
Let v(q) = -14*q**2 - 30*q - 24. Let w(u) = -20*u**2 - 44*u - 36. Let z(r) = 7*v(r) - 5*w(r). Factor z(c).
2*(c + 2)*(c + 3)
Let y(r) be the second derivative of r**7/84 - r**6/60 - 9*r**5/40 + 3*r**4/8 + 43*r + 1. Suppose y(m) = 0. What is m?
-3, 0, 1, 3
Let x(c) = -c**2 + 8*c - 14. Let i be x(4). What is w in -w**2 - 4*w**i - w**3 + w + 2 + 3*w**2 = 0?
-2, -1, 1
Let m(w) = -3*w**2 + 76*w. Let c(f) = f. Let x(s) = 2*c(s) + m(s). Suppose x(t) = 0. Calculate t.
0, 26
Let x = -41 + 48. Factor x*l - 38*l**2 + 39*l**2 - 2*l - 2*l.
l*(l + 3)
Let g be 3556/1524 + (1/2)/((-9)/6). Determine x, given that 0*x - 2 + 1/2*x**g = 0.
-2, 2
Let k(r) = -r**2 - 2*r + 6. Let u be k(-6). Let d = 20 + u. Find j such that -14*j + 5*j + 1 + 5*j**d + 5 - 2*j**2 = 0.
1, 2
Suppose 3*y - 10 = -4. Suppose -y*r**3 + 1 + 15*r - 1 + 5*r**3 - 12*r**2 - 6 = 0. What is r?
1, 2
Let s be (3 - 70/10)*(-15)/12. Let o(f) be the first derivative of f**2 + 9 - 1/5*f**s + f**4 + 0*f - 5/3*f**3. Factor o(v).
-v*(v - 2)*(v - 1)**2
Suppose 38*a - 18 = 29*a. Let m(x) be the third derivative of 1/20*x**5 - 1/40*x**6 + 0*x**3 + 0 + 0*x + 6*x**a + 1/4*x**4. What is d in m(d) = 0?
-1, 0, 2
Suppose -48*f - 237*f**2 + 216*f**2 - 36 + f**3 - 4*f**3 = 0. What is f?
-3, -2
Find r, given that -15*r**3 - 6*r**3 + 45*r**3 - 7*r**3 + 49152*r - 768*r**2 - 14*r**3 = 0.
0, 128
Let j(q) be the first derivative of q**4/6 + 4*q**3/3 + 3*q**2 - 67. Suppose j(d) = 0. Calculate d.
-3, 0
Let t(d) be the first derivative of d**7/63 - d**6/9 + d**5/3 - 5*d**4/9 + 5*d**3/9 - d**2/3 + 7*d + 26. Let z(r) be the first derivative of t(r). Factor z(c).
2*(c - 1)**5/3
Let r be 9 - (-1)/(((-3)/(-6))/(255/(-60))). Factor 0*f**2 - 1/6*f**3 + 1/3 + r*f.
-(f - 2)*(f + 1)**2/6
Let t(s) = -s**3 - 7*s**2 + 3*s - 3. Let g be t(-7). Let o be g/(-5) + (-1)/(-5). Factor 10*c**2 + 2*c**3 + 5 - 2 - 9*c - o*c**3 - c**2.
-3*(c - 1)**3
Factor 1335*p + 14*p**3 - 479*p**2 + 5*p**3 - 24*p**3 - 181*p**2 - 670.
-5*(p - 1)**2*(p + 134)
Let l = 2 + 1. Suppose -4*n + 55 = 5*p, -l = -5*p + n + 27. Factor -4*b**3 - 19 + 13 - 9*b + p*b**3.
3*(b - 2)*(b + 1)**2
Suppose 4 - 6 = -b. Factor 81 - 2*x + 34*x - 3*x**b + 7*x**2 - 17.
4*(x + 4)**2
Let l be (-3)/(-4) - 777/1260. Let w(o) be the first derivative of 0*o - l*o**3 + 0*o**4 + 2/25*o**5 + 0*o**2 - 1. Factor w(g).
2*g**2*(g - 1)*(g + 1)/5
Factor -3/7*s**2 - 17/7*s - 10/7.
-(s + 5)*(3*s + 2)/7
Let t(b) = 75*b**4 - 89*b**3 - 125*b**2 + 50*b + 11. Let w(l) = -15*l**4 + 18*l**3 + 25*l**2 - 10*l - 2. Let n(x) = -2*t(x) - 11*w(x). Factor n(s).
5*s*(s - 2)*(s + 1)*(3*s - 1)
Let f(i) = 4*i**3 + 27*i**2 - 7*i + 4. Let c be f(-7). Factor 0 - 1/6*v**5 - v**3 - 1/6*v + 2/3*v**2 + 2/3*v**c.
