3. Suppose u(n) = 0. Calculate n.
-1, 0, 1/4, 9
Let z(o) be the first derivative of 1/14*o**5 - 5 - 1/105*o**6 - 1/6*o**4 + 1/7*o**3 + 0*o**2 + 8*o. Let q(x) be the first derivative of z(x). Factor q(v).
-2*v*(v - 3)*(v - 1)**2/7
Let r be 2/(-12) + -13*(-2)/12. Determine i, given that -57*i**r - 30*i**3 - 51*i + 11*i - 3*i**2 + 0*i**2 - i**4 - 4*i**4 = 0.
-2, 0
Let f = -12362 + 49451/4. Let v = 7/18 + 121/36. Factor -3/2*t**3 + 0 + 9/2*t + f*t**4 - v*t**2.
3*t*(t - 3)*(t - 1)*(t + 2)/4
Let b(m) be the third derivative of -m**8/2016 + m**6/450 - 29*m**5/10 - 152*m**2. Let z(c) be the third derivative of b(c). Factor z(l).
-2*(5*l - 2)*(5*l + 2)/5
Suppose 0 = -30*u + 4 + 56. Let -16*d + 4*d**4 + 55*d**2 + 56*d**2 - 12 - 96*d**3 - 7*d**u + 16*d**5 = 0. Calculate d.
-3, -1/4, 1
Factor -153*t**3 - 104*t + 244*t**3 + 4*t**4 - 116*t**2 + 597*t**2 - 22*t.
t*(t + 9)*(t + 14)*(4*t - 1)
Factor 30*n + 319440*n**2 + 319438*n**2 - 638880*n**2 - 100.
-2*(n - 10)*(n - 5)
Factor 216 - 649/3*o + 1/3*o**2.
(o - 648)*(o - 1)/3
Let j be 4*36/(-384)*((-2)/(-17) + 1012/(-2244)). Determine w so that 0 - 9/4*w + j*w**2 = 0.
0, 18
Let o(m) be the second derivative of -m**5/4 - 5*m**4/6 + 65*m**3/6 - 25*m**2 + 2*m - 443. Suppose o(y) = 0. Calculate y.
-5, 1, 2
Let o = -2905 + 2915. Let g(l) be the first derivative of l**2 + o + 1/3*l**3 + l. Factor g(m).
(m + 1)**2
Suppose 0 = p - 4*r - 146 - 143, 5*p = 5*r + 1475. Let a = -243 + p. What is s in -54/5 - 36*s**2 + 140*s**3 + 98*s**4 - a*s - 686/5*s**5 = 0?
-3/7, 1
Let j be ((-16)/400)/(38/(-10)). Let k(n) be the third derivative of -2/285*n**5 + 1/285*n**7 + 0*n**3 + 0 + j*n**6 + 0*n + 0*n**4 + 13*n**2. Solve k(m) = 0.
-2, 0, 2/7
Let g(n) = 36*n - 21. Let z be g(11). Let j be 64/11 + (7 - z/55). Factor 21*m + 12*m**2 + 52 + 3*m**3 - 46 - j*m.
3*(m + 1)**2*(m + 2)
Let h(y) be the third derivative of 2*y**2 + 0*y + 55/12*y**4 - 5/2*y**3 + 49/96*y**6 + 4 - 175/48*y**5. Determine a, given that h(a) = 0.
2/7, 3
Let 100*y + 45*y**2 - 495*y**3 + 506*y**3 - y**4 - 667*y = 0. What is y?
-7, 0, 9
Solve 19*g**2 + 14*g**5 - 98*g**3 - 54*g**4 + 16*g - 16*g - 3*g**2 - 46*g**4 = 0 for g.
-1, 0, 1/7, 8
Let p(i) be the second derivative of i**4/90 - 14*i**3/45 - 32*i**2/15 - 2*i + 34. Solve p(c) = 0 for c.
-2, 16
Solve -3*t**4 + 2820*t - 1746*t**2 - 8*t**4 + 33*t**4 - 10*t**4 - 1416 - 9*t**4 + 339*t**3 = 0.
-118, 1, 2
Let l(g) be the first derivative of 5/4*g**6 + 89 + 12*g**3 - 8*g + 17*g**4 + 79/10*g**5 - 4*g**2. Let l(q) = 0. What is q?
-2, -1, -2/3, 2/5
Let f = -53950 - -53960. Factor 5/3*v**2 - 25/3*v - f.
5*(v - 6)*(v + 1)/3
Suppose 896/3*k - 8/3*k**3 + 2560/3 + 2/3*k**4 - 72*k**2 = 0. What is k?
-10, -2, 8
Let f(q) be the first derivative of -81*q**6/4 + 297*q**5/5 - 57*q**4/2 + 4*q**3 - 2243. Factor f(y).
