s) - 6*v(s). Determine x so that o(x) = 0.
-2/97, 3
Let y = -25251/22 - -430059/374. Suppose 10/17*a**2 - 46/17*a**3 + 6*a + 10/17*a**4 + y = 0. Calculate a.
-1, -2/5, 3
Let i(n) be the first derivative of 42 + 0*n + 2*n**2 + 4/3*n**3 + 1/4*n**4. Factor i(b).
b*(b + 2)**2
Factor 7803/5 - 1/5*j**5 - 8721/5*j - 622/5*j**3 + 43/5*j**4 + 3546/5*j**2.
-(j - 17)**2*(j - 3)**3/5
Let f(g) be the second derivative of -128*g**6/75 + 1488*g**5/25 - 2691*g**4/5 - 4464*g**3/5 - 2592*g**2/5 + 436*g. Factor f(k).
-4*(k - 12)**2*(8*k + 3)**2/5
Factor 4164/5*p + 2167362/5 + 2/5*p**2.
2*(p + 1041)**2/5
Let q(r) = 233*r**2 + 2706*r + 7647. Let j(t) = 2*t**2 + 4*t - 7. Let c(p) = 6*j(p) + q(p). Factor c(h).
5*(7*h + 39)**2
Let y = 122 - 134. Let p(d) = -15*d**5 - 3*d**4 - 12*d**3 + 12*d**2 + 12*d + 12. Let u(h) = -h**5 + h**4 + h**2 + h + 1. Let j(m) = y*u(m) + p(m). Factor j(b).
-3*b**3*(b + 1)*(b + 4)
Let u(x) be the third derivative of -x**5/80 + 19*x**4/16 - 35*x**3 + 2*x**2 + 13. Factor u(i).
-3*(i - 28)*(i - 10)/4
Let d(n) be the third derivative of n**7/1050 - 7*n**6/600 + 3*n**5/100 + 7*n**4/120 - n**3/3 + 460*n**2 + 1. Determine j so that d(j) = 0.
-1, 1, 2, 5
Let y = 138533 - 138531. Find u such that -27/8*u + 3/4 - 9/8*u**4 + 39/8*u**3 + 3/8*u**y - 3/2*u**5 = 0.
-2, -1, 1/4, 1
Factor -5/4*l**2 + 0 + 785/4*l.
-5*l*(l - 157)/4
Let y(h) be the second derivative of 19*h - 8/3*h**3 + 0 + 0*h**2 + 1/54*h**4. Find p such that y(p) = 0.
0, 72
Let k(r) be the first derivative of 3*r**4/2 + 3*r**3 - 27*r**2 + 24*r - 611. Factor k(t).
3*(t - 2)*(t + 4)*(2*t - 1)
Factor 56/17*t + 0*t**2 - 2/17*t**3 + 96/17.
-2*(t - 6)*(t + 2)*(t + 4)/17
Suppose -3*q = -j - 1185 + 1173, -3*j - 36 = 2*q. Solve 16/3 + 80/3*t**2 - 4/3*t**5 + 40/3*t**3 + 20*t + q*t**4 = 0 for t.
-1, 4
Factor 7/6*r - 1/6*r**2 + 13.
-(r - 13)*(r + 6)/6
Let a(t) be the first derivative of t**6/6 - 27*t**5/10 + 83*t**4/8 + 21*t**3/2 - 49*t**2/4 + 1780. Suppose a(q) = 0. Calculate q.
-1, 0, 1/2, 7
Let x(t) be the second derivative of -t**6/180 + t**5/5 + 55*t**4/72 - 13*t**3/6 + 4*t + 177. Determine n so that x(n) = 0.
-3, 0, 1, 26
Let q be (-5)/((-7)/((-35)/20))*-8. Factor -5*p**5 + 16*p + 19*p**3 - q*p**5 - 7*p**4 - 4 - 25*p**2 + 16*p**5.
(p - 2)**2*(p - 1)**3
Let x = -4157 - -4157. Let c(s) be the second derivative of -5/3*s**2 - 1/18*s**4 + x + 5*s - 2/3*s**3. Factor c(j).
-2*(j + 1)*(j + 5)/3
Let s = -7292/95 + 1466/19. Factor s*f**2 + 2/5*f - 2/5 - 2/5*f**3.
-2*(f - 1)**2*(f + 1)/5
Let n(b) be the second derivative of -b**4/60 + 1118*b**3/15 - 624962*b**2/5 - b + 146. Determine y, given that n(y) = 0.
1118
Let n(w) be the second derivative of 5*w**4/12 - 425*w**3/6 - 435*w**2 - 2319*w. Factor n(v).
5*(v - 87)*(v + 2)
Find j such that 133*j**3 - 688 + 3*j**4 - 620*j + 134*j**3 - 448*j - 1400 + 510*j**2 = 0.
