**6/360 - z**5/180 + z**4/72 + z**3/18 - 7*z**2. Factor u(a).
-(a - 1)*(a + 1)**2/3
Suppose -5*x + 3 = 4*p, 4*p - x = 6*p - 9. Let k = 10 - p. Factor -14*v**k + 5*v**4 + 10*v**2 - 4*v**3 + 9*v**4 - 6*v**2.
2*v**2*(v - 1)*(7*v - 2)
Let i(n) be the third derivative of -7/48*n**4 + 0*n + 4*n**2 - 1/6*n**3 - 1/48*n**6 - 1/420*n**7 - 3/40*n**5 + 0. Factor i(b).
-(b + 1)**3*(b + 2)/2
Let a(v) be the second derivative of -v**6/10 + 3*v**5/20 + v. Determine h so that a(h) = 0.
0, 1
Suppose -5*m - 21 = -v + 5, 5*v + 2*m - 103 = 0. Let n(p) = 7*p - 17. Let d be n(4). Factor -3 - v*x**2 - d*x + 2*x - 6*x + 9.
-3*(x + 1)*(7*x - 2)
Let p be -1 + (26 - (0 + 0)). Let m be 40/p*10/4. Determine r so that -6*r**2 - 2 + 2*r**2 - 3*r**m + 4*r**3 + 9*r**4 - 6*r + 2*r**5 = 0.
-1, 1
Determine i so that -39/4*i**3 - 3/4*i**4 - 36*i**2 + 0 - 27*i = 0.
-6, -1, 0
Let f(p) be the first derivative of 5*p**6/6 - 4*p**5 + 15*p**4/4 + 20*p**3/3 - 10*p**2 - 5. What is y in f(y) = 0?
-1, 0, 1, 2
Let j(b) be the second derivative of -b**5/40 + b**4/24 - 17*b. Suppose j(y) = 0. Calculate y.
0, 1
Let y(j) be the second derivative of j**8/4480 + j**7/1260 - j**6/1440 - j**5/120 + j**4/6 - 3*j. Let b(n) be the third derivative of y(n). Factor b(u).
(u + 1)**2*(3*u - 2)/2
Let l(q) be the second derivative of -q**7/168 - q**6/40 - 3*q**5/80 - q**4/48 - 3*q. Find b such that l(b) = 0.
-1, 0
Factor 1/10*p**2 - 1/5*p + 1/10.
(p - 1)**2/10
Let f(a) = -3*a**2 + 7*a + 5. Let t(h) be the third derivative of h**5/30 - h**4/6 - h**3/2 + 3*h**2. Let o(l) = 3*f(l) + 5*t(l). Suppose o(n) = 0. What is n?
-1, 0
Let h be (10/(-6))/((-8)/(-48)). Let q be 1/h*45/(-6). Factor -15/4*d**2 - q*d + 3/4 - 9/4*d**3.
-3*(d + 1)**2*(3*d - 1)/4
Let i(k) be the first derivative of -k**7/315 + k**5/45 - k**3/9 - 2*k**2 + 4. Let j(z) be the second derivative of i(z). Factor j(t).
-2*(t - 1)**2*(t + 1)**2/3
Let a(k) be the second derivative of k**4/18 + 4*k**3/9 + 4*k**2/3 + 2*k - 1. Factor a(s).
2*(s + 2)**2/3
Let r(o) = o**3 + 5*o**2. Let t be r(-5). Let l(u) be the second derivative of 1/80*u**5 + 0 + t*u**2 + 2*u + 1/24*u**3 + 1/24*u**4. Factor l(c).
c*(c + 1)**2/4
Suppose 4*m = 3*q + 20, q = -3*m - 4*q + 15. Suppose 4*u - 2*h = -u + 16, m*h = u + 6. Factor -3*b - 4*b**3 - 2*b**3 + 9*b + 2*b - 2*b**u.
-2*b*(b - 1)*(b + 2)**2
Suppose 0 = -a - a - 12. Let g(z) = 7*z**3 + z**2 - z - 7. Let d(l) = 15*l**3 + 2*l**2 - 2*l - 15. Let x(h) = a*d(h) + 13*g(h). Factor x(v).
(v - 1)*(v + 1)**2
Let k = 22 + -18. Let n(t) be the third derivative of -1/150*t**5 + 2/15*t**3 - 2*t**2 + 0 + 0*t + 1/60*t**k. Factor n(f).
-2*(f - 2)*(f + 1)/5
Let p(n) be the first derivative of -n**4/6 + 14*n**3/3 - 49*n**2 + 686*n/3 + 14. Determine y so that p(y) = 0.
7
Let h(b) = 2 - b**2 - 2 + 1. Let a(x) = -6*x**2 + 6. Let m(r) = 2*a(r) - 11*h(r). Factor m(v).
