e of 0*y + 1/21*y**3 + 0 - 1/105*y**5 + 1/84*y**4 - y**2. Factor j(k).
-2*(k - 1)*(2*k + 1)/7
Let u(b) be the second derivative of -b**5/30 - 7*b**4/18 - 5*b**3/3 - 3*b**2 + 13*b. Factor u(h).
-2*(h + 1)*(h + 3)**2/3
Let v(q) be the first derivative of 3/2*q**4 + 0*q**2 + 3/5*q**5 + q**3 + 0*q - 4. Find k such that v(k) = 0.
-1, 0
Let w = 55 - 53. Suppose 5/2*b + 1/2*b**3 + 2*b**w + 1 = 0. What is b?
-2, -1
Factor -6 + 6*m**3 + 3*m**4 + 10 - 4.
3*m**3*(m + 2)
Let y be 8/(-36) - (147/(-54) + 1). Factor b**3 + 1/4*b**4 + y*b**2 + b + 1/4.
(b + 1)**4/4
Suppose 0 = -14*m + 39 + 17. Let r(b) be the first derivative of 2/45*b**5 + 3 + 0*b + 2/27*b**3 + 0*b**2 - 1/9*b**m. Factor r(p).
2*p**2*(p - 1)**2/9
Let o(a) be the third derivative of a**7/1260 - 7*a**6/720 + a**5/24 - 13*a**4/144 + a**3/9 - a**2 + 8. Factor o(d).
(d - 4)*(d - 1)**3/6
Suppose -3*j**3 + 15*j + 5*j**2 - 6*j**4 - j**4 + 2*j**4 - 12*j**3 = 0. Calculate j.
-3, -1, 0, 1
Let s(g) = g**3 - 4*g**2 - 5*g + 4. Let n be s(5). Let u(y) be the second derivative of 0 - 1/9*y**n + 2*y + 1/3*y**2 + 1/9*y**3. Factor u(b).
-2*(b - 1)*(2*b + 1)/3
Let z = 5 - 1. Let d(h) be the first derivative of 0*h + 1 + 1/2*h**z - 2/3*h**3 + 2/5*h**5 - h**2. Determine u, given that d(u) = 0.
-1, 0, 1
Let s(b) be the first derivative of 4*b**3/3 - 4*b - 16. Let s(y) = 0. What is y?
-1, 1
Let d = -143/10 + 134/5. Factor -2*n**3 + 0*n**2 + 0*n - 10*n**4 + 0 - d*n**5.
-n**3*(5*n + 2)**2/2
Let p be 1 + 1 - 15/39*-30. Suppose 32/13 + p*x**2 - 128/13*x + 18/13*x**4 - 96/13*x**3 = 0. Calculate x.
2/3, 2
Factor -1578*d + 30*d**2 - 25*d**4 + 1578*d + 35*d**3.
-5*d**2*(d - 2)*(5*d + 3)
Let v(a) be the second derivative of -a**6/15 + a**5/10 + a**4/2 - a**3/3 - 2*a**2 + 7*a. Factor v(h).
-2*(h - 2)*(h - 1)*(h + 1)**2
Suppose b - 2*r = 2*b - 10, -3*b + 26 = 5*r. Determine y so that 6*y**3 + 3*y**3 + 2*y**b + 0*y**2 + 4*y**5 + 12*y**4 + y**5 = 0.
-1, -2/5, 0
Let b(n) be the third derivative of -n**7/28 - n**6/24 + 13*n**5/24 + 5*n**4/6 - 5*n**3/3 + 29*n**2. Let b(x) = 0. Calculate x.
-2, -1, 1/3, 2
Let t(q) be the second derivative of 1/18*q**4 - 3*q - 1/90*q**5 - 2/27*q**3 + 0*q**2 + 0. Suppose t(w) = 0. What is w?
0, 1, 2
Let s(t) = -2*t**4 - 4*t**3 + 2*t**2 + 4. Let b = 18 - 14. Let y(i) = -i + 1. Let f(u) = b*y(u) - s(u). Determine a so that f(a) = 0.
-2, -1, 0, 1
Suppose 5*k + x + 0*x = -5, 2*k - 5*x = 25. Let r(h) be the first derivative of 0*h**2 + 1/16*h**4 - 1/20*h**5 + 0*h - 2 + k*h**3. Factor r(v).
-v**3*(v - 1)/4
Let q(a) = -3*a**5 + 15*a**4 - 15*a**2 - 4*a + 7. Let i(h) = h**5 - 7*h**4 + 7*h**2 + 2*h - 3. Let x(n) = 7*i(n) + 3*q(n). Factor x(v).
