- 5403. Let w be g(6). Factor 0*u**2 - 4/3*u**w + 2/3*u**5 + 0 + 0*u**4 + 2/3*u.
2*u*(u - 1)**2*(u + 1)**2/3
Let u = 11017/177 + 547/177. Factor -364/9*q + u - 4/9*q**3 + 68/9*q**2.
-4*(q - 7)**2*(q - 3)/9
Let x(t) be the first derivative of -t**6/72 - 13*t**5/60 - 5*t**4/24 + 275*t**3/18 + 2875*t**2/24 + 4375*t/12 + 628. Determine l so that x(l) = 0.
-5, 7
Let y(c) be the second derivative of -c**7/28 - 9*c**6/8 - 519*c**5/80 - 99*c**4/8 + c**3/2 + 27*c**2 - 712*c. Let y(l) = 0. What is l?
-18, -2, -1, 1/2
Factor 0 - 2/3*i**2 + 326*i.
-2*i*(i - 489)/3
Let n(t) be the first derivative of -2*t**6/21 - 32*t**5/35 + 8*t**4/7 + 128*t**3/7 - 288*t**2/7 - 870. Factor n(g).
-4*g*(g - 2)**2*(g + 6)**2/7
Let x = 1118921/1491884 - 2/372971. Solve 9 + 9/4*q**3 - 6*q - 39/4*q**2 + 15/4*q**4 + x*q**5 = 0.
-3, -2, 1
Suppose 0 = -0*x + 3*x - 128 + 146, 4*s - 42 = 7*x. Find m such that -9/7*m - 1/7*m**3 + s - 6/7*m**2 = 0.
-3, 0
Let f be ((-8)/96)/(15 + 3654/(-243)). Suppose -51/4*b**2 - 3/8*b**5 - 3*b**4 - 69/8*b - f - 9*b**3 = 0. What is b?
-3, -2, -1
Suppose 4*b = z - b + 2, -b + 2 = -z. Let r be (1 + z/4)*188 - -2. Factor -3*n**3 - 18*n**2 + 36 - 18*n**3 + r*n - 3*n**4 + 60.
-3*(n - 2)*(n + 1)*(n + 4)**2
Let n = -360 - -372. Determine r, given that -12*r + 3 + 9 - 28 + 20*r**2 + n*r**3 - 4*r**4 = 0.
-1, 1, 4
Suppose -4*d + 9 = 1819*s - 1816*s, 0 = -5*d + 8*s - 24. Solve 0*m**2 + 0 - 1/4*m**4 + d*m + 7/4*m**3 = 0.
0, 7
Let o(r) be the third derivative of -1/30*r**5 + 0*r - 14*r**2 - 7/12*r**4 + 0*r**3 - 3. Solve o(d) = 0 for d.
-7, 0
Let -362*c**3 - 1578 - 578*c + 802*c**2 - 1405 - 6*c**4 + 28*c**3 + 3099 = 0. What is c?
-58, 1/3, 1
Factor 54/7*n - 22/7*n**3 + 2/7*n**4 + 30/7*n**2 + 0.
2*n*(n - 9)*(n - 3)*(n + 1)/7
Let s(o) be the third derivative of 1/735*o**7 - 1/70*o**5 + 2/7*o**3 - 4*o - o**2 - 1/140*o**6 + 0 + 1/12*o**4. Let s(x) = 0. Calculate x.
-1, 2, 3
Let o(p) be the second derivative of -3/2*p**2 - 1/60*p**5 - 7/36*p**4 - 59*p + 0 + 17/18*p**3. Factor o(d).
-(d - 1)**2*(d + 9)/3
Let -12320 - 819*v**2 + 22723*v + 3898*v**3 + 3*v**5 - 202*v**4 - 11125*v**2 - 4868*v**2 + 2710 = 0. Calculate v.
1, 10/3, 31
Suppose 0 = -8*t - 505 + 865. Solve 104 - 3*a**4 - 104 - t*a**3 - 81*a**2 - 39*a = 0.
-13, -1, 0
Let q be (4*6/(-54))/(495/(-1782)). Solve -24/5*p**2 - q*p + 0 + 114/5*p**4 + 58/5*p**3 + 8*p**5 = 0 for p.
-2, -1, -1/4, 0, 2/5
Let u(j) = 4*j**2 - 14*j + 10. Let t(d) = -17*d**2 + 57*d - 40. Let y = 242 - 236. Let s(n) = y*t(n) + 26*u(n). Determine i, given that s(i) = 0.
1, 10
Let n be 8/2 + 258/86. Let c be n + -3 + (-1488)/(-42). Find b such that 132/7*b**4 + 0 - 4*b**5 - 44/7*b**3 - 72/7*b - c*b**2 = 0.