-87, -2, 2
Suppose -14 - 1 = 30*p - 15. Let b(j) be the second derivative of 2/9*j**3 + 1/9*j**4 + 3*j - 4/3*j**2 + p. Factor b(k).
4*(k - 1)*(k + 2)/3
Let p(z) be the first derivative of -z**3/7 + 9*z**2/14 + 162*z/7 - 1422. Factor p(f).
-3*(f - 9)*(f + 6)/7
Let r(n) = 81*n**2 + 2*n - 24. Let o be r(4). Factor 1000*g**2 + 372 + 295*g**3 + 70*g**4 + 268 - o*g - 5*g**5 - 675*g**3.
-5*(g - 4)**2*(g - 2)**3
Let i(d) be the first derivative of d**5/5 + 49*d**4/4 + 255*d**3 + 3179*d**2/2 - 9826*d + 10800. Determine f, given that i(f) = 0.
-17, 2
Let o(g) be the third derivative of -1/3*g**3 - 24*g**2 + 1/18*g**4 - 1/360*g**6 + 1/120*g**5 + 0*g + 0. Factor o(c).
-(c - 2)*(c + 2)*(2*c - 3)/6
Let p = 290 + -263. Suppose -23*v + 7*v - 5*v**3 - 27 + p - 29*v + 30*v**2 = 0. Calculate v.
0, 3
Let p(q) = -7*q + 119. Let k be p(13). What is s in 177*s**3 - 57*s**3 + 33 + 46 + 65 - 528*s + 52*s**2 - k*s**4 = 0?
-2, 2/7, 3
Let y(q) = -9*q + 99. Let p be y(11). Find j, given that -18*j**3 + 12*j**2 + p*j**3 + 15*j**3 = 0.
0, 4
Let r(g) be the third derivative of -g**6/24 - 18*g**5 + 4*g**2 + 3*g - 3. Solve r(a) = 0.
-216, 0
Let a(k) be the second derivative of k**4/36 + 43*k**3/18 + 72*k**2 - 8*k - 34. Suppose a(c) = 0. Calculate c.
-27, -16
Let c(q) = -q**4 + q**3 + q**2 - q + 11. Let n(j) = -23*j**4 + 3*j**3 + 138*j**2 + 122*j + 63. Let w(y) = 3*c(y) - n(y). Factor w(r).
5*(r - 3)*(r + 2)*(2*r + 1)**2
Let l = 3692126/2769099 - -2/923033. Factor l - 4/3*m**2 - 1/3*m + 1/3*m**3.
(m - 4)*(m - 1)*(m + 1)/3
Let n be 9597/7645 - (13 + (-372)/30). Let v = n + 10/139. Factor -8/11 - v*x - 2/11*x**2.
-2*(x + 2)**2/11
Let i(r) = r**3 + 11*r**2 + 23*r + 57. Let z be i(-5). Factor 3*u**4 - z*u - 12*u**2 - 72*u**2 - 32 + 300*u**3 + u**4 - 320*u**3.
4*(u - 8)*(u + 1)**3
Let q be -2 + -22 + -14 + 43. Determine h, given that 424/7*h**3 + 128/7 + 74/7*h**4 + 4/7*h**q + 544/7*h + 110*h**2 = 0.
-8, -1, -1/2
Let l be (-4)/((-20)/5) - -4. Suppose -l*j + 4*j + 3*q + 6 = 0, 2*j - 12 = q. Suppose -34*t**2 + 31*t**2 + 9 - j = 0. What is t?
-1, 1
Let o(j) be the third derivative of -j**5/150 + 97*j**4/30 + 197*j**3/5 + 7*j**2 + j - 8. Suppose o(p) = 0. What is p?
-3, 197
Suppose 1808*a**2 + 705*a - 868*a**2 - 949*a**2 + 2196 = 0. Calculate a.
-3, 244/3
Let f(j) be the first derivative of 114 + 9/25*j**2 + 8/75*j**3 + 0*j. Solve f(a) = 0.
-9/4, 0
Suppose -108*d - 18*d**3 - 3/4*d**4 - 219/2*d**2 + 945/4 = 0. What is d?
-15, -7, -3, 1
Factor 0 - 96*y + 4/5*y**2.
4*y*(y - 120)/5
Let z(t) be the first derivative of 5*t**4/4 - 70*t**3/3 + 265*t**2/2 - 200*t - 46. Factor z(g).
5*(g - 8)*(g - 5)*(g - 1)
Factor -1/2*g**2 + 45 + 89/2*g.
-(g - 90)*(g + 1)/2
Let d(p) be the third derivative of -p**7/525 + 11*p**6/75 + 253*p**5/150 - 86*p**4/15 - 784*p**3/5 + 71*p**2 - 7*p + 6. Determine r, given that d(r) = 0.