-2*v*(v - 1)*(v + 1)**3
Let d(j) be the second derivative of j**4/36 - j**3/18 + 5*j. Factor d(q).
q*(q - 1)/3
Let u(o) be the second derivative of o**4/2 + 5*o**3/2 + 9*o**2/2 - 16*o. Factor u(a).
3*(a + 1)*(2*a + 3)
Let r = 16 - 13. Let m(w) = -w**3 - w**2 + w + 2. Let x be m(-2). Let -1 - p**2 + 1 - p**r + 2*p**x = 0. What is p?
-1/2, 0, 1
Factor m**4 + 6*m**5 + 3*m**4 + 2*m - 4*m**2 - 6*m**5 - 2*m**5.
-2*m*(m - 1)**3*(m + 1)
Let h be (7/7)/((-1)/3). Let x = 1 - h. Let -3*s**x - 2*s**5 + 3*s**2 + 11 + 5*s**5 - 3*s**3 - 11 = 0. Calculate s.
-1, 0, 1
Let q(t) be the second derivative of 0*t**4 + 3/10*t**5 - 4*t + 0*t**2 + 0 - 1/15*t**6 + 0*t**3. Solve q(v) = 0.
0, 3
Let u(k) be the first derivative of k**6/3 - 12*k**5/5 + 6*k**4 - 16*k**3/3 + 5. Factor u(o).
2*o**2*(o - 2)**3
Suppose 5*g = 3*g - 3*q - 3, -5*g - 4 = 4*q. Let b = 1 - 1. Factor 1/4*p - 1/2*p**3 + 1/4*p**5 + b*p**4 + 0*p**2 + g.
p*(p - 1)**2*(p + 1)**2/4
Let t = -2 + 5. Let k(p) be the second derivative of 1/30*p**6 + 0*p**t + 0*p**2 + 0*p**5 + 0 - 1/12*p**4 + p. Determine m, given that k(m) = 0.
-1, 0, 1
Let i(a) be the first derivative of -9*a**4/8 + 7*a**3/2 - 4*a**2 + 2*a - 4. Suppose i(q) = 0. Calculate q.
2/3, 1
Factor 1/3*v**5 - 2*v**4 - 2/3 + 3*v + 14/3*v**3 - 16/3*v**2.
(v - 2)*(v - 1)**4/3
Let p(j) = -j**3 - 9*j**2 - 7*j + 11. Let y be p(-8). Factor -3*i**4 - 1 - 12*i**2 + 8*i**y + 0 + 2*i**3 + 6*i.
-(i - 1)**3*(3*i - 1)
Let c(x) be the second derivative of -x**6/35 - 6*x**5/35 - 3*x**4/7 - 4*x**3/7 - 3*x**2/7 + 2*x - 7. Factor c(a).
-6*(a + 1)**4/7
Suppose 5*r + g - 3*g = -6, -3*g = r + 8. Let q be (-93)/(-33) - r/11. Let 2/7*j**2 + 2/7*j**4 + 4/7*j**q + 0*j + 0 = 0. What is j?
-1, 0
Suppose 4*s - 24 = -0*v + 2*v, 0 = 3*s + 2*v - 4. Suppose 3*x + 9 = s*g - 2, -2*x + 3*g = 9. Determine h, given that 2*h - 4 + 2*h**x + 0*h - 4*h + 4*h**2 = 0.
-2, -1, 1
Let z(v) be the third derivative of 27*v**8/56 - 3*v**7/7 - 8*v**6/15 - 2*v**5/15 - 2*v**2. Factor z(w).
2*w**2*(w - 1)*(9*w + 2)**2
Let a = -19/9 - -7/3. Find r, given that 2/9*r**2 + a - 4/9*r = 0.
1
Let q(d) be the second derivative of -d**5/40 - 7*d. Factor q(a).
-a**3/2
Let q be ((-1)/2)/((-2)/12). Suppose 7 = -j - q*g, 0*j - 2*g = -5*j + 16. Find s such that 7/3*s**5 + 5/3*s**j - 5/3*s**4 + 2/3*s - 3*s**3 + 0 = 0.
-1, -2/7, 0, 1
Let q(j) be the first derivative of -25*j**6/6 + 22*j**5 - 75*j**4/2 + 40*j**3/3 + 55*j**2/2 - 30*j - 66. Solve q(d) = 0 for d.
-3/5, 1, 2
Let u(f) be the second derivative of f**8/1008 - f**2 + 2*f. Let x(z) be the first derivative of u(z). Factor x(b).
b**5/3
Let f(d) be the second derivative of d**4/3 - 2*d**3/3 - 4*d**2 + 15*d. Factor f(r).
4*(r - 2)*(r + 1)
Let k = 50/1107 - 1/123. Let p(h) be the second derivative of 0 - h - k*h**4 - 1/9*h**2 - 1/9*h**3. Factor p(c).