-(v - 1)*(v + 1)
Solve 15/4*x**3 - 3*x - 3/4*x**4 + 15/4*x**2 - 3/4*x**5 - 3 = 0.
-2, -1, 1, 2
Factor 12 + 39*s - 6*s**2 - 11*s - 14*s.
-2*(s - 3)*(3*s + 2)
Let d(p) be the first derivative of -1/100*p**5 + 0*p**2 + 2*p + 1/30*p**3 - 3 + 0*p**4. Let s(y) be the first derivative of d(y). What is a in s(a) = 0?
-1, 0, 1
Let n = 37 - 32. Let q(c) be the third derivative of 1/45*c**n + 0 + 0*c + 0*c**3 + 1/18*c**4 + 3*c**2 + 1/360*c**6. What is s in q(s) = 0?
-2, 0
Let t be (28 - 1) + (-2)/(-2). Let l be t/(-8)*(-2)/4. Factor l*i**3 - 1/2 + 3*i**2 + 3/4*i.
(i + 1)**2*(7*i - 2)/4
Let r(a) be the first derivative of a**3/6 - a/2 - 3. Factor r(i).
(i - 1)*(i + 1)/2
Let j be 4/6 + 8/6. Suppose 0 = -9*c + 2*c. Suppose 0 + 2/11*u**3 - 2/11*u + c*u**j = 0. Calculate u.
-1, 0, 1
Factor -5*v**4 + 4*v**5 - 5*v**5 + 0*v**5.
-v**4*(v + 5)
Let d be (-1 - -1)/(-74 + 76). Factor 4/3 - 2*p + 2/3*p**3 + d*p**2.
2*(p - 1)**2*(p + 2)/3
Factor -128/3 - 2/3*a**2 - 32/3*a.
-2*(a + 8)**2/3
Let i(m) be the first derivative of -8 - 1/2*m**2 - 1/6*m**3 - 1/2*m. Factor i(v).
-(v + 1)**2/2
Let y = 64 - 61. Let l(c) be the third derivative of 0*c + c**2 + 0*c**4 + 1/15*c**7 + 1/30*c**6 + 0*c**y - 1/30*c**5 + 0 + 1/42*c**8. Factor l(d).
2*d**2*(d + 1)**2*(4*d - 1)
Let w(p) = -p**2 + p. Let o(h) = -2*h**2 - h - 1. Let n(c) = -o(c) - 3*w(c). Let z be n(1). Factor -8*v**3 + 12*v**2 + 0*v**4 - z*v + 2*v**4 + 2 - 4*v.
2*(v - 1)**4
Let c(f) be the first derivative of -4*f**5/5 - 2*f**4 + 4*f**2 + 4*f - 3. Find w, given that c(w) = 0.
-1, 1
Let k(y) = y**4 - y**3 - y**2 - 1. Let d(f) = f**4 + 2*f**3 - 4*f**2 - 6*f - 1. Let r(m) = d(m) - 4*k(m). Determine g so that r(g) = 0.
-1, 1
Let g(j) be the first derivative of 1/4*j**4 + 1/6*j**2 + 1/15*j**5 + 1/3*j**3 + 0*j - 3. Factor g(f).
f*(f + 1)**3/3
Let j = 3 - -1. Determine h so that 0*h**j + 2/5*h**5 - 6/5*h**3 + 0 - 4/5*h**2 + 0*h = 0.
-1, 0, 2
Let y = 615 + -615. Suppose 3/4*s**4 + 0*s**3 - 3/4*s**2 + y*s + 0 = 0. What is s?
-1, 0, 1
Factor 0*s**3 - 3/2 + 1/2*s**4 - 3*s**2 + 4*s.
(s - 1)**3*(s + 3)/2
Let r(k) be the third derivative of 0 + 1/30*k**5 - 4*k**2 + 1/4*k**4 + 2/3*k**3 + 0*k. Factor r(m).
2*(m + 1)*(m + 2)
Let d be -8*(-1 - 15/(-6)). Let t be ((-9)/21)/(d/32). Suppose 2/7 + t*x**2 - 10/7*x = 0. What is x?
1/4, 1
Let n = -19 + 6. Let k = -9 - n. Factor -12/5*b**3 - 2/5*b**k - 16/5*b + 0 - 24/5*b**2.
-2*b*(b + 2)**3/5
Factor 0*x + 0*x**2 + 0 + x**3 - 3/2*x**4 + 1/2*x**5.
x**3*(x - 2)*(x - 1)/2
Let w = 18 + -14. Let g(b) be the third derivative of -1/120*b**7 + 0*b**w + 0*b**5 + 0 + 0*b + 0*b**3 + 2*b**2 - 1/240*b**6. Factor g(o).
-o**3*(7*o + 2)/4
Let n(g) be the third derivative of 0*g**3 + 0*g**5 + 0*g**4 + 0*g + 0 + 0*g**6 - 1/168*g**8 - 1/105*g**7 + 2*g**2. Factor n(a).
