+ 1081*n**2. Find o, given that d(o) = 0.
-21, 3
Let y(n) be the second derivative of -27*n - 2 + 1/2*n**3 - 1/24*n**4 + 7/4*n**2. Let y(s) = 0. What is s?
-1, 7
Suppose -5*o + 5 = 2*v, v + 0*o - 5 = -5*o. Suppose -49*w = -66*w + 218*w - 603. Factor -2/3*t**2 - 4/9*t**w + v*t + 2/9*t**4 + 0.
2*t**2*(t - 3)*(t + 1)/9
Let h be (-13)/(52/(-20)) + 2962/(-592). Let y = h - -2371/888. Factor 13/3*t**3 + y - 2*t**2 + 5/3*t**4 - 20/3*t.
(t - 1)*(t + 2)**2*(5*t - 2)/3
Let g(n) be the third derivative of -2/15*n**7 - 4/15*n**5 + 3*n**2 + 0*n + 0*n**3 + 0*n**4 + 5 - 8/15*n**6. Suppose g(s) = 0. Calculate s.
-2, -2/7, 0
Let p(t) = 2*t - 23. Let i be p(15). Suppose -3 = n - i. Find j, given that 260*j + 96*j**2 + j**4 + 232 + 16*j**3 - n*j + 24 = 0.
-4
Let o(l) = -189*l - 376. Let w be o(-2). Let j(g) be the first derivative of -22 - 2/3*g**3 + 2/15*g**5 + 16/3*g**w + 8*g - g**4. Factor j(h).
2*(h - 6)*(h - 2)*(h + 1)**2/3
Suppose 3/7*m**3 + 144 - 261/7*m**2 + 744/7*m = 0. What is m?
-1, 4, 84
What is d in 12*d**4 - 83/2*d + 1/2*d**5 - 30 + 41*d**3 + 18*d**2 = 0?
-20, -3, -1, 1
Let v be 9/(-2)*(-28)/42. Factor -v*l**3 + 7*l - 12 - 4*l**3 - 9*l + 9*l**3 + 12*l**2.
2*(l - 1)*(l + 1)*(l + 6)
Let m(h) be the second derivative of -h**5/5 + 133*h**4/3 + 2*h**3/3 - 266*h**2 - 10*h - 133. Factor m(g).
-4*(g - 133)*(g - 1)*(g + 1)
Let s(x) be the second derivative of -1/110*x**5 + 5/11*x**3 - 127*x + 7/33*x**4 + 0 + 0*x**2. Factor s(u).
-2*u*(u - 15)*(u + 1)/11
Factor 694 + 256*w - 400 + 396*w**2 - 486.
4*(9*w - 4)*(11*w + 12)
Let f be (6/45)/(3 - (-135)/(-47)) + 3/(-27). Let s = -1119 - -5613/5. Factor 2/15*g**4 - s*g + 6/5*g**2 - 36/5 + f*g**3.
2*(g - 2)*(g + 3)**3/15
Let b(h) be the second derivative of 1/42*h**7 + 0*h**2 - 1/20*h**5 - 3*h + 0*h**3 + 17 + 1/4*h**4 - 1/10*h**6. Factor b(i).
i**2*(i - 3)*(i - 1)*(i + 1)
Let x(s) = -4*s**2 - 25*s + 5. Let o(j) = 4*j**2 + 26*j - 6. Suppose k + 6 = 3. Let q be (-7)/14*k*(-8)/2. Let a(m) = q*x(m) - 5*o(m). Factor a(t).
4*t*(t + 5)
Let b(r) = 3*r**2 + 2*r - 5. Let w(j) = -8*j**2 - j + 9. Suppose 65*h + 160 = 33*h. Let d(n) = h*b(n) - 2*w(n). Factor d(t).
(t - 7)*(t - 1)
Let u(w) be the first derivative of 26*w**5/5 - 187*w**4/5 + 1022*w**3/15 - 226*w**2/5 + 48*w/5 + 589. Determine q, given that u(q) = 0.
2/13, 3/5, 1, 4
Determine s so that -34567*s**2 + 45*s + 17283*s**2 + 17286*s**2 + 33 - 401 + 135*s = 0.
-92, 2
Let k be (-387 - -378) + 18/2. Let c(p) be the first derivative of 23 + 0*p**2 + k*p + 10/3*p**3 + 5/4*p**4. Factor c(s).
5*s**2*(s + 2)
Let k(p) be the first derivative of -p**5/180 - 2*p**4/27 - 19*p**3/54 - 2*p**2/3 - 144*p - 57. Let s(u) be the first derivative of k(u). Factor s(y).