-v*(v - 1)**4/6
Factor -1/3*s**2 + 2/3*s + 0 - 1/3*s**3.
-s*(s - 1)*(s + 2)/3
Let z(d) be the second derivative of 1/3*d**4 + 0*d**2 + 0 - 2/3*d**3 - 17*d. Determine o, given that z(o) = 0.
0, 1
Let u(b) be the first derivative of -b**6/21 + 4*b**5/35 + 9*b**4/7 + 64*b**3/21 + 23*b**2/7 + 12*b/7 + 22. Suppose u(q) = 0. Calculate q.
-1, 6
Let h be (-20)/(-100) - (1 - 1). Let 8/5*x + 7/5*x**2 + h*x**3 - 16/5 = 0. Calculate x.
-4, 1
Let o(t) = 5*t**3 + 36*t**2 + t - 39. Let w be o(-7). Let -w*b + 9/2*b**5 + 0 - 15/2*b**2 - 3/2*b**3 + 15/2*b**4 = 0. Calculate b.
-1, -2/3, 0, 1
Let k = 4708 - 4706. Find d, given that 12/5 + 4/5*d**3 + 4/5*d**k - 4*d = 0.
-3, 1
Let t = 77 + -72. Let o(z) be the second derivative of 1/9*z**3 + 0 - 7*z + 1/30*z**t + 0*z**2 - 1/9*z**4. Factor o(x).
2*x*(x - 1)**2/3
Suppose -4*u = 3*u - 28. Find c such that c**4 - 8*c**3 + 2*c**u - 2*c**4 + 6*c**3 = 0.
0, 2
Find n, given that 3*n**2 - 2659 + 2579 + 50*n - 8*n**2 = 0.
2, 8
Suppose 2*b + 42 = 4*b. Suppose z - 4*z - 3*v + b = 0, -4*v + 26 = 3*z. Determine q, given that 2*q**2 - q**2 - z*q**4 + q**2 = 0.
-1, 0, 1
Let c = 28 + -447/16. Let k(b) be the first derivative of 5/8*b**2 - 1/3*b**3 + c*b**4 - 1 - 1/2*b. Suppose k(o) = 0. What is o?
1, 2
Let o(r) = 1 + 7*r**2 + 0*r**2 + 9*r - r + 2*r**2. Let i(m) be the first derivative of -4*m**3/3 - 2*m**2 - m + 1. Let n(t) = -14*i(t) - 6*o(t). Solve n(j) = 0.
-2
Let t(j) be the first derivative of -j**4/4 - 16*j**3/3 - 39*j**2/2 + 160. Factor t(m).
-m*(m + 3)*(m + 13)
Let r = 7 + -5. Let x = 171 - 144. What is s in -8*s**3 + 8*s**2 + 2*s**4 - 35*s + x*s + 4*s**r + 2 = 0?
1
Let f(t) = t**2 - 3*t + 3. Let n be f(3). Let i be 0 - 1 - 6/(-2). Determine v, given that v + 2*v**2 - n*v**2 - 2 + i*v = 0.
1, 2
Suppose 0 = t - 4*m, 2*m = -2*t - 2*m + 12. Suppose -2*x + 4*x - a = 2, t*x = -3*a + 24. Factor -k**x + 5*k**3 + 2*k**3 - 4*k**3.
2*k**3
Let a(z) be the first derivative of -1/3*z**2 - 5 - 5/6*z + 1/18*z**3. Factor a(j).
(j - 5)*(j + 1)/6
Let o = 59 + -55. Factor -4*w**2 - 2 + o*w + 1 + 9.
-4*(w - 2)*(w + 1)
Let a(i) be the third derivative of i**6/540 - 14*i**5/135 + 49*i**4/27 - 100*i**2. Factor a(b).
2*b*(b - 14)**2/9
Determine l, given that 4*l**3 + 4*l**4 - 52*l**2 - 3 + 17*l - 21*l + 51 = 0.
-4, -1, 1, 3
Factor -43*n**3 - 42*n**2 - 6*n**2 - 4*n**4 + n**3 + 10*n**3.
-4*n**2*(n + 2)*(n + 6)
Let h be (-1 - -1)/(-5*2/(-5)). Let b(f) be the first derivative of -2/3*f**3 - 2*f**2 + 3 + h*f. Suppose b(x) = 0. Calculate x.
-2, 0
Let j(p) be the second derivative of p**5/60 + 2*p**4/3 + 32*p**3/3 + 256*p**2/3 + 4*p + 18. Factor j(x).
(x + 8)**3/3
Let z = -50 - -56. Factor z + 3*p**2 + p - 5 - p**3 - 4*p**2.
-(p - 1)*(p + 1)**2
Let u(f) be the second derivative of 1 - 3/80*f**5 + 0*f**2 + 3*f - 3/16*f**4 - 1/4*f**3. Determine l, given that u(l) = 0.
