 - 1)
Let w = 18 + -9. Suppose -4*u = -57 + w. Suppose -140*l + u*l**2 + 3*l**4 + 140*l + 12*l**3 = 0. Calculate l.
-2, 0
Suppose -891 = -17*l - 211. Factor -32 - l*h + h**4 - 23/2*h**3 + 42*h**2.
(h - 4)**3*(2*h + 1)/2
Let d(z) be the second derivative of -z**9/10584 + z**8/1176 - z**7/420 + z**6/420 - 7*z**3/6 - 18*z. Let u(w) be the second derivative of d(w). Factor u(f).
-2*f**2*(f - 3)*(f - 1)**2/7
Let b(t) be the third derivative of -t**5/360 + t**4/36 - t**3/12 - 2*t**2 + 12. Factor b(m).
-(m - 3)*(m - 1)/6
What is r in 2*r**4 + 80/3*r + 46*r**2 + 0 + 64/3*r**3 = 0?
-8, -5/3, -1, 0
Let k(y) be the third derivative of -y**6/24 + 17*y**5/12 - 155*y**4/24 + 25*y**3/2 + 2*y**2 + 42*y. Factor k(h).
-5*(h - 15)*(h - 1)**2
Let c(r) be the second derivative of -1/45*r**6 + 19*r - 1/45*r**5 + 2/189*r**7 - 1/9*r**2 + 0 + 2/27*r**4 + 0*r**3. What is b in c(b) = 0?
-1, -1/2, 1
Let j(w) = w**4 - w**3 - 2*w + 1. Let x(z) = 12*z**5 - 92*z**4 + 92*z**3 - 12*z**2 + 12*z - 6. Let b(h) = 6*j(h) + x(h). Find d, given that b(d) = 0.
0, 1/6, 1, 6
Suppose -5*w = 3*x - 47 - 60, w = x + 15. Factor 2*b**2 + 19 + b - w + 5*b.
2*b*(b + 3)
Let v = -3 - -13. Let g(t) = -t**2 + 7*t + 10. Let q be g(8). Factor 17 + 0 + 25*y - 7*y + v + 3*y**q.
3*(y + 3)**2
Let r = -184468/11 + 16770. What is j in 9/11*j**3 - 2/11*j**2 - 9/11*j + r = 0?
-1, 2/9, 1
Let q = -1946 - -1948. Factor 4/3*y**3 - 4/3*y**4 + 4/3*y**q + 0 - 4/3*y.
-4*y*(y - 1)**2*(y + 1)/3
Let s(p) be the first derivative of p**3 - 21*p**2/2 + 30*p + 14. Suppose s(c) = 0. Calculate c.
2, 5
Let c(k) be the second derivative of -k**4/4 + 11*k**3/2 - 15*k**2 - 25*k - 2. Suppose c(l) = 0. Calculate l.
1, 10
Let q(h) be the first derivative of -2*h**3/3 - 2*h**2 - 2*h + 19. Suppose q(a) = 0. What is a?
-1
Let z = 31728/11 + -2884. Factor 0 - 2/11*s - z*s**2 - 2/11*s**3.
-2*s*(s + 1)**2/11
Let w be (-207)/(-6210) + (20/(-24))/(-5). Determine j, given that -6/5 + w*j**2 + j = 0.
-6, 1
Let z(k) = -k + 8. Let u be ((-4)/15)/((-5)/25)*3. Let h be z(u). What is x in -54/5*x**2 + 26/5*x - 4/5 - 14/5*x**h + 46/5*x**3 = 0?
2/7, 1
Let 1658/9*s**2 + 242/9*s**4 - 1364/9*s**3 + 8 + 248/3*s = 0. What is s?
-2/11, 3
Let i be (-6 - (3 + -7)) + 6. Let g(h) be the second derivative of -3/80*h**5 + 3*h**2 + 3/8*h**i + 0 + h - 3/2*h**3. Solve g(a) = 0.
2
Let j(v) be the first derivative of -2*v**5/45 + 5*v**4/18 + 4*v**3/9 - 15. Solve j(h) = 0.
-1, 0, 6
Let 151*i - 72*i**3 - 359*i + 3*i**4 - 320*i + 404*i**2 + i**4 - 1008 + 0*i**4 = 0. Calculate i.
-1, 6, 7
Let c(a) be the first derivative of -a**6/3420 + a**4/57 + 4*a**3/3 - 16. Let o(u) be the third derivative of c(u). Suppose o(m) = 0. What is m?
-2, 2
Find u, given that u**4 - 11/6*u**3 + 1/6*u + 2/3*u**2 + 0 = 0.
-1/6, 0, 1
Let j be (-3 - 2)*(-1551)/385 + 3/(-21). Determine r so that -5/4*r**3 - 45/4*r**2 - j - 30*r = 0.