-2*a**4*(a + 1)
Let c(f) be the first derivative of 0*f - 1/12*f**6 - 6 - 1/5*f**5 + 1/3*f**3 + 1/4*f**2 + 0*f**4. Factor c(q).
-q*(q - 1)*(q + 1)**3/2
Let t(l) be the first derivative of 3/5*l**3 - 3 - 3/2*l**2 + 6/5*l. Factor t(b).
3*(b - 1)*(3*b - 2)/5
Let z(y) = -32*y**4 - 39*y**3 + 25*y**2 + 48*y + 16. Let x(g) = -8*g**4 - 10*g**3 + 6*g**2 + 12*g + 4. Let u(b) = 9*x(b) - 2*z(b). Solve u(s) = 0.
-1, -1/2, 1
Let g(j) be the second derivative of j**5/30 + j**4/6 - 39*j. Let g(v) = 0. Calculate v.
-3, 0
Suppose m + u - 4 + 2 = 0, 2 = u. Let q be ((-8)/70)/((-3)/30). Factor 6/7*f**3 - q*f**2 + m + 2/7*f.
2*f*(f - 1)*(3*f - 1)/7
Let r = -123 - -617/5. Factor 2/5 - 2/5*q**2 + 2/5*q**3 - r*q.
2*(q - 1)**2*(q + 1)/5
Find u, given that 6/5*u + 0 - 16/5*u**2 - 6/5*u**3 = 0.
-3, 0, 1/3
Let y(n) be the third derivative of -n**6/540 + n**5/135 + n**4/108 - 2*n**3/27 - 11*n**2. Let y(c) = 0. Calculate c.
-1, 1, 2
Let a(f) be the third derivative of -f**6/75 - f**5/75 + f**4/30 + 74*f**2. Factor a(x).
-4*x*(x + 1)*(2*x - 1)/5
Let i(j) be the second derivative of j**5/10 - 7*j**4/6 + 5*j**3 - 9*j**2 + 7*j. Determine c so that i(c) = 0.
1, 3
Let l(t) be the third derivative of 0*t - 1/18*t**6 - 1/504*t**8 + 1/9*t**3 + 0 + 1/9*t**5 - 5/36*t**4 - 9*t**2 + 1/63*t**7. What is s in l(s) = 0?
1
Let a(x) = x**2 + 2*x - 3. Let g = 1 - 4. Let f be a(g). Factor 2/7*k**2 + f - 2/7*k.
2*k*(k - 1)/7
Let s(z) = 8*z**4 - 21*z**3 + 5*z**2 + 21*z - 8. Let y(v) = 4*v**4 - 10*v**3 + 2*v**2 + 10*v - 4. Suppose c = 4*c + 15. Let i(j) = c*y(j) + 2*s(j). Factor i(p).
-4*(p - 1)**3*(p + 1)
Suppose 4*b - 4*s + 16 = 0, -4*s + 16 = 5*b - 0*s. Let i(c) be the first derivative of -1/3*c**3 + b*c - 1/2*c**2 - 3. Factor i(d).
-d*(d + 1)
Find q, given that 30*q - 2*q**3 + 22*q**3 + 40*q**2 + 13 - 5 - 2*q**5 = 0.
-1, 4
Let g(l) be the first derivative of 3/10*l**5 - 9/8*l**4 + 0*l**3 - 5 + 3*l**2 + 0*l. Factor g(w).
3*w*(w - 2)**2*(w + 1)/2
Let t be (-2)/6 - (-4)/12. Let x(g) be the second derivative of t - 1/10*g**5 + 0*g**4 + g + 0*g**3 + 0*g**2 - 1/15*g**6. Factor x(o).
-2*o**3*(o + 1)
Suppose -2*q = 3*c - 8, -5*c - 2*q + 26 = -5*q. Let d = 9 - c. Factor -2*f**d + 3*f**2 + 3*f - f - 4*f**4 + f**2.
-2*f*(f - 1)*(f + 1)**3
Suppose 3*w = 4*w + 3*u - 17, -5*w + 3*u = 5. Find j such that 4/3 - 4/3*j + 1/3*j**w = 0.
2
Let m(y) be the second derivative of 1/40*y**6 - y + 1/8*y**4 - 9/8*y**2 + 0 - 1/2*y**3 + 3/20*y**5. Factor m(t).
3*(t - 1)*(t + 1)**2*(t + 3)/4
Let y(h) = 6*h**2 + 24*h - 25. Let t(x) = -3*x**2 - 12*x + 12. Let v(m) = -5*t(m) - 3*y(m). Solve v(p) = 0 for p.
-5, 1
Let x = -32/7 + 34/7. Suppose 0 + 4/7*q + x*q**2 = 0. What is q?