 - d**7/140 + d**5/20 - d**4/8 - 2*d**3/3 + 4*d**2. Let u(p) be the first derivative of x(p). Factor u(c).
3*(c - 1)**3*(c + 1)
Suppose -5*y - r = -6 - 0, 2*y - 5*r - 24 = 0. Let a(u) = 2*u**3 - 10*u**2 + u - 2. Let i be a(5). Solve -k**2 + i*k - 2 - 5*k + y*k - 3*k = 0.
-2, -1
Let c(s) be the second derivative of -1/21*s**7 - 9/10*s**5 - 4*s - 2/3*s**3 + 1/3*s**6 + 0 + 7/6*s**4 + 0*s**2. Determine g, given that c(g) = 0.
0, 1, 2
Suppose 4*s - 32 = -5*m, -2*m - 1 = -5*s + 6. Let o be -5*((-21)/(-15) + -2). Factor 3*c**m - o*c**4 + 4*c**3 - 2*c**5 - 2*c.
-2*c*(c - 1)**2*(c + 1)**2
Let n be ((-24)/(-9))/(0 - 6/(-9)). Find q such that 0 - 7/3*q**n - 2/3*q + 5/3*q**5 + 7/3*q**2 - q**3 = 0.
-1, 0, 2/5, 1
Let h be (9/(-15))/((-2)/(-10)). Let t be (-1)/h*-1*-2. Factor -1/3*s + 0 + t*s**2 + 1/3*s**5 + 0*s**3 - 2/3*s**4.
s*(s - 1)**3*(s + 1)/3
Factor -8/5 + 22/5*x + 8/5*x**3 + 38/5*x**2.
2*(x + 1)*(x + 4)*(4*x - 1)/5
Let q(l) = -27*l**4 - 36*l**3 - 8*l**2 - 11. Let b(g) = 7*g**4 + 9*g**3 + 2*g**2 + 3. Let a(w) = -22*b(w) - 6*q(w). Factor a(i).
2*i**2*(i + 2)*(4*i + 1)
Let p(s) = -s**5 - 3*s**4 - 3*s**3 - 3*s**2 + 2*s - 2. Let z(u) = u**5 + u**4 - u**3 - u + 1. Let h(d) = 2*p(d) + 4*z(d). Factor h(l).
2*l**2*(l - 3)*(l + 1)**2
Let g(i) = 1. Let k(y) = 32*y**2 - 8*y**3 - 7*y**3 - 5 - 10*y + 0*y - 3*y**3. Let v(c) = g(c) + k(c). Factor v(m).
-2*(m - 1)**2*(9*m + 2)
Let o be (7/(-2))/(1/(-4)). Suppose -5*m + o - 4 = 0. Factor 4/5*n**2 + m*n**3 + 0*n + 0 + 6/5*n**4.
2*n**2*(n + 1)*(3*n + 2)/5
Let t(j) be the third derivative of 0*j - j**4 + 1/70*j**7 - 11/80*j**6 + 21/40*j**5 + j**3 - j**2 + 0. What is u in t(u) = 0?
1/2, 1, 2
Let m(r) = -r**3 - 3*r**2 + 2*r - 5. Let w be m(-4). Let f(s) be the first derivative of -3/4*s**2 - w*s - 2 + 1/2*s**3. Let f(i) = 0. What is i?
-1, 2
Let v(n) be the first derivative of 3*n**4/4 - 38*n**3/3 + 57*n**2/2 - 22*n + 34. Let v(f) = 0. What is f?
2/3, 1, 11
Suppose 7*g = 4*g - 6. Let c(f) = -6*f**3 - 2*f**2 + 14*f + 14. Let n(k) = 7*k**3 + k**2 - 13*k - 13. Let o(w) = g*n(w) - 3*c(w). Factor o(q).
4*(q - 2)*(q + 1)*(q + 2)
Factor 20/9*r**3 + 0*r + 0 - 8/9*r**4 - 8/9*r**2.
-4*r**2*(r - 2)*(2*r - 1)/9
Let x(w) be the third derivative of -7*w**6/40 + 4*w**5/5 - 11*w**4/8 + w**3 + 15*w**2. Solve x(a) = 0 for a.
2/7, 1
Let v(x) be the first derivative of 4*x**5/5 - x**4 - 4*x**3 + 10*x**2 - 8*x - 21. Factor v(j).
4*(j - 1)**3*(j + 2)
Let a(c) be the third derivative of 2*c**7/105 - c**5/3 + 8*c**3/3 + 2*c**2. Let a(m) = 0. What is m?
-2, -1, 1, 2
Let i = 52 - 48. Factor 8/3*u**2 + 0 + 4*u**3 - 6*u**i + 0*u + 5/3*u**5.
u**2*(u - 2)**2*(5*u + 2)/3
Let k(t) = -t**3 - t**2 - t + 1. Let h(a) = a**4 - 6*a**3 - 7*a**2 - 6*a + 6. Let n(d) = -h(d) + 6*k(d). Let n(s) = 0. What is s?
