be the first derivative of -x**4/6 + 4*x**3/9 + 7*x**2/3 + 8*x/3 - 1. Factor p(d).
-2*(d - 4)*(d + 1)**2/3
Suppose -31 = -g + 4*q + 23, -4*g + q = -201. Let k be 30/(-12)*(-16)/g. Factor k*f + 2/5*f**2 + 2/5.
2*(f + 1)**2/5
Let p(h) be the third derivative of -1/60*h**6 + 1/54*h**5 - 1/135*h**7 + 0*h + 1/12*h**4 + 2/27*h**3 - 3*h**2 + 0. Let p(g) = 0. What is g?
-1, -2/7, 1
Let y = 18 - 14. Let u(t) = -t**2 + 4*t + 4. Let k be u(y). Determine g, given that -4/11*g**3 + 2/11*g + 2/11*g**k + 2/11*g**5 + 2/11 - 4/11*g**2 = 0.
-1, 1
Let t(k) be the second derivative of k**6/15 + 4*k**5/5 + 11*k**4/3 + 8*k**3 + 9*k**2 - 30*k. Factor t(s).
2*(s + 1)**2*(s + 3)**2
Let z(a) be the first derivative of 0*a + 0*a**2 + 1 - 1/15*a**3. Solve z(f) = 0 for f.
0
Let x(p) be the first derivative of -p**6/2160 - p**5/720 - 2*p**3/3 - 1. Let w(h) be the third derivative of x(h). Determine m so that w(m) = 0.
-1, 0
Factor -2*t - 3*t**3 + 4*t + 0*t + t.
-3*t*(t - 1)*(t + 1)
Let x(j) be the third derivative of 1/36*j**4 + 0 - j**2 + 0*j + 1/18*j**3 + 1/180*j**5. Factor x(r).
(r + 1)**2/3
Let n = -1 + 5. Factor -5*v**4 + 6*v**n - 4*v**4 - v**2 - 3*v**3 - v**5.
-v**2*(v + 1)**3
Let n be (-12463)/(-33) + (-1)/(-3). Let z = 3406/9 - n. Factor 0 + z*k**3 - 2/9*k + 2/9*k**2.
2*k*(k + 1)*(2*k - 1)/9
Let a = -19 - -96/5. Let v(y) be the second derivative of -2/15*y**3 + a*y**2 - 1/10*y**4 + 2*y + 0. Factor v(u).
-2*(u + 1)*(3*u - 1)/5
Factor -27*p**3 - 3*p + 27*p - 42*p**2 - 3*p**2 + 12.
-3*(p + 2)*(3*p - 2)*(3*p + 1)
Suppose -4*u - 1 - 11 = -5*t, 4*u = 3*t - 4. Determine z so that 8*z**u + 20*z**3 + 2*z - 3*z + z = 0.
-2/5, 0
Let x(q) be the second derivative of -1/12*q**4 - 4*q + 0 - q**2 + 1/2*q**3. Factor x(a).
-(a - 2)*(a - 1)
Let z(o) = o**2 - 5*o - 9. Let i(k) be the second derivative of k**3/3 + 5*k**2/2 - 3*k. Let v(m) = -5*i(m) - 3*z(m). Factor v(x).
-(x - 2)*(3*x + 1)
Let v(p) be the first derivative of 2/3*p**3 + 1/12*p**4 + p - 2 + 2*p**2. Let g(t) be the first derivative of v(t). Factor g(o).
(o + 2)**2
Determine t, given that 4/9 - 2/9*t**3 + 0*t**2 + 2/3*t = 0.
-1, 2
Let z(q) = 3*q + q**2 - 2 + 3 - q**3 - 2*q. Let r be z(-2). Factor -1 - 8*a + 1 - 3*a**2 + r*a.
-3*a*(a - 1)
Let k(y) be the third derivative of -y**7/140 + y**5/40 - y**2. Factor k(n).
-3*n**2*(n - 1)*(n + 1)/2
Let m be (-2)/9 - (-65)/9. Suppose 2*b = m*b. Suppose 2/7 - 2/7*z**2 + b*z = 0. What is z?
-1, 1
Let q be (0 + -3)/((-6)/8). Let l(d) = 4*d - 21. Let n be l(6). Suppose 10/11*p**2 - 24/11*p**n - 18/11*p**q + 24/11*p + 8/11 = 0. Calculate p.
-1, -2/3, 1
Let k = -81/4 - -575/28. Factor 18/7*n**2 + 12/7*n + k + 8/7*n**3.
2*(n + 1)**2*(4*n + 1)/7
Let g(c) be the second derivative of c**7/105 + c**6/30 + c**5/30 - 3*c**2 + 3*c. Let t(p) be the first derivative of g(p). Factor t(h).