-4, 3, 49
Let p(v) be the third derivative of v**8/168 + 4*v**7/15 - v**6/5 - 32*v**5/3 + 112*v**4/3 - 2*v**2 - 38*v - 52. Suppose p(d) = 0. What is d?
-28, -4, 0, 2
Find a, given that 99*a**4 - 28304501*a + 1361*a**3 + 72 + 28304615*a - 287*a**3 - 1359*a**2 = 0.
-12, -2/11, 1/3, 1
Let k be (-24)/(-52)*1911/4851. Find n such that 0 - 30/11*n - 28/11*n**2 + k*n**3 = 0.
-1, 0, 15
Let a be (2/(-1764)*-21)/((-4)/(-12)). Let p(c) be the first derivative of 0*c - 3/35*c**5 - a*c**2 - 1/4*c**4 - 13 - 5/21*c**3. Factor p(m).
-m*(m + 1)**2*(3*m + 1)/7
Let n be ((-6435)/(-66))/(-15) + (6/(-4) - -1) - -11. Suppose 46/3*j**2 + 8*j - 134/3*j**n + 4*j**5 + 0 - 124/3*j**3 = 0. What is j?
-1, -1/3, 0, 1/2, 12
Let l(n) be the first derivative of -n**4 + 40*n**3/3 - 66*n**2 + 144*n - 601. Factor l(y).
-4*(y - 4)*(y - 3)**2
Solve 64/11 + 8/11*v**2 + 56/11*v - 2/11*v**3 = 0 for v.
-2, 8
Let k be 1922 + (24/(-20))/(16/40). Let t = k + -1917. Factor -2*c**4 + 2/3 + 4/3*c**3 + 2/3*c**5 - 2*c + 4/3*c**t.
2*(c - 1)**4*(c + 1)/3
Let y(f) be the third derivative of -f**7/315 + 17*f**6/36 - 587*f**5/30 - 2021*f**4/36 + 3698*f**3/9 - 754*f**2. Suppose y(a) = 0. Calculate a.
-2, 1, 43
Let s = 4 - -2. Suppose 0*h + 3*h = s. Factor -3*k + 4*k**5 + k - 8*k**h - 19*k**4 - 2*k + 27*k**3 + 0*k**2.
k*(k - 2)**2*(k - 1)*(4*k + 1)
Let u(g) be the third derivative of -3*g**2 + 4/13*g**3 - 11*g - 1/130*g**5 - 1/780*g**6 + 0 + 1/39*g**4. Factor u(q).
-2*(q - 2)*(q + 2)*(q + 3)/13
Let v = -59 - -61. Factor -2*p**2 + 309 + 6*p**v - 329 + 16*p.
4*(p - 1)*(p + 5)
Let 26/3*n**4 + 184/3*n**3 + 404/3*n**2 + 88*n + 6 = 0. Calculate n.
-3, -1, -1/13
Factor 13/2*i**2 - 1/2*i**4 + 0 - 5*i**3 + 11*i.
-i*(i - 2)*(i + 1)*(i + 11)/2
Let m(z) = 3*z**5 - 15*z**3 - 8*z**2 - 8. Let w(t) = -16*t**5 - t**4 + 76*t**3 + 39*t**2 + 44. Let q(a) = 11*m(a) + 2*w(a). Factor q(b).
b**2*(b - 5)*(b + 1)*(b + 2)
Factor -487379386/3*s**2 + 991694873*s - 1/3*s**5 - 1496031771 - 624094*s**3 - 791*s**4.
-(s - 3)**2*(s + 793)**3/3
Let m = -5449/6 - -16507/18. What is l in 32/3*l + 22/9*l**3 + m*l**2 + 0 + 2/9*l**4 = 0?
-4, -3, 0
Let n(w) = 7*w**2 + 47*w - 136. Let g(c) = -c**2 - 2*c - 2. Let j(s) = -4*g(s) - n(s). Suppose j(i) = 0. Calculate i.
-16, 3
Suppose 6*x - 65 = -23. Suppose 34*b**5 + 2*b**5 - b**2 + 52*b**3 - x*b**2 - 80*b**4 = 0. Calculate b.
0, 2/9, 1
Let z(m) = -7*m**3 - 167*m**2 + 168*m + 368. Let l(t) = -9*t**3 - 165*t**2 + 168*t + 372. Let h(u) = -5*l(u) + 6*z(u). Factor h(a).
3*(a - 58)*(a - 2)*(a + 1)
Let f(p) be the second derivative of p**7/2 + 41*p**6/5 + 879*p**5/20 + 169*p**4/2 + 60*p**3 - 153*p 