-(y + 1)*(y + 3)*(y + 4)/9
Let l(n) be the first derivative of -n**4/21 + 8*n**3/7 - 22*n**2/7 - 58*n - 25. Let q(i) be the first derivative of l(i). Factor q(s).
-4*(s - 11)*(s - 1)/7
Suppose -140 = 58*k - 72*k. Factor k - 7 - 3 - 8*a**2 - a**3 - 16*a.
-a*(a + 4)**2
Let q = -400 + 404. Factor 145*r**q + 6*r**2 - 6*r**2 - 4*r**5 - 185*r**4.
-4*r**4*(r + 10)
Let t = 2154 + -2149. Suppose 4*g - 61*s - 5 = -62*s, t = s. What is z in -4/7*z**2 - 20/7*z + g = 0?
-5, 0
Let j(y) be the second derivative of y**4/6 - 499*y**3/3 - 16*y + 41. Suppose j(c) = 0. Calculate c.
0, 499
Let 672*s**2 - 5760*s + 86*s**3 + 14*s**4 - 12*s**4 + 681 - 681 = 0. Calculate s.
-24, 0, 5
Factor -18*r**4 + 286*r**3 + 3*r**5 - 930*r**2 - 48*r**4 - 507*r**2 + 960*r + 209*r**3 + 45*r**2.
3*r*(r - 8)**2*(r - 5)*(r - 1)
Let g be (-2)/10*525/168*144/(-180). Factor -g - 1/4*i**2 + 3/4*i.
-(i - 2)*(i - 1)/4
Let p = -5238 - -5242. Let k(i) be the second derivative of -5/6*i**p - 5/4*i**3 - 14*i + 0 + 0*i**2 - 1/8*i**5. Factor k(n).
-5*n*(n + 1)*(n + 3)/2
Suppose 0*o + 0 + 26/3*o**2 + 34/3*o**3 + 8/3*o**4 = 0. What is o?
-13/4, -1, 0
Suppose 4*l + 27 = 4*t - 53, 0 = t - 5*l - 40. Let r = t - -680. Factor 695 - r + 10*d + 15*d**2 + 5*d**3.
5*d*(d + 1)*(d + 2)
Let r(o) be the third derivative of o**6/30 - 72*o**5/5 - 145*o**4/2 - 436*o**3/3 - 651*o**2. Determine n, given that r(n) = 0.
-1, 218
Let t(n) be the third derivative of -125*n**7/168 - 4385*n**6/96 - 7667*n**5/80 - 1735*n**4/96 - 17*n**3/12 + 4*n**2 + 995*n. Solve t(x) = 0.
-34, -1, -1/25
Let p(l) be the third derivative of l**6/600 + 14*l**5/75 + 145*l**4/24 - 841*l**3/15 + 47*l**2 - 1. Factor p(r).
(r - 2)*(r + 29)**2/5
Let k = -239131 + 239133. Solve -34/11*o - 54/11*o**k + 12/11 - 8/11*o**3 = 0 for o.
-6, -1, 1/4
Let i(p) be the first derivative of p**6/57 + 16*p**5/95 + 1272. Factor i(n).
2*n**4*(n + 8)/19
Let i(q) be the second derivative of -q**5/10 + 8*q**4/3 - 43*q**3/3 - 60*q**2 - 847*q. Factor i(u).
-2*(u - 12)*(u - 5)*(u + 1)
Let k(q) be the first derivative of 2*q**3/9 + 911*q**2/3 - 608*q - 6604. Factor k(b).
2*(b - 1)*(b + 912)/3
Let o(r) be the first derivative of 3*r**2 + 4/5*r**5 + 14/3*r**3 - 38 + 2/3*r + 19/6*r**4. Solve o(w) = 0.
-1, -1/6
Determine w, given that 3389 - 2*w**2 + 3383 - 2*w**2 - 6772 + 3348*w = 0.
0, 837
Let c(j) be the second derivative of -20/3*j**3 + 30*j**2 + 5/12*j**4 - 2 - 4*j. What is f in c(f) = 0?
2, 6
Let g be (((-64)/176)/1)/(-21*4/66). Factor 71874/7 - 6534/7*x - g*x**3 + 198/7*x**2.
-2*(x - 33)**3/7
Let w be 30160/(-203) + 0/2. Let d = -148 - w. Factor 0*a - d + 3/7*a**2 - 1/7*a**3.
-(a - 2)**2*(a + 1)/7
Let x = 5884/11 - 41023/77. Factor -9/7 - x*f + 24/7*f**2.
