 Let p(g) be the second derivative of -3/8*g**3 - 3/16*g**4 - 3/8*g**2 - 3/80*g**b + 2*g + 0. Factor p(u).
-3*(u + 1)**3/4
Let u(z) be the second derivative of -z**6/120 + z**5/40 + 7*z**4/48 + z**3/6 - 54*z. Factor u(k).
-k*(k - 4)*(k + 1)**2/4
Let r(f) be the third derivative of f**7/210 + f**6/60 - f**4/12 - f**3/6 + 5*f**2 - 6*f. What is g in r(g) = 0?
-1, 1
Suppose -5*y + 19 = -6. Let x = -3 + y. Factor -3*w - w**2 + 0*w**x + 2*w.
-w*(w + 1)
Let g = -7635 - -587910/77. Let m = 1/11 + g. Factor m*r**3 + 0*r**2 - 2/7*r**4 + 0*r + 0.
-2*r**3*(r - 1)/7
Let u(h) = -2*h - 2. Let j(o) = o**2 - 3*o - 5. Let t = -7 - -12. Let y(v) = t*u(v) - 2*j(v). Factor y(g).
-2*g*(g + 2)
Suppose -3*w + 3 = -5*r, -5*w = -5*r - w - 4. Let y(u) be the third derivative of r*u + 0 + 0*u**5 + 1/120*u**6 + 2*u**2 - 1/24*u**4 + 0*u**3. Factor y(a).
a*(a - 1)*(a + 1)
Let d(n) be the third derivative of -1/20*n**5 + 0 + 1/70*n**7 - n**2 - 1/8*n**4 + 0*n**3 + 1/40*n**6 + 0*n. Factor d(v).
3*v*(v - 1)*(v + 1)**2
Let v(q) = -3*q - 1. Let n be v(-2). Find f, given that 19*f**4 + 34*f**2 + 83*f**3 - 8 - 135*f**4 + 8*f**5 - 5*f**n + 32*f**5 - 28*f = 0.
-2/5, -2/7, 1, 2
Let w(p) be the third derivative of p**6/30 - 3*p**5/5 + 4*p**4 - 40*p**3/3 - 25*p**2. Solve w(s) = 0.
2, 5
Suppose 43*o = 38*o + 50. Let l be (-8)/(-4) - 16/o. Factor -1/5*t**3 - l + 1/5*t + 2/5*t**2.
-(t - 2)*(t - 1)*(t + 1)/5
Let a(k) be the first derivative of -3*k**4/8 + k**3/2 + 3*k**2/2 + 4. Solve a(n) = 0 for n.
-1, 0, 2
Let u(z) = -3*z**3 - 15*z**2 + 25*z - 7. Let s(h) = h**3 + 8*h**2 - 13*h + 4. Let q(i) = 11*s(i) + 6*u(i). Solve q(a) = 0 for a.
-1, -2/7, 1
Suppose 5*p + 3 - 13 = 0. Suppose p*q - 14 = -4. Determine a so that 0*a + a**3 - 7/2*a**q + 0 + 0*a**2 - 5/2*a**4 = 0.
-1, 0, 2/7
Suppose 4*z - 10 = b, -z - 2*b = 2*z - 13. Determine j, given that -1/3*j + 0 - 2*j**z - 1/3*j**5 - 4/3*j**2 - 4/3*j**4 = 0.
-1, 0
Let g(h) be the second derivative of h**4/6 - 10*h**3/3 + 25*h**2 - 11*h. Factor g(d).
2*(d - 5)**2
Let n(o) be the second derivative of 3*o**5/10 + 3*o**4/4 - 3*o**2/2 + 10*o. Factor n(z).
3*(z + 1)**2*(2*z - 1)
Let v(m) be the first derivative of -m**5/5 - 3*m**4/4 - m**3 - m**2/2 + 6. Determine k, given that v(k) = 0.
-1, 0
Suppose 0 = z - t + 1, 3*z + 0*t = 5*t - 9. Let q(w) be the first derivative of 1/2*w**4 - 4/3*w**3 + z + 0*w**2 + 0*w. Factor q(n).
2*n**2*(n - 2)
What is v in 0*v**2 + 2/7*v + 0*v**4 + 2/7*v**5 - 4/7*v**3 + 0 = 0?