-2, -1, 0
Let t be (12/15 + 2)/((-16)/(-20)). Let q(g) be the second derivative of -9/4*g**4 + 0 + 3*g**2 - t*g**3 - 8*g. What is u in q(u) = 0?
-1, 2/9
Factor -20*k**2 + 20 + 15/4*k**3 + 15*k.
5*(k - 4)*(k - 2)*(3*k + 2)/4
Let u(h) = h**3 - 30*h**2 - 32*h - 16. Let r be u(31). Let s be 12/72 - r/42. Solve -3/7*v**4 - 3/7*v**5 + 6/7*v + s*v**3 + 15/7*v**2 + 0 = 0.
-1, 0, 2
Find i such that 3/2*i - 3/4*i**3 + 0 + 9/4*i**2 - 9/4*i**4 - 3/4*i**5 = 0.
-2, -1, 0, 1
Let p(x) be the third derivative of -x**6/40 + 3*x**5/20 - 3*x**4/8 + x**3/2 - 51*x**2. Factor p(l).
-3*(l - 1)**3
Let n = 35 + -33. Factor 0*s - 5 - s**n - 3*s + 3.
-(s + 1)*(s + 2)
Let m(w) be the third derivative of w**6/240 + 7*w**5/120 - w**4/6 - 83*w**2 - 1. Let m(d) = 0. What is d?
-8, 0, 1
Let a(l) be the second derivative of -32*l**6/75 - 44*l**5/25 - 169*l**4/60 - 11*l**3/5 - 9*l**2/10 - 23*l + 2. Determine h so that a(h) = 0.
-1, -3/8
Let u(m) be the third derivative of m**5/720 - 67*m**4/288 + 65*m**3/36 + 101*m**2 + 2. Suppose u(b) = 0. Calculate b.
2, 65
Let t be 4040/(-72) + 4/(-18). Let g = t + 57. Suppose 0 + 1/3*l + 1/3*l**3 - g*l**2 = 0. Calculate l.
0, 1
Suppose -4*j - 27 = 3*g, -2*j + 28 = -3*j - 5*g. Let d = j - -4. Factor -d - 1 + v**2 - 3*v**2 + 3*v - 7*v.
-2*(v + 1)**2
Let b(a) = -45*a**3 - 654*a**2 - 2947*a - 3608. Let j(d) = 135*d**3 + 1959*d**2 + 8842*d + 10823. Let w(s) = -7*b(s) - 2*j(s). Factor w(y).
5*(y + 2)*(3*y + 19)**2
Let d(f) be the third derivative of f**8/336 - f**7/210 + 40*f**2 + 2*f. Solve d(v) = 0.
0, 1
Let y(g) = -11*g**2 + 25*g - 41. Let q(f) = -5*f**2 + 12*f - 20. Suppose 5*a - 6 = -t + 35, 0 = -3*a + 4*t + 43. Let u(b) = a*q(b) - 4*y(b). Factor u(x).
-(x - 4)**2
Let u be 1/((-40)/(-16)) - 23/30. Let q = 3/10 - u. Suppose -q*i**4 + 0*i**2 + 0*i**3 + 0 + 0*i + 2/3*i**5 = 0. What is i?
0, 1
Suppose -8*c = -12*c + 16. Let p(q) be the first derivative of 0*q**2 - 1/8*q**c - 1/10*q**5 + 1/6*q**3 + 0*q - 3 + 1/12*q**6. Factor p(l).
l**2*(l - 1)**2*(l + 1)/2
Let w(h) = h**2 - 8*h + 3. Suppose 4*g - 22 = 10. Let t be w(g). Suppose c + c**2 + 1/3 + 1/3*c**t = 0. What is c?
-1
Let x(u) = 10*u**4 + 2*u**3 + 12*u**2 - 42*u. Let t(s) = -8*s**4 - 3*s**3 - 11*s**2 + 41*s. Let o(m) = -6*t(m) - 5*x(m). Suppose o(j) = 0. What is j?
-2, 0, 3
Let l be ((-3)/(-2))/((-840)/(-224)). What is z in 0 - 2/5*z**2 - l*z = 0?
-1, 0
Let h(o) be the first derivative of o**8/504 - o**7/105 + 2*o**5/45 + 25*o**2/2 - 28. Let v(m) be the second derivative of h(m). Find s, given that v(s) = 0.
-1, 0, 2
Let o(w) = -9*w**2 - 9*w. Suppose 3*s - 27 = -9. Let c(m) = 8*m**2 + 8*m. Let g(i) = s*c(i) + 5*o(i). Factor g(h).
3*h*(h + 1)
Let i = 442 + -438. Factor -1/3*c**5 + 2/3*c**2 - 1/3*c**i - 1/3*c - 1/3 +