3*(f - 1)*(8*f + 3)/7
Suppose -16 - 190/11*q**3 - 2/11*q**5 - 436/11*q**2 - 36/11*q**4 - 456/11*q = 0. Calculate q.
-11, -2, -1
Factor -163/5 + 4/5*x**2 - 651/5*x.
(x - 163)*(4*x + 1)/5
Let b(l) be the first derivative of -126 + 1/3*l**3 + 42*l - 23/2*l**2. Factor b(t).
(t - 21)*(t - 2)
Let h(r) be the second derivative of -r**7/210 + r**6/30 + 2*r**3/3 + 4*r**2 + 69*r. Let f(p) be the second derivative of h(p). Factor f(x).
-4*x**2*(x - 3)
Let q(o) be the second derivative of 150*o + 0 + 8/15*o**3 - 1/30*o**4 - 12/5*o**2. Factor q(f).
-2*(f - 6)*(f - 2)/5
Let x(w) = -33*w - 326. Let d be x(-10). Find m, given that 5*m**4 - 8*m**3 + 0*m**4 - 1526 - m**d + 4*m**5 + 1526 = 0.
-2, 0, 1
Let a(l) be the first derivative of l**7/56 + l**6/40 - 3*l**5/80 - l**4/16 + 86*l - 4. Let j(w) be the first derivative of a(w). Factor j(n).
3*n**2*(n - 1)*(n + 1)**2/4
Let o(m) be the first derivative of -2/15*m**6 + 6*m**2 + 143 + 16/25*m**5 - 112/15*m**3 + 0*m + 2*m**4. What is h in o(h) = 0?
-3, 0, 1, 5
Factor 6144 - 3*l**4 - 2544*l**2 - 90*l**3 + 2433*l + 1992*l**2 - 129*l.
-3*(l - 4)*(l + 2)*(l + 16)**2
Factor -21/4*z**3 + 0 - 19/4*z - 1/4*z**4 - 39/4*z**2.
-z*(z + 1)**2*(z + 19)/4
Let a(o) be the third derivative of -o**7/252 - 7*o**6/144 - o**5/8 - o**4/4 + 3*o**2 - 2*o. Let c(k) be the second derivative of a(k). Factor c(h).
-5*(h + 3)*(2*h + 1)
Let u(d) be the second derivative of -d**7/14 - 11*d**6/10 - 51*d**5/20 + 11*d**4/4 + 9*d**3 - 12080*d. Determine r, given that u(r) = 0.
-9, -2, -1, 0, 1
Suppose -25 = 5*s, 0*q = -q + 5*s + 72. Let m = 49 - q. Let -69*p**2 + 2 + 0*p - m*p**5 + 4*p**3 - 2*p + 2*p**4 + 65*p**2 = 0. Calculate p.
-1, 1
Let f(k) be the second derivative of 0*k**3 - 7/18*k**4 + 0 + 1/30*k**5 - 33*k + 0*k**2. Let f(w) = 0. Calculate w.
0, 7
Let x(q) be the first derivative of q**4/6 + 16*q**3/9 - 3842. Determine t so that x(t) = 0.
-8, 0
Let y(p) be the third derivative of 8/3*p**3 - 3 - 1/90*p**5 + 0*p - 5/36*p**4 + 5*p**2. Factor y(a).
-2*(a - 3)*(a + 8)/3
Let q(c) be the first derivative of -2059*c**2 + 1884*c**2 + 115*c + 89 + 5*c**3 + 123. Factor q(l).
5*(l - 23)*(3*l - 1)
Let q be -8 + 9 + (-1212)/(-132) + -10. Let -2/11*r**4 + 0*r**2 + q*r**3 + 0 + 0*r = 0. Calculate r.
0, 1
Let i(z) be the third derivative of 1/240*z**5 - 11*z - 1/96*z**4 + 0 - 1/4*z**3 + 3*z**2. Suppose i(l) = 0. What is l?
-2, 3
Let t(c) be the first derivative of -c**3/3 - 407*c**2 - 165649*c - 1427. Suppose t(m) = 0. What is m?
-407
Suppose 0 = 2*a + 2. Let u = 3 + a. Determine m so that 5*m + 287*m**u + m + 9*m**3 - 302*m**2 = 0.
0, 2/3, 1
Let u = 167576/3 + -55816. Factor 0 + 2/9*p**4 - 1024/9*p + u*p**2 - 16/3*p**3.
2*p*(p - 8)**3/9
Let c(v) be the second derivative of -1/36*v**4 - 54*v**2 - 2 - 21*v + 2*v**3. Find k such that c(k) = 0.
18
Let m(x) be the second derivative of -3*x - 7/12*x**5 + 6*x**3 + 1/72*