**5/60 - n**4/8 - 71*n**2. Let j(l) = 0. Calculate l.
-3/11, 0
Suppose -10*p + 162 = 17*p. Let d(z) be the first derivative of -z**3 - 3/5*z**5 - 9/4*z**4 + p*z + 9 + 9/2*z**2. Solve d(r) = 0 for r.
-2, -1, 1
Suppose -4*p + 1386*p**4 + 0*p**3 + 4*p**2 + 4*p**3 + 2*p - 1390*p**4 - 2*p = 0. Calculate p.
-1, 0, 1
Suppose 4*z - 3*w = 4, -5*z + 2*w + 3 = -2*z. Let p(x) = -4*x + 2*x + 9*x - 8*x. Let t(k) = 16*k**2 + 53*k + 12. Let g(y) = z*p(y) + t(y). Factor g(l).
4*(l + 3)*(4*l + 1)
Let z(p) = 2*p**4 + 4*p**3 + 2*p**2 - 8*p + 1. Let t(x) = x**4 - x**3 - x**2 + x + 1. Let w(l) = -5*t(l) + 5*z(l). Factor w(b).
5*b*(b - 1)*(b + 3)**2
Let k = 179 + -126. Factor -d**5 + 2 + k*d - 4*d**3 + 0*d**3 - 4*d**4 - 48*d + 2*d**2.
-(d - 1)*(d + 1)**3*(d + 2)
Let t = 8 + -26. Let n = t - -22. Suppose 1 - 41*y + 3 + 41*y - n*y**2 = 0. What is y?
-1, 1
Let f(c) be the first derivative of 4*c**3/21 - 134*c**2/7 + 264*c/7 + 212. Factor f(o).
4*(o - 66)*(o - 1)/7
Let y be ((-6)/(-7))/((-2970)/(-154) + -17). Find d, given that -3/4 - y*d + 3/8*d**2 = 0.
-1, 2
Let c = -97 + 212. Let g = c - 569/5. Factor g*x + 3/5*x**2 + 0.
3*x*(x + 2)/5
Let m(i) = -19*i**3 + 12*i**2 + 7*i. Suppose -74 = 4*q - 46. Let h(t) = -13*t**3 + 8*t**2 + 5*t. Let y(o) = q*h(o) + 5*m(o). Solve y(z) = 0.
0, 1
Let h(m) be the second derivative of -5/12*m**4 + 0 - 1/20*m**5 - 7/6*m**3 - 3/2*m**2 - 8*m. Factor h(q).
-(q + 1)**2*(q + 3)
Suppose 203*b + 72*b - 506 = 22*b. Factor -1/2*n**4 + 1/4*n**5 + 0 + n**b + n - 3/4*n**3.
n*(n - 2)**2*(n + 1)**2/4
Let b(s) be the second derivative of -s**5/240 + s**4/48 - s**3/24 - 11*s**2/2 - 7*s. Let r(p) be the first derivative of b(p). Factor r(l).
-(l - 1)**2/4
Let d(v) be the first derivative of -v**3/9 + 103*v**2/3 - 10609*v/3 + 74. Suppose d(m) = 0. Calculate m.
103
Let y(j) be the first derivative of j**4/26 - 10*j**3/39 - 6*j**2/13 + 250. Factor y(p).
2*p*(p - 6)*(p + 1)/13
Let w(b) be the third derivative of b**6/1260 + b**5/105 + b**4/21 + 23*b**3/6 - 27*b**2. Let p(x) be the first derivative of w(x). Factor p(s).
2*(s + 2)**2/7
Suppose 4*z + 14 = -0*z + 26. Let o = -2 - -2. Factor 0*m + o*m**z + 2/9 - 4/9*m**2 + 2/9*m**4.
2*(m - 1)**2*(m + 1)**2/9
Let s(f) = 5*f**3 + 15*f**2 - 31*f + 11. Let g(a) = -a**3 - 3*a**2 + 6*a - 2. Suppose 0 = -5*o + 8*o + 66. Let r(b) = o*g(b) - 4*s(b). What is j in r(j) = 0?
-4, 0, 1
Let r be 124/(-4)*(-1)/1. Suppose 5*z - r = q - 3*q, 5*z - 28 = -q. Factor 6*l**3 + 1 + 0*l - q*l - l**2 + 1 - 3*l**3 - l**4.
-(l - 2)*(l - 1)**2*(l + 1)
Let d(h) be the second derivative of 3*h**5/40 - h**4 + 21*h**3/4 - 27*h**2/2 + 4*h - 4. Solve d(b) = 0.
2, 3
Let o = 208 + -209. Let m be 91/78 - o/6. Factor 2/3 + m*s + 0*s**2 - 2/3*s**4 - 4/3*s**3.
