c**2 + 0*c**k. Factor b(s).
-3*s*(s - 1)**2*(s + 1)**2/2
Let q(r) be the second derivative of -5*r**4/12 - 5*r**3/2 - 5*r**2 + r + 187. Suppose q(i) = 0. Calculate i.
-2, -1
Solve h**5 + 106*h**4 - 24 - 102*h**4 + 13 - 2*h**2 + 76*h - 23*h**3 - 45 = 0.
-7, -2, 1, 2
Suppose -8*l = -12*l + 28. Determine s so that l*s**4 - 33*s**2 - 11*s**4 + 5*s**2 - 12*s - 20*s**3 = 0.
-3, -1, 0
Let t(x) = 3*x**3 - 27*x**2 + 27*x - 18. Let v(l) = 6*l**3 - 52*l**2 + 56*l - 35. Let f(y) = 5*t(y) - 3*v(y). Factor f(o).
-3*(o - 5)*(o - 1)**2
Suppose 0 = 3*n - 3*f - 6, 0*n - 7 = n - 4*f. Suppose 0 = n*z - 20. Find a such that 4*a**2 - 3*a**2 - z - 5*a**2 + 8 + 2*a**3 - 2*a = 0.
-1, 1, 2
Suppose h = -0 + 2. Suppose 3*o = h*o. Factor 0*u + o + 2/11*u**2 + 2/11*u**3.
2*u**2*(u + 1)/11
Let u(g) be the third derivative of 3*g**3 + 9*g - 3*g**2 + 0 - 5/8*g**4 - 1/20*g**5. Let u(s) = 0. What is s?
-6, 1
Let p(d) = d**4 + d**3 - d**2 + d. Let v(g) = 3*g**5 - 13*g**4 - 31*g**3 + 85*g**2 - 4*g. Let f(y) = 4*p(y) + v(y). Factor f(o).
3*o**2*(o - 3)**2*(o + 3)
Let h = 21 - 18. Let c = -5 + 7. Factor 4 + 2 - b - h*b**c + 4*b.
-3*(b - 2)*(b + 1)
Let u(h) be the second derivative of 1/6*h**4 + 0 + 3*h**2 + 10*h + h**3. Let j(o) = -4*o**2 - 11*o - 11. Let k(f) = 6*j(f) + 11*u(f). Factor k(r).
-2*r**2
Let g(v) be the third derivative of -1/70*v**5 - 1/140*v**6 + 0*v + 0*v**3 + 0 - 1/735*v**7 - 1/84*v**4 + 31*v**2. Factor g(d).
-2*d*(d + 1)**3/7
Let 56*g**3 - g + g**4 + 5*g**5 + 29*g**4 + g - 11*g**3 = 0. Calculate g.
-3, 0
Let b(a) = 527*a + 4745. Let h be b(-9). Factor h - 1/3*u**2 - 1/3*u.
-(u - 2)*(u + 3)/3
Let q(r) = -r + 13. Let i be q(9). Factor -10*u**2 + 10*u**4 + 2*u**2 - 36*u**3 - 38*u**i.
-4*u**2*(u + 1)*(7*u + 2)
Solve 5/2*y**5 - 18*y**2 + 25*y**3 + 0 - 27/2*y**4 + 4*y = 0 for y.
0, 2/5, 1, 2
Suppose -4*c + 20 = 0, -3*q + c + 1 + 6 = 0. Let 8 + q*s**2 + 8*s**2 - 29*s**3 - 7*s**3 + 20*s**3 + 36*s = 0. What is s?
-1, -1/4, 2
Suppose -2*r = 2*x - r - 8, 5*x + 4*r - 26 = 0. What is c in -2*c**3 - 68*c**x + 14*c**3 - 12*c + 36*c**2 = 0?
-1/3, 0, 3
Let n be (9/6)/(2*1/4). Suppose -198*m + 3*m**5 + 0*m**3 - 9*m**2 + 192*m + n*m**3 + 9*m**4 = 0. What is m?
-2, -1, 0, 1
Suppose -18/5*h**3 + 0*h + 24/5*h**2 + 0 - 6/5*h**4 = 0. Calculate h.
-4, 0, 1
Let u = 0 - -20. Factor -5*y - 5*y**4 - 77*y**3 + 57*y**3 - u*y**2 + 5*y.
-5*y**2*(y + 2)**2
Let c = -21 - -25. Suppose -432*u + 26*u**c + 54 - 134*u**3 - 2*u**5 + 95 + 342*u**2 + 67 = 0. What is u?
2, 3
Let m(y) be the second derivative of -y**7/21 + y**6/3 + y + 14. Suppose m(o) = 0. Calculate o.
0, 5
Let f(s) be the first derivative of s**4/6 - 8*s**3/9 - 11*s**2/3 - 4*s - 497. Solve f(q) = 0.