2*h**2*(h + 1)**2
Let o(y) be the second derivative of -y**9/7560 - y**8/2240 + y**6/720 - y**4/4 + 3*y. Let f(p) be the third derivative of o(p). Factor f(g).
-g*(g + 1)**2*(2*g - 1)
Factor -20*h**2 - 6*h + 26*h - 25 + 85*h.
-5*(h - 5)*(4*h - 1)
Let f(m) = -m + 9. Let s be f(8). Factor s - x**2 - 1/2*x**3 + 1/2*x.
-(x - 1)*(x + 1)*(x + 2)/2
Let m(r) be the first derivative of 50*r**6/3 - 4*r**5 - 16*r**4 - 16*r**3/3 + 19. Factor m(q).
4*q**2*(q - 1)*(5*q + 2)**2
Suppose -5*g - 3*j + j + 10 = 0, 0 = -3*j + 15. What is k in 2*k**2 + g + 6/7*k**4 + 4/7*k + 16/7*k**3 = 0?
-1, -2/3, 0
Let n be 22/33 - 20/(-6). Suppose -2*d = -n*u + 4, 2*d - 7*d = -5*u. Determine b, given that 2/5*b**d + 18/5 - 12/5*b = 0.
3
Let w(d) be the second derivative of -3*d**5/10 + 3*d**4/4 + 7*d**2/2 - 4*d. Let y(s) = -5*s**3 + 8*s**2 + 6. Let a(o) = 6*w(o) - 7*y(o). Factor a(u).
-u**2*(u + 2)
Let t(j) be the first derivative of -j**5/10 + j**4/8 + j**3/2 - j**2/4 - j + 4. Factor t(q).
-(q - 2)*(q - 1)*(q + 1)**2/2
Let h(x) be the first derivative of -x**6/15 - 2*x**5/25 + x**4/5 + 4*x**3/15 - x**2/5 - 2*x/5 + 8. Let h(v) = 0. What is v?
-1, 1
Let l = -29 + 32. Let w be 4/(32/30) - l. Factor -w*h**3 - 1/2*h**2 + 1/4*h + 0.
-h*(h + 1)*(3*h - 1)/4
Let r = -9 + 7. Let g(b) = -3*b**2 + 3*b + 2. Let f(k) = k**2 - k. Let h(a) = r*f(a) - g(a). Factor h(j).
(j - 2)*(j + 1)
Let y(t) = 9*t**4 + 12*t**3 + 3*t - 3. Let u(g) = g**4 + g**3 - g**2 + g - 1. Let m(r) = 3*u(r) - y(r). Determine v so that m(v) = 0.
-1, -1/2, 0
Let x(d) be the first derivative of 27*d**4 - 44*d**3/3 - 40*d**2 + 44*d + 4. Let s(v) = -12*v**3 + 5*v**2 + 9*v - 5. Let t(r) = -28*s(r) - 3*x(r). Factor t(f).
4*(f - 1)*(f + 1)*(3*f - 2)
Let h = -922 + 4628/5. Find r such that 14/5*r**2 - 2/5*r**3 - 6*r + h = 0.
1, 3
Let m(u) be the third derivative of 0 + 0*u**5 + 1/600*u**6 + 0*u**4 - u**2 + 0*u**3 + 0*u. Find z such that m(z) = 0.
0
Factor -6/7*v**4 + 3/7*v**5 + 0*v + 0*v**2 + 0 + 3/7*v**3.
3*v**3*(v - 1)**2/7
Suppose -2*b = 4*i + b - 3, -4*b = 12. Factor -5*y**4 - 4 + 3*y**4 + 4*y**2 + 2*y**2 + 2*y**3 + y - i*y.
-2*(y - 2)*(y - 1)*(y + 1)**2
Let p = -416/99 + 28/9. Let i = p - -130/99. Solve 0*t**4 + 0*t**2 + 0*t + 0 + i*t**5 + 0*t**3 = 0 for t.
0
Let v(c) be the third derivative of 2*c**2 + 4/21*c**3 + 1/210*c**5 + 0*c - 1/21*c**4 + 0. Factor v(j).
2*(j - 2)**2/7
Let l(a) be the second derivative of -2*a + 0 + 1/12*a**4 + 1/2*a**2 - 1/3*a**3. What is o in l(o) = 0?
1
Let w(l) = 15*l**3 + 21*l**2 - 9*l + 9. Let q = -20 - -11. Let n(u) = 7*u**3 + 10*u**2 - 4*u + 4. Let m(k) = q*n(k) + 4*w(k). Factor m(a).
-3*a**2*(a + 2)
Let s(j) be the first derivative of -2*j**3/45 + 12. Solve s(q) = 0.
0
Solve 1/4*h - 1/2*h**3 + 1/2*h**2 - 1/4 - 1/4*h**4 + 1/4*h**5 = 0 for h.