-4, -1
Let a(w) = 8*w**4 + 4*w**3 + w**2 + 3*w + 5. Let x(s) = -s**4 - s**3 - 1. Let z = 40 - 12. Let k(t) = z*x(t) + 4*a(t). Factor k(v).
4*(v - 2)*(v - 1)**2*(v + 1)
Let f(w) be the third derivative of -w**5/90 - 4*w**4/9 + 17*w**3/9 - 2*w**2 - 11*w. Let f(a) = 0. Calculate a.
-17, 1
Let k = 7147/360 - 178/9. Let s(z) be the third derivative of 0 + 1/20*z**5 + 3/8*z**4 + 1/70*z**7 - z**3 + 0*z - k*z**6 + 2*z**2. Factor s(m).
3*(m - 2)*(m - 1)**2*(m + 1)
Suppose 0 = -6*o + 62 - 14. Determine l so that -o*l - 3 - 3 - 3*l**2 + 0*l - 3*l = 0.
-3, -2/3
Suppose -5*q + 21 = -3*h + 9, 2*q - 12 = 3*h. Suppose q = w + 5*c - 17, -3*w + 18 = -4*c + 8*c. Determine k, given that 0*k**w + 0 - 1/4*k**3 + 0*k = 0.
0
Let w = -1/73 - 2108/657. Let l = -3 - w. Factor l*o**3 + 0*o - 2/3*o**2 + 8/9.
2*(o - 2)**2*(o + 1)/9
Let p(c) be the second derivative of 2*c**7/105 - 8*c**6/25 + 57*c**5/25 - 134*c**4/15 + 104*c**3/5 - 144*c**2/5 + 182*c. Let p(o) = 0. Calculate o.
2, 3
Let d = 83 - 79. Let x be d/6 - (-6 + 6). Factor x*j**2 + 0 - 2/3*j.
2*j*(j - 1)/3
Let q be (-5)/15*-33 - 5. Let l be -3*(-1)/q*1. Determine m, given that -1/2 + 1/2*m - 1/2*m**3 + l*m**2 = 0.
-1, 1
Let q(a) be the first derivative of a**4/16 - 2*a**3/3 - 9*a**2/8 + 112. Factor q(f).
f*(f - 9)*(f + 1)/4
Suppose d = -d + 30. Factor 20*g**3 - d*g**2 + 33*g - 5*g**4 - 33*g + 0*g**2.
-5*g**2*(g - 3)*(g - 1)
Let z be (-14)/5*(-45)/180. Let j(n) be the second derivative of 7/3*n**4 + z*n**5 + 6*n - 1/2*n**6 + 4/3*n**3 + 0 + 0*n**2. Factor j(b).
-b*(b - 2)*(3*b + 2)*(5*b + 2)
Find y such that -6*y**2 - 17*y**2 - 8*y + 14*y**3 - 4*y**3 + 7*y**2 = 0.
-2/5, 0, 2
Solve -2/7*q + 0 - 8/7*q**4 - 8/7*q**2 - 12/7*q**3 - 2/7*q**5 = 0.
-1, 0
Let m(d) = 4 + 0*d + 3 + 9*d - 4*d. Let r be m(-1). What is c in 1/2*c**r + 0 - 1/2*c**4 + 1/2*c - 1/2*c**3 = 0?
-1, 0, 1
Let i = 79 - 76. Factor -4*z**5 - 10*z**4 - 5*z**4 + 3*z**5 + 15*z**2 + 6*z**5 - 5*z**i.
5*z**2*(z - 3)*(z - 1)*(z + 1)
Suppose 32 + 296/3*d + 56*d**2 - 14/3*d**4 - 2*d**3 = 0. Calculate d.
-2, -3/7, 4
Let c be (5 - (-51)/(-12)) + 8/(-12). Let i(r) be the first derivative of -c*r**3 + 1/4*r + 1/16*r**4 + 7 - 1/8*r**2. Determine b, given that i(b) = 0.
-1, 1
Let i(b) be the third derivative of b**6/160 - b**5/20 - 21*b**4/32 - 2*b**2 + 29*b. Suppose i(r) = 0. Calculate r.
-3, 0, 7
Suppose 4*d = -d - 3*g - 10, 4*g - 10 = 5*d. Let v be (2 + -2)/(5/10*d). Let v*p**2 + 0 - 2/7*p**5 - 2/7*p + 4/7*p**3 + 0*p**4 = 0. What is p?
-1, 0, 1
Let q(o) be the second derivative of -1/60*o**5 - 7/18*o**4 + 38*o - 2 - 8/3*o**2 + 31/18*o**3. Suppose q(d) = 0. What is d?
-16, 1
Determine q, given that 1/2*q**2 - 2 + 0*q = 0.
-2, 2
Let y(a) be the second derivative of -3*a + 0*a**4 + 0 - 2/5*a**6 + 0*a**3 + 0*a**2 + 3/14*a**7 + 3/20*a**5. Factor y(k).