-1, 0, 1
Let l(r) be the second derivative of -r**7/42 + r**5/20 - 4*r. Find q such that l(q) = 0.
-1, 0, 1
Let w(f) be the second derivative of -1/30*f**6 + 0 - 1/6*f**3 + 1/6*f**4 + 1/10*f**5 - 2*f - 1/42*f**7 - 1/2*f**2. Find d, given that w(d) = 0.
-1, 1
Let j(c) be the second derivative of 0*c**2 + 0 + 2*c + 0*c**3 + 1/20*c**5 - 1/60*c**6 + 0*c**4 - 1/84*c**7. Find u, given that j(u) = 0.
-2, 0, 1
Let f(c) be the first derivative of c**4/6 - c**3 + 2*c**2 - 2*c + 3. Let t(i) be the first derivative of f(i). Suppose t(d) = 0. Calculate d.
1, 2
Suppose -6*z + z + 20 = 0. Let -5*w + w**z + 4*w - w**3 + 2*w + 4*w**2 - 5*w**2 = 0. What is w?
-1, 0, 1
Let p = 7 - 4. Let y(h) be the second derivative of 1/20*h**5 + 0 + 0*h**2 - 1/6*h**4 - 2*h + 1/6*h**p. Suppose y(j) = 0. What is j?
0, 1
Let o(s) be the first derivative of -6 + 0*s - 1/3*s**2 + 4/15*s**5 + 1/9*s**6 + 0*s**4 - 4/9*s**3. Factor o(p).
2*p*(p - 1)*(p + 1)**3/3
Let f be (-4)/(-8) + 0 - 1/(-6). Factor 2/3*u**2 + f*u + 0.
2*u*(u + 1)/3
Let u be -36 + 38 - 6/4. Let -1/6*w**2 - 1/2*w**4 - u*w**3 + 0*w - 1/6*w**5 + 0 = 0. What is w?
-1, 0
Let m be -1 + 0 - (-1 - 0). Let f be 6/(-18)*(0 - m). Factor -16*b**3 + 0 - 30*b**4 - 8/3*b**2 + f*b - 50/3*b**5.
-2*b**2*(b + 1)*(5*b + 2)**2/3
Factor 550/7*n + 16/7*n**4 + 60*n**2 + 136/7*n**3 + 250/7.
2*(n + 1)*(2*n + 5)**3/7
Find y such that -3/4*y**3 - 3/4*y + 0 + 3/2*y**2 = 0.
0, 1
Let h(x) be the third derivative of -x**8/2016 - x**7/630 + x**5/180 + x**4/144 + 3*x**2. Suppose h(k) = 0. What is k?
-1, 0, 1
Let j(b) be the second derivative of b**4/54 + b**3/9 + 29*b - 2. Factor j(v).
2*v*(v + 3)/9
Let n = -21 + 25. Let 0*q + 0*q**4 + 0*q + n*q**3 + 2*q**4 = 0. Calculate q.
-2, 0
Let h(f) be the third derivative of -4*f**6/135 + 2*f**5/27 - 2*f**4/27 + f**3/27 - f**2. Factor h(b).
-2*(2*b - 1)**2*(4*b - 1)/9
Let 4*a**3 - a + 6*a - 3*a - 5*a**2 - a**4 + 0*a**2 = 0. What is a?
0, 1, 2
Let r(u) = -u**2 + 15*u + 36. Let a be r(17). Factor 3*w**a - 18/5 - 39/5*w.
3*(w - 3)*(5*w + 2)/5
Let v(u) be the first derivative of 0*u - 1/10*u**6 + 0*u**4 - 6/25*u**5 + 3/10*u**2 - 4 + 2/5*u**3. Factor v(x).
-3*x*(x - 1)*(x + 1)**3/5
Let l(d) be the second derivative of d**6/255 + d**5/85 - d**4/102 - 2*d**3/51 - 58*d. Factor l(n).
2*n*(n - 1)*(n + 1)*(n + 2)/17
Solve -1/2*o + 1/2*o**2 - 1 = 0 for o.
