative of -6144*g**2 - 384*g**u - 3/20*g**5 - 2 - 12*g**4 + 2*g. Factor i(s).
-3*(s + 16)**3
Let h(u) = -u**5 + u**3 + u. Let b(a) = 4*a + 16*a + 23*a**3 - 4 - 25*a**2 + 118*a**5 - 121*a**5 - 7*a**4. Let r(x) = -b(x) + 4*h(x). Factor r(y).
-(y - 2)**2*(y - 1)**3
Let q = 95 - 68. Let w be 2*((-1)/(-6))/(3/q). Let x(s) = -1. Let g(c) = -3*c**2 - 60*c - 297. Let t(f) = w*x(f) + g(f). Let t(o) = 0. Calculate o.
-10
Let b(f) be the third derivative of f**5/15 + 164*f**4 + 161376*f**3 + f**2 + 147. Let b(t) = 0. Calculate t.
-492
Suppose 2*o**3 - 40*o**2 - 25*o + 62*o**2 + 65*o - 40*o**2 = 0. Calculate o.
0, 4, 5
Let k(d) be the first derivative of -8*d**5/5 + 65*d**4 - 488*d**3 - 466*d**2 + 800*d - 4643. Solve k(l) = 0 for l.
-1, 1/2, 8, 25
Let n(y) be the second derivative of 1/3*y**3 - 8*y + 0 + 1/84*y**4 + 7/2*y**2. Factor n(q).
(q + 7)**2/7
Let j be (-132 - 2)/(-6 - (-539)/91). Factor 35 + j*z**2 + 12*z + 1738*z**2 - 3479*z**2.
(z + 5)*(z + 7)
Let j = -613 - -613. Let -264*i**2 + j*i**4 + 30*i + 5*i**4 + 239*i**2 - 10*i**3 = 0. What is i?
-2, 0, 1, 3
Let u(p) be the second derivative of -5*p**5/3 + 20*p**4/9 + 512*p**3/9 + 512*p**2/3 - 849*p. Factor u(c).
-4*(c - 4)*(5*c + 8)**2/3
Let r(d) be the first derivative of -d**6/24 + 7*d**5/4 - 6*d**4 - 9915. Factor r(s).
-s**3*(s - 32)*(s - 3)/4
Let d(m) = 6*m**2 + 1848*m - 1800. Let i(v) = 49*v**2 + 14783*v - 14382. Let g(f) = -25*d(f) + 3*i(f). Factor g(r).
-3*(r - 1)*(r + 618)
Let -20*o**3 - 28*o + 2*o**4 - 3*o**2 + 40*o**2 + 2*o**2 + 7*o**2 = 0. Calculate o.
0, 1, 2, 7
Let u be 36/14*(-2)/(-1). Let h = 218996/217 + -30426/31. Factor h*j**2 + 128/7 + 2/7*j**4 - 288/7*j - u*j**3.
2*(j - 8)**2*(j - 1)**2/7
Suppose -16 = -2*a - 2*m, -a - 3*m + 6 = 2. Suppose -4*i + 3*g + 17 = 0, g + a = 2*i - g. What is t in 14*t**2 - 14*t**2 - 4*t**3 - 4*t**i = 0?
-1, 0
Let f be (2 - 2)/(189 - 175). Let k(o) be the second derivative of 5*o + 1/16*o**4 - 3/8*o**2 + 0*o**3 + f. Solve k(t) = 0.
-1, 1
Suppose 2*t = -8, t - 497 = -2*p + 449. Suppose 4*x - 246 - 113 = -5*d, 5*x + d = p. Factor -22*h**2 + h - x*h**3 - 64*h**4 - h - 14*h**2.
-4*h**2*(4*h + 3)**2
Determine p, given that -1825/3*p - 304 - 1/3*p**3 - 914/3*p**2 = 0.
-912, -1
Factor 22*w**2 - 56*w**2 - 54 + 15*w**2 + 22*w**2 + 21*w.
3*(w - 2)*(w + 9)
Let j(r) be the first derivative of -142/3*r**3 - 76*r**2 + 17*r**4 - 39 + 18/5*r**5 + 40*r. Find t, given that j(t) = 0.
-5, -1, 2/9, 2
Let q be 4/10*(22/((-1056)/(-270)) - 5). Let l(g) be the second derivative of 1/48*g**4 + g**2 - 7*g + 0 + q*g**3. Let l(i) = 0. Calculate i.
-4, -2
Suppose -3252*a**4 - 3227*a**4 + 19 - 134*a**2 + 12*a**3 + 6594*a**4 + 6*a**5 - 18*a = 0. Calculate a.
-19, -1, -1/2, 1/3, 1
Suppose -16*g = -20*g + 34 + 2, 5*i - 18 = -2*g. Factor l - 1/8*l**4 + 3/4*l**3 - 3/2*l**2 + i.
-l*(l - 2)**3/8
Let x = 41020 + -861403/21. Let f(s) be the second derivative of -1/70*s**5 - 24*s - 4/21*s**4 + 0 - x*s**3 - 10/7*s**2. Suppose f(d) = 0. Cal