-3*y**2*(y - 2)*(9*y - 2)**2/2
Let y(n) be the first derivative of 4/3*n**3 - 66 + 26*n**2 + 48*n. Factor y(f).
4*(f + 1)*(f + 12)
Let m(o) = -o**2 - o - 1. Let j(c) be the first derivative of -c**4/2 - c**3/3 - c**2/2 + 3*c + 7. Let f = -17 - -22. Let r(s) = f*m(s) + j(s). Factor r(i).
-2*(i + 1)**3
Let t(s) be the first derivative of -120*s**2 - 35 - 1/2*s**4 + 200*s + 14*s**3. Factor t(h).
-2*(h - 10)**2*(h - 1)
Factor 2499 - 92*v**2 + 94*v**2 - 3235 - 76*v.
2*(v - 46)*(v + 8)
Suppose 0 = -2*a + 70 - 54. Let w = a + -5. Find c, given that -c**w + 5*c**3 + 2048 - 15*c**2 + 111*c**2 + 768*c = 0.
-8
Let f = -989423/3 + 329821. Solve -f + 2*h**2 - 56/3*h = 0.
-2/3, 10
Let j(o) = -32*o**3 + 125*o**2 - 1821*o + 7452. Let q(t) = -182*t**3 + 751*t**2 - 10925*t + 44712. Let i(p) = -34*j(p) + 6*q(p). Suppose i(r) = 0. Calculate r.
9, 46
Let o be 6/(-39) + (-15789)/(-1482). Factor -3/4*n**4 + o*n**3 - 84*n - 48 - 99/4*n**2.
-3*(n - 8)**2*(n + 1)**2/4
Let d = 22688/605 - 4344/121. Solve 8 + 2/25*b**2 - d*b = 0.
10
Let a(y) be the second derivative of y**7/3780 + 13*y**6/540 + 169*y**5/180 - y**4/12 - y**3/2 + 84*y. Let v(o) be the third derivative of a(o). Factor v(l).
2*(l + 13)**2/3
Suppose 5*n = 5*u + 170, 0 = -4*n - 10*u + 13*u + 139. Let 698*f**3 - 34*f**4 + n*f**4 - 716*f**3 = 0. What is f?
0, 6
Let k = 3433/14 - 3417/14. Factor -2/7*q**2 + 0*q + k.
-2*(q - 2)*(q + 2)/7
Let d(g) be the second derivative of -g**5/25 - 29*g**4/15 + 124*g**3/15 + 625*g. Factor d(b).
-4*b*(b - 2)*(b + 31)/5
Suppose 13*h - 18 = -5*h. Suppose 11*o = -5*v + 13*o - 2, -o = 3*v - h. Factor 0*c + v - 1/6*c**3 - 1/2*c**2.
-c**2*(c + 3)/6
Let j(u) = -2*u**4 + u**3 + 2*u**2 - u + 1. Let b(a) = -7*a**4 - 14*a**3 - 3*a**2 + 84*a + 6. Let l(q) = b(q) - 6*j(q). Factor l(w).
5*w*(w - 3)**2*(w + 2)
Let h(p) be the first derivative of -p**4/42 + 11*p**3/21 - 18*p**2/7 + 31*p + 70. Let w(f) be the first derivative of h(f). Find i such that w(i) = 0.
2, 9
Suppose v + 6*i + 75 = 0, 16*v - 31 = 10*v + i. Factor 5/2*m - 1 + 1/2*m**v - 2*m**2.
(m - 2)*(m - 1)**2/2
Suppose 2225*y - 3740 = 355*y. Solve 0*o + 2/9*o**4 - 2*o**3 - 20/9*o**y + 0 = 0 for o.
-1, 0, 10
Let r(a) be the second derivative of -a**5/15 - 10*a**4/9 - 14*a**3/3 - 78*a + 43. Factor r(c).
-4*c*(c + 3)*(c + 7)/3
Let y(d) be the third derivative of -27*d**5/4 - 30*d**4 - 160*d**3/3 + 140*d**2. Factor y(g).
-5*(9*g + 8)**2
Let r be -1 + -8 + 386/6. Let p = r - 164/3. What is m in -p*m**2 + 2 - 4/3*m = 0?
-3, 1
Let i(l) be the third derivative of -l**7/840 - l**6/160 - l**5/120 + l**2 + 96. Factor i(h).
-h**2*(h + 1)*(h + 2)/4
Let w be (1/2)/((-1)/(-34)). Let s be (-110)/6*(w - 957/55). Factor -4*t + 2*t**3 + s*t**2 - 16/3.