-1, 6
Let m(p) = -16*p + 11. Suppose 0*n - y + 8 = -n, -2*n + y = 13. Let r be m(n). Factor 7*t**4 - r*t**2 - 4*t**4 + 3 + 85*t**2.
3*(t - 1)**2*(t + 1)**2
Let f(v) be the second derivative of -3*v**5/20 - 13*v**4/14 - 13*v**3/14 + 9*v**2/7 - 106*v. Factor f(x).
-3*(x + 1)*(x + 3)*(7*x - 2)/7
Let u be (3/(-2))/(39/(-52)). Suppose -2*r = -5*k - 24, 0 - 2 = 3*r + u*k. Factor -11 + 13*m - 7 + 24 - 5*m**r.
-(m - 3)*(5*m + 2)
Let m be (-44)/10*(-3 + -2). Suppose -2*x - 34 = -0*r - 5*r, -5*r - 4*x + m = 0. Factor 32/3*h - 14*h**2 + r*h**3 - 8/3.
2*(h - 1)*(3*h - 2)**2/3
Let n = -15 + 19. Let g be (-11)/2 + n - -3. Determine z so that z**5 + 0 - 1/2*z - 3/2*z**2 + g*z**4 - 1/2*z**3 = 0.
-1, -1/2, 0, 1
Let x be (-3)/(-27) + (-132)/(-108). Suppose -4/3*m**3 - 4/9*m**5 + 4/9*m**2 + 0 + 0*m + x*m**4 = 0. Calculate m.
0, 1
Let g be 560/3654 + 6/87. Factor -2/9*q**3 - g*q**2 + 0*q + 0.
-2*q**2*(q + 1)/9
Let b = -34 - -46. Let -2*c**5 - 2*c**4 - 2*c**2 + c**3 + 4*c + 0*c + 5*c**3 + b*c**2 = 0. Calculate c.
-1, 0, 2
Let w be 1 + (2/175)/((-7)/595). Let a(t) be the third derivative of w*t**7 + 0 + 0*t - 5*t**2 - 2/15*t**6 - 1/6*t**4 + 0*t**3 + 7/30*t**5. Factor a(q).
2*q*(q - 1)**2*(3*q - 2)
Let g(b) be the second derivative of b**5/10 - 8*b**4 + 256*b**3 - 4096*b**2 + b + 36. Determine m, given that g(m) = 0.
16
Let h(z) = 2*z - 43. Let j be h(22). Suppose 2*p = 7 - j. What is l in 20/3*l**2 + 4/3*l + p*l**3 + 0 = 0?
-2, -2/9, 0
Let m(l) = l**3 + 20*l**2 + 19*l - 3. Let j be m(-19). Let g be 6/28*(-4)/j. Find x such that 0*x - g*x**3 + 2/7*x**2 + 0 = 0.
0, 1
Let o(q) = -q**2 + 9*q + 10. Let s be o(10). Suppose s = 6*v - 8*v. What is j in 2/7*j**2 + 2/7*j + v = 0?
-1, 0
Let o be 4/6*18/3. Factor -15*q**3 + 29*q**3 - 3*q**2 + o*q - 15*q**3.
-q*(q - 1)*(q + 4)
Suppose 2*q = 9*q - 21. Factor -y**3 + 0*y**q - 3*y**3 + 0*y**3.
-4*y**3
What is v in 32/7 - 3/7*v**3 + 53/7*v**2 - 82/7*v = 0?
2/3, 1, 16
Let o(d) be the third derivative of d**6/48 + 3*d**5/20 - d**4/6 - 297*d**2. Factor o(s).
s*(s + 4)*(5*s - 2)/2
Let z = -537 + 541. Let j = -5 + 7. Solve -r**5 + 7*r**z + 10*r**5 + 5*r**4 - 18*r**j - 12*r**3 + 6 + 0*r + 3*r = 0.
-1, 2/3, 1
Let j(v) be the third derivative of -v**8/588 - 127*v**7/1470 + v**6/5 + 47*v**5/210 - 41*v**4/42 + 11*v**3/14 + 704*v**2. What is a in j(a) = 0?
-33, -1, 1/4, 1
Factor -s - 3/2*s**3 - 9/4*s**2 - 1/4*s**4 + 0.
-s*(s + 1)**2*(s + 4)/4
Let m be 567/(-315)*6/81*3*-3. Find n, given that -21/5*n + 12/5*n**2 - m = 0.
-1/4, 2
Let o(d) be the second derivative of d**7/56 - 4*d**6/5 + 51*d**5/16 + 35*d**4/8 - 89*d**3/2 + 87*d**2 - 13*d. Suppose o(k) = 0. Calculate k.
-2, 1, 2, 29
Factor 320/3*l - 64 + 16*l**3 - 64*l**2 - 4/3*l**4.
-4*(l - 6)*(l - 2)**3/3
Let x(i) be the third derivative of -i**8/3024 + 2*i**7/945 - i**6/216 + i**5/270 - i**2 + 32. Factor x(m).