-1, 0, 1
Solve 0 - n - 1/2*n**3 - 3/2*n**2 = 0.
-2, -1, 0
Let n = 15 - 10. Factor 2*x**3 + 3*x**3 - 7*x**4 + x**2 - 2*x**2 + 3*x**n.
x**2*(x - 1)**2*(3*x - 1)
Let n(z) = z + 7. Let t be n(-5). Find m, given that 5*m - 5*m - 2*m**3 - 4*m + 6*m**t = 0.
0, 1, 2
Suppose -10 = 2*l, -4*y - 2*l - l = 7. Factor 2*x - x**y - x**2 - 2*x**3 + 1 + 0 + 1.
-2*(x - 1)*(x + 1)**2
Factor 0 - 3/8*u**2 + 3/4*u.
-3*u*(u - 2)/8
Let c = -5 - -5. Suppose c = -3*p + p. Factor 10/7*g**2 - 8/7*g**3 + p - 2/7*g.
-2*g*(g - 1)*(4*g - 1)/7
Suppose w - 1 = -5*x - 5, 3*x + 12 = w. Let a be -1 + 4 + w/(-2). Factor 8/9*k**4 - 2/9*k - 2/9*k**5 + 8/9*k**2 + a - 4/3*k**3.
-2*k*(k - 1)**4/9
Let v(b) = -b**2 + b + 1. Let r(y) be the first derivative of -2*y**3 + 4*y**2 + 7*y - 1. Let i(g) = 2*r(g) - 14*v(g). Factor i(z).
2*z*(z + 1)
Let u = -7/40 + 3/8. Factor 0*z**2 + 3/5*z - u*z**3 - 2/5.
-(z - 1)**2*(z + 2)/5
Let g(d) be the second derivative of 3/20*d**5 + 8/3*d**3 + 3*d - 13/12*d**4 + 0 - 2*d**2. Find p, given that g(p) = 0.
1/3, 2
Let s(b) = 3*b - 1. Let c be s(1). Determine m so that 15*m**2 - 7*m**c - 3*m**2 - 3*m**2 + m**3 + m = 0.
-1, 0
Let v(i) = -i**3 + i**2. Let x(b) = 2*b**3 + 6*b**2 - 4*b - 4. Let l(p) = 2*v(p) - x(p). Suppose l(h) = 0. What is h?
-1, 1
Let f(d) = -2*d**2 + 4*d. Let l(r) = 3*r**2 - 6*r. Suppose 2*t - 1 = 9. Let y = t + -12. Let j(b) = y*f(b) - 5*l(b). Factor j(c).
-c*(c - 2)
Let k(r) = -r + 3 - 2 - r**3 + 2*r**3 - r**2. Let m(u) = 3*u**4 + 12*u**3 - 15*u**2 - 12*u + 12. Let o(b) = 12*k(b) - m(b). Let o(g) = 0. What is g?
-1, 0, 1
Let r(k) be the second derivative of k**5/25 - 7*k. Factor r(u).
4*u**3/5
Let g(h) be the second derivative of h**7/126 + h**6/15 + h**5/5 + 5*h**4/18 + h**3/6 + 2*h. Suppose g(c) = 0. Calculate c.
-3, -1, 0
Let v(p) = -7*p**3 + 8*p**2 + 7*p + 4. Let j(l) = l**2 + 1 + 6*l + 0 + 0*l**3 - 5*l - l**3. Let s(t) = -6*j(t) + v(t). Suppose s(n) = 0. What is n?
-1, 1, 2
Factor 378*q + 7*q**3 - 5*q**3 + 11*q + 211*q - 60*q**2 - 2000.
2*(q - 10)**3
Suppose -2*v + 3 = -3. Let r be (-12)/45 - (-2)/v. Factor 2/5 - r*x**2 + 0*x.
-2*(x - 1)*(x + 1)/5
Let g(o) be the third derivative of -o**6/30 + o**5/3 + 20*o**2. Determine d, given that g(d) = 0.
0, 5
Let a(z) = -z**5 - z**4 + z**2 - z. Let q(h) = 6*h**5 + 6*h**4 + 2*h**5 - 6*h**2 - 2*h**3 + 0*h**5 + 6*h. Let p = -1 + 7. Let l(g) = p*a(g) + q(g). Factor l(j).
2*j**3*(j - 1)*(j + 1)
Let o(i) = -i**2 + 3*i. Let x(s) = -s**2 + 5*s. Let f(p) = -7*o(p) + 4*x(p). Let b be f(1). Solve -k**2 - k + 0*k**b + 2*k = 0.
0, 1
Determine o so that -94/11*o**2 - 16/11 + 18/11*o**3 + 92/11*o = 0.