-2*(c + 1)*(2*c + 1)/9
Let z(d) be the third derivative of d**8/10080 + d**7/5040 - d**3/3 - 8*d**2. Let q(x) be the first derivative of z(x). Suppose q(j) = 0. Calculate j.
-1, 0
Let y(c) be the third derivative of c**7/210 - c**6/20 + 13*c**5/60 - c**4/2 + 2*c**3/3 + 11*c**2. Let y(q) = 0. What is q?
1, 2
Let d(f) be the third derivative of -f**6/160 - f**5/12 - 9*f**4/32 - 5*f**3/12 + 20*f**2. Factor d(b).
-(b + 1)*(b + 5)*(3*b + 2)/4
Let d(t) = t**3 + t**2. Let i(s) = -2*s**4 - 4*s**3 - 16*s**2 + 2*s. Let f(b) = -10*d(b) - i(b). Factor f(g).
2*g*(g - 1)**3
Let l(t) be the first derivative of -t**3/12 + t**2/4 + 3*t/4 + 17. Factor l(m).
-(m - 3)*(m + 1)/4
Let w = 712 - 17806/25. Let n = w - -199/100. Solve 0 - 1/2*l - 3/4*l**3 - 7/4*l**2 + n*l**4 + 5/4*l**5 = 0.
-1, -2/5, 0, 1
Let z = -26 + 44. Let g(r) = 8*r + z*r**2 + 7*r - 7*r**2 + 1 - 10. Let k(m) = -5*m**2 - 7*m + 4. Let v(y) = -6*g(y) - 13*k(y). Factor v(u).
-(u - 2)*(u + 1)
Let k(u) be the third derivative of u**5/330 - u**4/44 + 2*u**3/33 + 6*u**2. Solve k(z) = 0.
1, 2
Let n(b) be the first derivative of -1/10*b**5 + 1/8*b**4 + 0*b**2 + 0*b**3 - 5 + 0*b. Factor n(d).
-d**3*(d - 1)/2
Suppose 2*x + 5*j - 1 + 3 = 0, 5*x + 5*j - 10 = 0. Suppose d + 9 = x*d. Factor -2/5*o**2 + 0 + 1/5*o**d + 0*o + 1/5*o**4.
o**2*(o - 1)*(o + 2)/5
Suppose -100 = -5*g + 5*f, g + 32 = 3*g + 2*f. Let d be (-14)/(-10) - g/(-30). Factor 2/7*q**d + 0 - 4/7*q.
2*q*(q - 2)/7
Let q = 605 + -60499/100. Let p(u) be the third derivative of 0*u + 9/10*u**3 + 2*u**2 + q*u**5 - 3/20*u**4 + 0. Suppose p(z) = 0. Calculate z.
3
Suppose 0 = -0*d - 3*d + 6. Let j be -5*((-6)/9)/d. Factor -2/3*s - j*s**4 + 0 - 4*s**3 - 3*s**2.
-s*(s + 1)**2*(5*s + 2)/3
Let f(j) be the first derivative of j**7/1050 + j**6/300 - j**5/100 - j**4/30 + 2*j**3/15 + j**2/2 + 3. Let s(r) be the second derivative of f(r). Factor s(p).
(p - 1)**2*(p + 2)**2/5
Let g(i) = i**2 + 3*i - 3. Let f be g(2). Let q(p) = 2*p - 9. Let x be q(f). Factor 5*z**3 - 2*z**3 - 6*z**4 + 6*z**2 + 2*z**x - z**3 - 4*z.
2*z*(z - 2)*(z - 1)**2*(z + 1)
Let m(c) be the first derivative of c**6/2 + 12*c**5/5 + 3*c**4 - 36. What is w in m(w) = 0?
-2, 0
Suppose 0 = -9*m + 4*m - 60. Let p be 82/126 - m/(-28). What is h in p*h**3 - 2/9*h**2 - 2/9*h + 2/9 = 0?
-1, 1
Let y = -75 - -75. Determine i, given that -1/2*i**5 + 0*i + 0 + 0*i**2 + 0*i**4 + y*i**3 = 0.
0
Let z(s) be the first derivative of 4*s**3/3 - 22*s**2 - 18. Let z(m) = 0. Calculate m.
0, 11
Let h(o) be the second derivative of o**4/36 + o**3/6 - 2*o**2/3 + 12*o. Factor h(l).
(l - 1)*(l + 4)/3
Let l(z) be the first derivative of z**4 - 8*z**3/3 + 2*z**2 + 2. Let l(d) = 0. Calculate d.
0, 1
Let t(l) = 15*l**4 - 24*l**3 - 9*l**2 + 14*l. Let i(g) = 15*g**4 - 23*g**3 - 8*g**2 + 13*g. Let s(u) = 4*i(u) - 3*t(u). Factor s(n).
5*n*(