3*k**3*(k - 1)*(3*k - 1)
Factor 10*a**3 - 10*a + 193*a**2 - 100*a**2 - 108*a**2 + 15.
5*(a - 1)*(a + 1)*(2*a - 3)
Let p(o) = -2*o**3 + 23*o**2 + 39*o - 60. Let g(i) = i**3 - 11*i**2 - 20*i + 30. Let n(r) = 7*g(r) + 3*p(r). Let n(f) = 0. What is f?
-3, 1, 10
Let y = -38 + 62. Solve -3/2*o**2 + 12*o - y = 0 for o.
4
Find i such that -10*i**3 - 15853*i**2 - 10*i**3 + 4*i**4 + 15865*i**2 + 36*i = 0.
-1, 0, 3
Solve 15/7*w**3 + 246/7*w**2 + 24 + 516/7*w = 0 for w.
-14, -2, -2/5
Suppose -3*o = 4*p - 96 + 27, p + 2*o = 21. Suppose 3*i = -0*i + p. Solve 3*f + 0 + 2 + 3*f**2 + i*f**2 - 13*f = 0.
1/4, 1
Let o(p) = p**3 - 4*p**2 - 11*p + 3. Let n(z) = 6*z**2 + 10*z - 2. Let q(t) = 3*n(t) + 2*o(t). Find f such that q(f) = 0.
-4, -1, 0
Let a = 6569/8780 - -4/2195. Suppose -3/2 + 3/4*h + a*h**2 = 0. Calculate h.
-2, 1
Let g(j) = -6*j**4 + 2*j**3 + 10*j**2 + 5*j. Let d(a) = a**5 + 5*a**4 - 2*a**3 - 12*a**2 - 6*a. Let y(z) = 5*d(z) + 6*g(z). Let y(i) = 0. Calculate i.
0, 1/5, 2
Let h(f) = 4*f**5 + 22*f**4 + 18*f**3 - 26*f**2 - 20*f + 2. Let w(g) = 4*g**5 + 21*g**4 + 19*g**3 - 27*g**2 - 20*g + 3. Let l(r) = 3*h(r) - 2*w(r). Factor l(n).
4*n*(n - 1)*(n + 1)**2*(n + 5)
Suppose -3*f + 44 = 2*x, 4*x + f = 80 - 12. Factor 57*z**3 - x*z**2 + 8*z**4 + 7*z**3 - 36*z**4.
-4*z**2*(z - 2)*(7*z - 2)
Let k(n) = -11*n**3 + 23*n**2 + 43*n - 223. Let b(a) = 9*a**3 - 24*a**2 - 42*a + 222. Let i(z) = 7*b(z) + 6*k(z). Suppose i(p) = 0. Calculate p.
-6, 2
Let i be (-10)/(-6) + 13/39. Let j(w) = -w + 3. Let c be j(i). Factor 2*m + 3*m**2 + c - 2*m**3 + m + 6*m**3 - 3*m**3.
(m + 1)**3
Let f(z) = z**2 - 22*z - 133. Let n be f(27). Solve -8/5*b + 2/5*b**n + 6/5 = 0.
1, 3
Let h be (-9)/60*(-58)/1827. Let p(z) be the third derivative of 0 + 0*z - 4*z**2 - 1/28*z**4 + h*z**5 + 2/21*z**3. Determine y so that p(y) = 0.
1, 2
Let w(d) be the third derivative of -1/15*d**3 - 1/100*d**5 + 1/1050*d**7 + 0 - 1/600*d**6 + 0*d + 1/24*d**4 + 19*d**2. Factor w(l).
(l - 1)**3*(l + 2)/5
Let q(v) = v + 13. Let w be q(-13). Suppose f + 0*f = -2*y - 2, w = -2*f - 3*y - 2. Solve 1/2 - 1/6*x**f - 1/3*x = 0 for x.
-3, 1
Let h be (0 + (-2)/6)*(-11 + -1). Factor 8*c**3 + 6*c**h - 8*c**3 + 3*c - 3*c**5 - 6*c**2.
-3*c*(c - 1)**3*(c + 1)
Let j(r) be the second derivative of 1/180*r**6 - 5*r + 1/3*r**3 - 7/2*r**2 - 1/36*r**4 + 0 - 1/30*r**5. Let t(y) be the first derivative of j(y). Factor t(w).
2*(w - 3)*(w - 1)*(w + 1)/3
Let w(f) be the second derivative of -1/48*f**4 + 1/12*f**3 + 0*f**2 - 1/80*f**5 + 13*f + 0. Let w(u) = 0. Calculate u.
-2, 0, 1
Factor -72/7*u - 3/7*u**2 + 0.
-3*u*(u + 24)/7
Let i(f) be the seco