2/9, 1, 4
Let w(m) be the second derivative of m**7/840 + m**6/240 + m**5/240 + 3*m**2/2 - 2*m. Let v(q) be the first derivative of w(q). Factor v(t).
t**2*(t + 1)**2/4
Let m(z) be the second derivative of -z**6/240 - z**5/20 - z**4/4 - z**3/6 - 5*z. Let x(k) be the second derivative of m(k). Factor x(i).
-3*(i + 2)**2/2
Let k = -15 + 15. Let o(z) be the second derivative of -1/9*z**4 - z + k*z**2 + 0 + 1/18*z**3 + 1/15*z**5. Factor o(u).
u*(2*u - 1)**2/3
Let p be (-55)/(-22)*2/10. Let -1/2*s**4 + p + 0*s**2 - s + s**3 = 0. Calculate s.
-1, 1
Suppose 0 = -5*h + 3*h - 4*s - 6, -2*h + 4*s + 26 = 0. Factor v**4 - h*v**4 - 8*v + v**4 - 4*v**2 + 8*v**3 + 7*v**4.
4*v*(v - 1)*(v + 1)*(v + 2)
Factor -2*h**2 + 2*h**4 + 3*h**2 + 2*h**5 + 0*h**4 - 5*h**4.
h**2*(h - 1)**2*(2*h + 1)
Let c be 1 + -3 + 4 + 2. Let g be (-38)/(-10) + c/20. Factor 10*j - 13*j**2 + 7/2*j**3 + g.
(j - 2)**2*(7*j + 2)/2
Suppose -4*l - 15 = l. Let w be ((-2)/l)/(2/9). What is c in 2*c**2 + 3*c**5 + 0*c**w + 2*c**3 - 2*c**4 - 5*c**5 = 0?
-1, 0, 1
Let q(a) be the third derivative of 0*a**4 + 0*a - 1/75*a**5 - 4*a**2 + 0*a**6 + 1/15*a**3 + 0 + 1/525*a**7. Suppose q(z) = 0. What is z?
-1, 1
Let f(v) be the first derivative of -v**6/11 + 32*v**5/55 - 12*v**4/11 + 16*v**2/11 + 19. Factor f(n).
-2*n*(n - 2)**3*(3*n + 2)/11
Let k(z) be the first derivative of -z**3 + 7 - 9 + 2*z**3. Factor k(d).
3*d**2
Factor 0*i**2 - 6/5*i**3 + 0 + 9/5*i**4 + 0*i - 3/5*i**5.
-3*i**3*(i - 2)*(i - 1)/5
Let y(x) be the first derivative of -x**4/2 + 8*x**3/3 + 11*x**2 + 12*x - 7. Factor y(o).
-2*(o - 6)*(o + 1)**2
Let k be 4*(30/8)/(-5). Let g be (-1)/(k/(-4) + -1). Factor -o + g*o - 2 + 0*o**2 - o**2.
-(o - 2)*(o - 1)
Let i(p) be the first derivative of p**6/15 - 2*p**5/25 - p**4/5 + 41. What is b in i(b) = 0?
-1, 0, 2
Suppose 2*n - 5*p = 8, p - 12 = -5*n + 8. Let s = 6 - n. Let 4*g + 0 + g**s - 2 + 6 = 0. What is g?
-2
Let j(q) = q + 1. Let w be j(2). Let t(v) = -5*v**4 + v**3 + v**2 + 3. Let y(m) = 9*m**4 - 3*m**3 - m**2 - 5. Let k(r) = w*y(r) + 5*t(r). Solve k(h) = 0 for h.
0, 1
Suppose w = 6*q - 2*q + 16, 32 = 2*w + 3*q. Let g be ((-2)/12)/((-2)/w). Suppose -g - 2*k - 2/3*k**2 = 0. Calculate k.
-2, -1
Let m(x) be the second derivative of x**5/120 + x**4/72 - x**3/18 + 21*x. Factor m(j).
j*(j - 1)*(j + 2)/6
Let r(k) be the third derivative of -k**5/390 + k**4/156 - 3*k**2. Factor r(v).
-2*v*(v - 1)/13
Let m = -1637 - -14735/9. Factor 1/3*n - 1/9 - 1/9*n**5 - m*n**3 + 1/3*n**4 - 2/9*n**2.
-(n - 1)**4*(n + 1)/9
Let v(z) be the second derivative of -z**5/90 + 2*z**4/27 - z**3/9 - 7*z. Factor v(w).
-2*w*(w - 3)*(w - 1)/9
Solve -96/5*v - 48*v**2 + 1216/5*v**3 + 32/5 - 1542/5*v**4 + 126*v**5 = 0.
-2/7, 2/5, 2/3, 1
Let l(y) be the second derivative of y**7/84 - y**6/30 - y**5/20 + y**4/6 + y**3/12 - y**2/2 - 8*y. Solve l(k) = 0 for k.
-1, 1, 2
Let y(r) = -95*r**5 + 180*r**4 - 35*r**3 - 40*r**2