-1, -2/7, 0, 3
Let n(a) = -6*a**2 + 6*a. Suppose 0*v + 39 = -13*v. Let r(q) = -11*q**2 + 10*q + 1. Let o(g) = v*r(g) + 5*n(g). Factor o(y).
3*(y - 1)*(y + 1)
Suppose 54*s + 160 + 136 = 458. Solve 150*g + 500 + 1/2*g**s + 15*g**2 = 0.
-10
Let v(g) = g**3 - 6*g**2 + 20*g - 72. Let r be v(5). Suppose -121*b - 45 - 2*b**4 - 40*b**r - 110*b**2 - 3*b**4 - 4*b + 5*b = 0. Calculate b.
-3, -1
Let 7030 - 13799 + 7233 + 4*y**2 + 132*y = 0. Calculate y.
-29, -4
Let 11663979*q + 2506940006 - 18585*q**2 + 7377379*q - 12017014601 + 5385721*q + 5*q**3 - 1400264*q = 0. Calculate q.
1239
Solve -15*d**5 - 29*d**2 - 15*d**5 + 0*d**3 + 4*d**3 + 44*d**4 + 26*d**5 - 15*d**2 = 0 for d.
-1, 0, 1, 11
Suppose 5*b + 4*v + 5 = 16, 0 = -b - 5*v - 2. Factor 14*h - h**2 - 5*h**2 + b*h**2 + 2*h**2.
-h*(h - 14)
Let s(w) be the first derivative of 35*w**2 - 5/6*w**6 - 117 - 65/4*w**4 + 25*w**3 + 0*w - 15*w**5. Find k, given that s(k) = 0.
-14, -1, 0, 1
Suppose 62 = -13*o - 3. Let u be ((-480)/(-56) + -8)/(o/(-7)). Determine d, given that -4/5*d**2 - u*d + 0 = 0.
-1, 0
Suppose -d = 6*z - 8*z + 90, -2*z + 2*d = -88. Suppose -13*p + z = 10*p. Factor -19/8*s + 1/2*s**3 - 1/2 - 11/8*s**p.
(s - 4)*(s + 1)*(4*s + 1)/8
Suppose -2199*u + 200535 = -36957. Find y, given that 12*y**3 + 432*y - 1/2*y**4 - 648 - u*y**2 = 0.
6
Factor 13/4 - 10*o + 3/4*o**2.
(o - 13)*(3*o - 1)/4
Suppose -4*k + 2 = -i + 4, k = i - 8. Let u = -112 + 114. Factor 4*p**u + i*p**3 - 4*p**3 + 11*p**2 - p**3 - 20.
5*(p - 1)*(p + 2)**2
Let f(x) be the third derivative of -75*x**2 + 15/4*x**3 + 0 + 0*x - 13/8*x**4 + 11/40*x**5. Let f(u) = 0. Calculate u.
1, 15/11
Let w(u) = -14*u + 282. Let a be w(19). Let x(g) be the first derivative of -a + 4/13*g - 2/13*g**3 + 1/13*g**2. Factor x(f).
-2*(f - 1)*(3*f + 2)/13
Suppose -245*r = -22*r + 51 - 497. Factor 8*h + 24 + 2/3*h**r.
2*(h + 6)**2/3
Solve -2/7*c**3 - 1724/7*c**2 + 1726/7*c + 0 = 0 for c.
-863, 0, 1
Let z = 366525 + -366523. Determine n, given that -3/8*n**z - 93/8 - 12*n = 0.
-31, -1
Let h(d) be the third derivative of -d**5/30 - 8*d**4/15 + 12*d**3 + 556*d**2 + 1. Factor h(i).
-2*(i + 10)*(5*i - 18)/5
Let 8*d + 30 + 2*d**4 + 1536442*d**3 + 68*d + 64*d**2 - 1536422*d**3 = 0. Calculate d.
-5, -3, -1
Factor 46/5*j - 8/5*j**3 - 2*j**2 + 12/5.
-2*(j - 2)*(j + 3)*(4*j + 1)/5
Suppose 64/5*q - 2/5*q**4 + 0 - 72/5*q**2 + 24/5*q**3 = 0. Calculate q.
0, 2, 8
Suppose 0 = -c - 2*c - x + 30, 3*x - 9 = 0. Let b be 2/(-2) - (c + -13). Factor -2*g + 24*g + b*g + 20*g**2 + 5*g**3 + 10.
5*(g + 1)**2*(g + 2)
Let f(x) be the first derivative of -8/11*x + 5 - 2/11*x**5 + 7/11*x**4 - 20/11*x**2 + 2/11*x**3. Find o, given that f(o) = 0.
-1, -1/5, 2
Let t(n) = 6*n**4 - 22*n**3 + 112*n**2 - 160*n + 64. Let a(m) = m**4 - 4*m**3 + 22*m**2 - 32*m + 13. Let y(c) = -11*a(c) + 2*t(c). Factor y(f).