-m**2*(m - 2)*(m - 1)**2/9
Factor -2/5*c**4 - 2*c**2 + 4/5*c + 8/5*c**3 + 0.
-2*c*(c - 2)*(c - 1)**2/5
Factor 12*r**2 + 8*r**4 + 146*r + 28*r**3 - 285*r + 139*r.
4*r**2*(r + 3)*(2*r + 1)
Let z(c) be the second derivative of -c**5/5 - 199*c**4 - 79202*c**3 - 15761198*c**2 - 3*c + 39. Suppose z(q) = 0. Calculate q.
-199
Factor 6/5*h - 38/5*h**2 + 12/5*h**3 + 0.
2*h*(h - 3)*(6*h - 1)/5
Let g(v) = 2*v**3 - v**2 - 5*v + 7. Let f(i) = i**3 + i**2 - i - 1. Let l(a) = -f(a) + g(a). Solve l(c) = 0.
-2, 2
Let f = 4399/17532 - 4/4383. Factor z - 1/2*z**2 + 3/4 - f*z**4 - z**3.
-(z - 1)*(z + 1)**2*(z + 3)/4
Factor 0 + 1/2*f**4 - 5/2*f**2 + 2*f**3 + 0*f.
f**2*(f - 1)*(f + 5)/2
Let k(b) be the second derivative of -b**7/147 + 4*b**5/35 - 16*b**3/21 + 137*b. Determine p so that k(p) = 0.
-2, 0, 2
Let u = -2/711 - -950/711. Let z(i) be the first derivative of -5 + i**4 - 1/3*i**6 - i**2 - u*i**3 + 2*i + 2/5*i**5. Factor z(q).
-2*(q - 1)**3*(q + 1)**2
Let q = -346/65 + 77/13. Factor -q*a - 4/5 + 1/5*a**2.
(a - 4)*(a + 1)/5
Suppose -2*a = 2*j + 62, -5*a - 47 = -5*j - 172. Let i be (-8)/j + (-78)/(-21). Factor 16*x**3 + 9*x**2 - 12 - 2*x**3 - 5*x + 3*x**i - 7*x - 2*x**3.
3*(x - 1)*(x + 1)*(x + 2)**2
Solve 486*i**3 - 80/17 - 1458/17*i**4 + 1096/17*i - 5076/17*i**2 = 0.
2/9, 5
Suppose 15*i = 10*i + 15. Suppose 2*t + 0*t = i*t. Factor t*x**2 - 2/7*x + 0 + 2/7*x**3.
2*x*(x - 1)*(x + 1)/7
Let w(m) be the third derivative of -m**5/150 - m**4/2 - 15*m**3 - 86*m**2. Factor w(n).
-2*(n + 15)**2/5
Let a be (28/60)/((-63)/(-54)). Let l be 4/(-14) + (-24)/(-35). Determine j, given that -a*j - l*j**2 + 4/5 = 0.
-2, 1
Let o = 21 + -25. Let t be 3*((-60)/16 - o). What is k in -t*k**2 + 1/4*k**3 + 1 + 0*k = 0?
-1, 2
Solve 5/7*c**5 - 7*c**3 - 17/7*c**4 - 20/7 + 44/7*c + 37/7*c**2 = 0 for c.
-2, -1, 2/5, 1, 5
Suppose 2*n - 3 - 3 = 0. Let o be (1/(-4))/((-45)/12 + n). Determine v so that -o*v**2 + 0*v**3 + 0 - 1/6*v + 1/6*v**5 + 1/3*v**4 = 0.
-1, 0, 1
Suppose 5*s + 5*y = -10, s + 1 + 7 = -4*y. Let t(a) be the second derivative of 3/4*a**4 - 6*a**2 + s + 0*a**3 - 2*a + 3/20*a**5. Factor t(i).
3*(i - 1)*(i + 2)**2
Suppose -4*x - 4*c + 48 = 20, 0 = 4*c - 20. Suppose -1/2*m**3 - 1/2*m**x + 0 + 1/2*m**4 + 1/2*m = 0. Calculate m.
-1, 0, 1
Let g be 3 + -1*2/(-2). Suppose g*z - 7*z = -57. Determine s, given that 4*s**3 + 2*s**4 - 2*s**3 + 19 - z = 0.
-1, 0
Let y(u) = -u**5 - 5*u**4 - 15*u**3 + 11*u**2 + 10*u - 6. Let d(f) = f**5 + 4*f**4 + 16*f**3 - 11*f**2 - 10*f + 7. Let t(r) = 6*d(r) + 7*y(r). Factor t(s).
-s*(s - 1)*(s + 1)**2*(s + 10)
Let s(f) be the third derivative of -f**6/360 + 7*f**5/20 - 147*f**4/8 + 1029*f**3/2 - 18*f**2. Factor s(u).
-(u - 21)**3/3
Let t = -49 + 51. Let a(c) be the first derivative of 6/5*c**5 + 1 