-1, 1
Let a = 13 + -13. Suppose 12 = -3*m + 4*j, a = 2*m + 6*j - 3*j - 9. Factor 0*h**3 + m + 2/7*h - 4/7*h**2 + 4/7*h**4 - 2/7*h**5.
-2*h*(h - 1)**3*(h + 1)/7
Suppose 0 = 3*a - 5*w - 21, 5*a = 3*w + 1 + 18. Let y(s) = s**3 + s**2 - s + 2. Let l be y(-2). Factor l + 4/7*v**3 + 0*v**4 + 0*v**a - 2/7*v - 2/7*v**5.
-2*v*(v - 1)**2*(v + 1)**2/7
Factor 5*q**5 + q**2 + 9*q**2 - 2*q**4 - 12*q**4 - 5*q + 4*q**4.
5*q*(q - 1)**3*(q + 1)
Let m(x) be the first derivative of x**6/16 - 3*x**5/40 - 3*x**4/16 + x**3/4 + 3*x**2/16 - 3*x/8 - 34. Determine a so that m(a) = 0.
-1, 1
Let d = -33/7 - -39/7. Factor -3/7*l**3 - d - 12/7*l**2 - 15/7*l.
-3*(l + 1)**2*(l + 2)/7
Suppose -3*o + g = 2*g - 3, 0 = o + 5*g - 15. Suppose 2*d + 5 = -2*i - 1, o = -4*d + i + 3. Factor 1/4*n**4 + 1/4*n**2 - 1/2*n**3 + 0*n + d.
n**2*(n - 1)**2/4
Factor -359*t + 5*t**5 - 17*t**2 - 30*t**3 - 23*t**2 + 344*t.
5*t*(t - 3)*(t + 1)**3
Let k(d) be the third derivative of 3*d**2 + 1/100*d**6 + 1/525*d**7 + 1/150*d**5 + 0 + 0*d - 2/15*d**3 - 1/20*d**4. Determine g so that k(g) = 0.
-2, -1, 1
Let q(f) be the first derivative of -f**7/1050 - f**6/300 - f**5/300 - 3*f**2 + 2. Let s(v) be the second derivative of q(v). Find b, given that s(b) = 0.
-1, 0
Let c(s) be the first derivative of s**4/24 - s**2/4 + s/3 + 1. Factor c(p).
(p - 1)**2*(p + 2)/6
Let f be ((-1)/3)/((-6)/54). Factor 0*a + 0 - 2/7*a**4 + 2/7*a**f + 0*a**2.
-2*a**3*(a - 1)/7
Let q = 172/5 - 34. Factor 0 + q*v**4 + 2/5*v - 2/5*v**2 - 2/5*v**3.
2*v*(v - 1)**2*(v + 1)/5
Let l(a) = a - 6. Let y be l(6). Let q = -37/3 + 113/9. Factor y - q*j**2 - 2/9*j**4 + 0*j - 4/9*j**3.
-2*j**2*(j + 1)**2/9
Let f(c) be the first derivative of -3*c**5/20 + c**3/2 - 4*c + 3. Let z(l) be the first derivative of f(l). Factor z(a).
-3*a*(a - 1)*(a + 1)
Let p(g) be the second derivative of 1/18*g**4 + 1/3*g**2 - g + 0 - 2/9*g**3. Factor p(v).
2*(v - 1)**2/3
Let f(u) be the third derivative of -u**7/420 + u**6/120 - 15*u**2. Factor f(m).
-m**3*(m - 2)/2
Let d(u) be the second derivative of 0*u**3 + 0 + 0*u**5 + 0*u**2 + 1/30*u**6 + 5*u + 1/42*u**7 + 0*u**4. Find f, given that d(f) = 0.
-1, 0
Let h(d) = d**3 - 7*d**2 - d + 1. Let k(c) = c - 2*c**3 + 3*c + 0*c + 8*c**2 - 2*c. Let b(l) = -4*h(l) - 3*k(l). Determine m so that b(m) = 0.
-2, -1, 1
Suppose 5*h - 4*x - 55 = 0, -5*x + 3 + 0 = 4*h. Suppose 2*l = h*l - 5. Factor -l + k**3 + 4*k - 3*k**2 + 0 - k.
(k - 1)**3
Suppose -4*z + 6 = -2*a, -4*a - 12 = -3*z - 0*a. Factor z + 2/15*u**2 - 4/15*u.
2*u*(u - 2)/15
Let u(x) be the second derivative of x**2 + 0 - 2*x - 1/21*x**3 - 1/420*x**6 + 1/84*x**4 + 1/210*x**5. Let n(m) be the first derivative of u(m). Factor n(o).
-2*(o - 1)**2*(o + 1)