(f - 3)*(f - 1)**2*(f + 5)
Let l(w) = -2*w + 30*w - 4*w + 5*w + 16. Let m be l(9). Factor -3 + 277*i - m*i + 3*i**2.
3*(i - 1)*(i + 1)
Let m(p) = 0*p**2 + 2*p**2 - 128*p - 101*p - 69 - 71 + 255*p. Let l be m(-22). Let -l - 1/2*d**3 - 12*d**2 - 96*d = 0. What is d?
-8
Let b be 3/(-4)*-8*(-13)/(-39). Suppose 4 = b*u - 3*t, -49*t + 45*t + 8 = 4*u. Let -7/5*j - 2/5 - j**u = 0. What is j?
-1, -2/5
Let r = -82846/9 - -9206. Solve 0*l**2 + 0 + r*l - 2/9*l**3 = 0 for l.
-2, 0, 2
Suppose 0 = -h - 28 - 154. Let i = -89 - h. Let 14*x**2 + 102*x**3 - 6*x - i*x**3 + x**2 = 0. What is x?
-2, 0, 1/3
Let w(z) be the first derivative of 1/48*z**4 + 32 + 23*z + 0*z**2 + 0*z**3. Let r(t) be the first derivative of w(t). Find h such that r(h) = 0.
0
Let a = 353797 - 353797. What is x in 3/4*x**5 + 3/2*x**2 - 3/2*x**4 + 0*x**3 + a - 3/4*x = 0?
-1, 0, 1
Solve 0 + 7248/5*f - 4/5*f**2 = 0.
0, 1812
Let s be 414/5*(48 - 43). Let k be (-38)/(-72) + 92/s. Let -5/4*c**4 - 1/4*c - 1/4 - 1/2*c**3 + k*c**5 + 3/2*c**2 = 0. Calculate c.
-1, -1/3, 1
Let i(j) be the second derivative of j**6/10 + 3*j**5/4 - j**4/4 - 5*j**3/2 + 193*j - 2. Determine p, given that i(p) = 0.
-5, -1, 0, 1
Let 24 - 1/2*f + 1/2*f**3 - 24*f**2 = 0. Calculate f.
-1, 1, 48
Let j(h) = -57*h + 345. Let f be j(6). Suppose 2 + 35 = f*w - 5*s, 0 = 5*w + 4*s. Determine b so that 0 + 4/5*b**2 + 0*b + 14/5*b**3 + 2*b**w = 0.
-1, -2/5, 0
Let q(d) = 90*d**2 + 415*d + 715. Let r(k) = -k**3 + 92*k**2 + 414*k + 714. Let h be (-37)/(-7) - ((-16)/(-56) + 0). Let n(y) = h*r(y) - 6*q(y). Factor n(x).
-5*(x + 4)*(x + 6)**2
Let m(b) be the second derivative of -b**5/130 + 47*b**4/78 - 475*b**3/39 - 1875*b**2/13 - 9903*b. Find g such that m(g) = 0.
-3, 25
Let q = -11945 + 12085. Let h(w) be the first derivative of q*w**2 + 25/2*w**4 - 20 - w**5 - 160*w - 60*w**3. What is n in h(n) = 0?
2, 4
Factor 45*s**2 - 165*s**2 + 37*s**2 + 42*s**2 + 38*s**2 + 198*s.
-3*s*(s - 66)
Factor 0*u + 34/3*u**5 + 2*u**3 + 0 + 40/3*u**4 + 0*u**2.
2*u**3*(u + 1)*(17*u + 3)/3
Let w = -45352 - -226778/5. Find q such that -2/5*q**3 - 54/5*q - w*q**2 - 54/5 = 0.
-3
Let p be (-6 - -4)*1 - (-25 - -5). Let z be ((-29)/((-261)/(-30)))/((-16)/p). Factor 9/4*v**2 - 15/4*v + 3/4*v**4 - 3 + z*v**3.
3*(v - 1)*(v + 1)**2*(v + 4)/4
Let u(c) be the first derivative of c**4/84 - c**3/42 - c + 43. Let v(f) be the first derivative of u(f). Solve v(k) = 0.
0, 1
Suppose -13/4*k**2 - 11/4*k + 1/4*k**4 + 11/4*k**3 + 3 = 0. What is k?
-12, -1, 1
Let z(y) be the second derivative of y**4/12 + 955*y**3/3 + 912025*y**2/2 + y - 1036. Let z(t) = 0. What is t?
-955
Let i = -110 - -166. Factor i*x**4 - 2*x**3 - 6*x**2 - 54*x**4 + 2*x**2.
2*x**2*(x - 2)*(x + 1)
Suppose -19*k = -24*k + 805. Let a = -15 + k. Suppose m**4 + 2*m**3 - 4*m**3 