-2*(s - 1)*(s + 1)**3/3
Let a(d) = -6*d**2 - 133*d - 203. Let t(n) = -n**2 - 22*n - 34. Let j(b) = -6*a(b) + 39*t(b). Factor j(v).
-3*(v + 2)*(v + 18)
Suppose -4*h - k + 1 = -0, h - 4*k = -4. Factor -2*g + h*g**3 + g + g**3.
g*(g - 1)*(g + 1)
Let r(o) = -o**3 + o + 1. Let a(z) = -7*z**3 + 6*z**2 - 3*z + 10. Let j(w) = a(w) - 6*r(w). Determine i, given that j(i) = 0.
1, 4
Let c(s) = -4*s**2 + 3*s - 4. Let o(y) = -6*y**2 + 0*y**2 - 3*y**2 + 3*y**2 + 5*y - 6. Let j(a) = -7*c(a) + 5*o(a). Suppose j(r) = 0. What is r?
1
Let z(d) be the third derivative of d**8/280 - 4*d**7/525 + d**6/300 - 16*d**2 + 4. Let z(h) = 0. What is h?
0, 1/3, 1
Determine h so that -2572125/4 + 81225/4*h - 855/4*h**2 + 3/4*h**3 = 0.
95
Let v(q) be the second derivative of q**6/10 - 24*q**5/5 + 61*q**4/4 - 15*q**3 + 173*q. Solve v(g) = 0 for g.
0, 1, 30
Suppose -3*b + 2*l + 282 = 45, 3*b - 246 = 5*l. Factor -4*c + 77*c**2 - b*c**2 + c**3.
c*(c - 2)*(c + 2)
Factor -1034 + 95*m**4 - 117*m**3 + 5*m**5 + 1034 + 17*m**3.
5*m**3*(m - 1)*(m + 20)
What is o in -12/17*o**2 + 28/17*o**3 + 6/17*o**5 - 2/17*o + 2/17 - 22/17*o**4 = 0?
-1/3, 1
Suppose -33 = -5*v + 27. Factor -5 + 2*c + v*c**2 - 2*c - 20*c - 3.
4*(c - 2)*(3*c + 1)
Let k(g) = -3*g**3 - g**2 + g. Let a(n) = 10*n**3 + 38*n**2 - 86*n + 44. Let d(x) = -a(x) - 2*k(x). Find p, given that d(p) = 0.
-11, 1
Factor 405*n**3 - 29*n**3 - 68*n**2 - 19*n**4 + 59*n**3 - 137*n**4 + 15*n**5 - 82*n**2.
3*n**2*(n - 5)**2*(5*n - 2)
Let b = -4 + 6. Factor -10*d**3 + 0*d + d - 6*d + 4 - 16*d**b + 3*d.
-2*(d + 1)**2*(5*d - 2)
Suppose 4 = l + 10. Let s(h) = -h**2 - 6*h + 3. Let v be s(l). Find r such that 2*r**v - 4 + 3 + 1 - 2*r**4 = 0.
0, 1
Suppose 2*m - 4*z = 0, -4*z - 32 = -m + 3*m. Let w(b) = -2*b - 12. Let h be w(m). Suppose 2*a**4 - 20*a - 6*a**4 - h*a**5 + 20*a = 0. Calculate a.
-1, 0
Let y(s) be the first derivative of 5*s**4/32 - s**3/8 - s**2/8 - 620. Find v such that y(v) = 0.
-2/5, 0, 1
Suppose -11*u + 0*u = -33. Suppose -14 = -s + 3*j, u*j + 10 - 6 = -4*s. Factor -s + 3/2*h**2 + 0*h + 1/2*h**3.
(h - 1)*(h + 2)**2/2
Let n(f) be the second derivative of f**6/30 - f**5/5 - 11*f**4/12 - f**3 - 3*f + 52. Factor n(o).
o*(o - 6)*(o + 1)**2
Suppose -3/7*c - 3/7*c**5 - 9/7*c**4 + 6/7*c**3 + 18/7*c**2 - 9/7 = 0. What is c?
-3, -1, 1
Let b(p) be the second derivative of -p**6/30 - p**5/15 + p**4/3 - 10*p**2 + 16*p. Let t(j) be the first derivative of b(j). Solve t(m) = 0 for m.
-2, 0, 1
Let c = -997/345 + 91/23. Let k(o) be the first derivative of 6/5*o**2 + 8 + 0*o + 1/5*o**4 - c*o**3. What is n in k(n) = 0?
0, 1, 3
Let i(n) be the second derivative of -n**4/30 - 22*n**3/15 - 121*n**2/5 - 2*n + 52. Find d, given that i(d) = 0.
-11
Suppose 4*s = -21 - 3. Let k = s - -11. Factor -14*p**4 - 4*p**2 - 13*p**3 + 0*p**2 - k*p**3.