2*(t - 1)*(t + 4)*(3*t + 2)/3
Suppose 4*s + 14 = -2*a, -s - 1799*a + 1804*a + 35 = 0. Factor s - 3/2*k**3 - 57*k**2 - 1083/2*k.
-3*k*(k + 19)**2/2
Let l(p) be the first derivative of p**3/12 - 3*p**2 - 81*p/4 + 730. Let l(s) = 0. What is s?
-3, 27
Let x = 25 + 5. Let v = x - 24. Factor 6*f**3 - 3*f**4 + 3 - 13*f**2 + 13*f**2 - v*f.
-3*(f - 1)**3*(f + 1)
Let o = -4843/11 - -2952/55. Let i = o + 387. What is y in -1/5*y**2 + 1/5*y**4 + 0 - 2/5*y + i*y**3 = 0?
-2, -1, 0, 1
Determine f so that -211*f**2 + 58 + 1 - 31 + 215*f**2 - 32*f = 0.
1, 7
Let l(h) = -31*h**2 + 1. Let z(f) = -215*f**2 - 12228*f + 18690505. Let m(n) = -14*l(n) + 2*z(n). Determine r so that m(r) = 0.
3057
Let h(s) be the second derivative of -13*s**4/120 - 139*s**3/20 - 8*s**2/5 + 3380*s. Find t, given that h(t) = 0.
-32, -1/13
Let i(n) = 3*n + 30. Let z be i(-9). Factor -9*m - m**2 + 3*m**3 - 4 + z + 3 - m**4 + 6*m.
-(m - 2)*(m - 1)**2*(m + 1)
Let l be 537/153 + (-366)/2074. Determine f, given that -20/3*f**2 - 2/3 + 10/3*f - l*f**4 + 2/3*f**5 + 20/3*f**3 = 0.
1
Suppose -26 - 22 = -3*q. Suppose 64*j - q*j**4 + 30*j**4 + 0 - 44*j**2 - 2*j**5 + 2*j**4 + 64 - 26*j**3 = 0. What is j?
-1, 2, 4
Let m(s) be the first derivative of 3*s**5/20 - 3*s**4/16 - 5*s**3/2 - 3*s**2 + 3172. Factor m(i).
3*i*(i - 4)*(i + 1)*(i + 2)/4
Suppose -2 = -2*r - 3*j, 0 = 7*r - 3*j - 2445 + 2411. Factor -r*f - 1/6*f**2 - 22/3.
-(f + 2)*(f + 22)/6
Let x(t) = -t**3 + 6*t**2 - 5*t + 2. Suppose 4*v + 2 = -2*u, 3*u - 5*v - 9 - 21 = 0. Let m be x(u). Factor -6*n - m*n + 5*n**2 + 5 - 2*n.
5*(n - 1)**2
Let b(t) = -t**3 - 5*t. Let h(g) = 2*g**3 + 81*g**2 - 880*g + 2275. Let v(a) = 4*b(a) + 4*h(a). Factor v(m).
4*(m - 5)**2*(m + 91)
Let y(o) be the second derivative of 1/24*o**4 + 1/60*o**6 + 3/40*o**5 - 1/4*o**3 - o - 12 - 1/2*o**2. Factor y(a).
(a - 1)*(a + 1)**2*(a + 2)/2
Let i be (-141194)/(-134974) + (-9)/(-93). Find v such that -6/7*v**3 + 24/7*v - 2/7*v**4 + i*v**2 + 0 = 0.
-3, -2, 0, 2
Let g = 37405/14 + -112075/42. Suppose 0*d**2 + 1/6*d**4 + g*d - 5/6*d**3 - 8/3 = 0. What is d?
-2, 1, 2, 4
Factor 63/2*w + 3/2*w**2 - 33.
3*(w - 1)*(w + 22)/2
Let n(o) = 40*o**2 + 759*o - 34. Let t(i) = -14*i**2 - 254*i + 12. Let g(v) = 6*n(v) + 17*t(v). Solve g(l) = 0 for l.
-118, 0
Let w(k) be the first derivative of k**6/60 + 7*k**5/30 + 11*k**4/12 + 5*k**3/3 - 9*k**2 - 9. Let i(f) be the second derivative of w(f). Factor i(d).
2*(d + 1)**2*(d + 5)
Let m(t) be the first derivative of -t**3/15 + 59*t**2/10 - 360. What is q in m(q) = 0?
0, 59
Let h(l) be the third derivative of -l**6/900 - l**5/150 - 107*l**2 - 4. Find p such that h(p) = 0.
-3, 0
Let l(f) = -15*f - 28 + 37 - 14. Let v be l(-3). Determine j, given that -20*j**3 + v*j + 12*j**2 + 25*j**3 + 13*j**2 + 17 