-2*p**2*(p + 1)*(7*p + 2)
Let g(q) be the first derivative of q**6/15 - 2*q**5/5 + 5*q**4/6 - 2*q**3/3 + 6*q - 8. Let c(l) be the first derivative of g(l). Factor c(i).
2*i*(i - 2)*(i - 1)**2
Suppose 1/3*o**4 + 0 + 25/3*o**2 - 14/3*o**3 - 4*o = 0. What is o?
0, 1, 12
Let k(y) be the third derivative of y**8/168 + 2*y**7/21 + 7*y**6/15 + 4*y**5/5 + 705*y**2. Factor k(f).
2*f**2*(f + 2)**2*(f + 6)
Let p(b) be the second derivative of -3*b**5/20 - 3*b**4/4 - b**3 - 71*b - 1. Find h, given that p(h) = 0.
-2, -1, 0
Let t(z) be the first derivative of 2*z**3/9 - 3*z**2 + 28*z/3 - 31. Factor t(d).
2*(d - 7)*(d - 2)/3
Factor 189/2*t - 3/2*t**2 - 93.
-3*(t - 62)*(t - 1)/2
Let j(f) = -3*f - f + 3*f + 4 - 6. Let o be j(-6). What is t in 6 - 91*t**o - 3*t**2 + 83*t**3 - 21*t + 30*t**5 + 4*t**4 - 8*t**3 = 0?
-1/2, 2/5, 1
Let c(x) be the first derivative of -7 + 0*x + 3/32*x**4 - 1/4*x**3 + 3/16*x**2. Factor c(k).
3*k*(k - 1)**2/8
Suppose 0 = -2*i - 12, 4*l + i + 8 = 14. Determine q so that 0 + 2/9*q**l - 2/3*q - 4/9*q**2 = 0.
-1, 0, 3
Factor -10*n**3 - 127*n - 30*n**2 + 5*n**4 - 10*n**2 + 127*n.
5*n**2*(n - 4)*(n + 2)
Let y be -7*(-2)/8 + -6 + 5. Let v(c) be the first derivative of 2*c**3 + 0*c - 3 - y*c**4 - 3/2*c**2. Factor v(p).
-3*p*(p - 1)**2
Let -1/3*g**2 - 5 - 8/3*g = 0. Calculate g.
-5, -3
Solve 6 + 9/2*j + 3/4*j**2 = 0 for j.
-4, -2
Let u(g) be the second derivative of 0*g**3 - 1/15*g**4 - 1/50*g**5 + 0 + 0*g**2 - 4*g. Solve u(o) = 0 for o.
-2, 0
Suppose 0 = 3*n + n - 32. Let y = 5 + n. Determine r so that -3*r - 19*r**2 - 4*r**3 + r**3 + y*r**2 = 0.
-1, 0
Suppose 0 = 2*c + 6*f - 3*f - 21, 0 = -c - 10*f + 53. Find h such that -2/11*h**4 - 8/11*h - 8/11*h**c - 2/11 - 12/11*h**2 = 0.
-1
Let i(u) be the second derivative of 0 + 9/5*u**2 + 17*u + 1/20*u**4 + 1/2*u**3. Factor i(y).
3*(y + 2)*(y + 3)/5
Let k = -749 + 764. Factor -3/2*r**2 - 75/2 + k*r.
-3*(r - 5)**2/2
Suppose 587*b - 602*b + 30 = 0. What is z in -15/2*z**4 - 3/2*z - 3*z**3 + 9*z**b - 3/2 + 9/2*z**5 = 0?
-1, -1/3, 1
Let c(x) = 6*x**5 + 4*x**4 - 36*x**3 - 136*x**2 + 8. Let i(p) = 17*p**5 + 13*p**4 - 107*p**3 - 406*p**2 + 22. Let f(s) = 11*c(s) - 4*i(s). Factor f(q).
-2*q**2*(q - 4)*(q + 4)**2
Solve 0*v**2 + 1/3*v**5 + 0 + 0*v**3 + 0*v**4 + 0*v = 0 for v.
0
Let h(a) be the first derivative of 5*a**4/2 - 6*a**3 - 38*a**2 - 48*a - 185. Suppose h(i) = 0. Calculate i.
-6/5, -1, 4
Let r(n) be the first derivative of -6 + 1/5*n**3 - 6/5*n**2 + 12/5*n. Find g such that r(g) = 0.
2
Let 27/5*y**2 + 32/5*y + y**3 - 3/5*y**4 + 12/5 - 1/5*y**5 = 0. What is y?
-2, -1, 3
Let h be 0 - ((-486)/54 + 7/1). Factor 6/11*b**h + 8/11*b + 3/11 - 1/11*b**4 + 0*b**3.
-(b - 3)*(b + 1)**3/11
Let t = 62497/5 + -12499. Factor -6/5 - t*i**2 + 8/5*i.