-1, 2
Let g = -11 - -13. Factor -7*k**2 + 74 - g*k + 7*k**4 + 2*k**3 - 74.
k*(k - 1)*(k + 1)*(7*k + 2)
Determine u, given that 2/5*u**3 - 2/5 + 6/5*u - 6/5*u**2 = 0.
1
Let u(p) = -2*p + 8. Let y be u(4). Factor 0*z**2 + 0*z + y + 0*z**4 - 1/5*z**3 + 1/5*z**5.
z**3*(z - 1)*(z + 1)/5
Let s(p) = p**2 + p. Let m(v) = -9*v**2 + 21*v + 30. Let z(f) = m(f) + 4*s(f). Find l such that z(l) = 0.
-1, 6
Let s = 16/21 + -3/7. Let k(t) be the first derivative of 0*t + t**4 - 8/15*t**5 - 8/9*t**3 - 2 + 1/9*t**6 + s*t**2. Factor k(q).
2*q*(q - 1)**4/3
Let a(h) be the second derivative of h**4 - 2*h**3/3 + 5*h. What is m in a(m) = 0?
0, 1/3
Let y(d) be the second derivative of -d**5/100 - d**4/60 - 10*d. Solve y(z) = 0 for z.
-1, 0
Suppose 4*c + 8 = -4*d, -4 = 2*d + 5*c + 6. Let g = 29/13 + -103/52. Let -g*z**2 + d - 1/2*z = 0. What is z?
-2, 0
Let c be -2*((0 - 2) + 0). Suppose 2*b - 19 = -5*i - 0*b, 0 = -4*i + 3*b + 6. Factor -1/3*y**c - 1/3*y**i + 0 + 0*y**2 + 0*y.
-y**3*(y + 1)/3
Let l = 2/265 - -16954/795. Factor -26/3*r - 10/3*r**5 + 4/3 - 76/3*r**3 + 44/3*r**4 + l*r**2.
-2*(r - 1)**4*(5*r - 2)/3
Let q(x) be the first derivative of 1/36*x**4 + 2/45*x**5 + 0*x - 1/60*x**6 + 1/2*x**2 + 3 - 2/9*x**3. Let u(o) be the second derivative of q(o). Factor u(i).
-2*(i - 1)**2*(3*i + 2)/3
Let t(g) be the second derivative of -g**6/1260 + g**5/105 - g**4/21 + 5*g**3/6 + 5*g. Let f(o) be the second derivative of t(o). Suppose f(x) = 0. What is x?
2
Let u be (3/(-4))/((-2)/8). Suppose 10 = u*y + 1. Factor -y*l**2 + l + 0*l**2 + 8*l.
-3*l*(l - 3)
Let h(f) be the second derivative of -2*f**7/35 + 9*f**6/50 - 9*f**5/50 + f**4/20 - 9*f. Determine b so that h(b) = 0.
0, 1/4, 1
Let d(z) = -2*z**2 + 3 + z + 0*z - 5 + 5. Let q(x) = 2*x**2. Let k(t) = 3*t**2 + 1. Let a(m) = 2*k(m) - 4*q(m). Let p(r) = -5*a(r) + 4*d(r). Factor p(o).
2*(o + 1)**2
Let v be 32/14*2/8. Let k(c) be the first derivative of -v*c - 1 - 3/7*c**2 - 2/21*c**3. Factor k(m).
-2*(m + 1)*(m + 2)/7
Let z be (14/(-4))/((-5)/20). Let m be (-4)/z + (-12)/(-42). Determine n, given that 0*n + m + 2/3*n**2 = 0.
0
Let o(u) be the second derivative of -u**7/112 - u**6/16 - 3*u**5/16 - 5*u**4/16 - 5*u**3/16 - 3*u**2/16 - 11*u. Determine k, given that o(k) = 0.
-1
Suppose 0 = 3*h + 32 - 44. Let t(k) be the second derivative of 0 - 1/48*k**h - 1/24*k**3 + 1/4*k**2 + 2*k. Solve t(l) = 0.
-2, 1
Let l be 1*((-152)/(-4))/2. Let p be (-3)/18 + l/42. Factor p*b**5 - 2/7 + 4/7*b**2 - 4/7*b**3 - 2/7*b**4 + 2/7*b.
2*(b - 1)**3*(b + 1)**2/7
Let p(r) be the first derivative of 3*r**4/4 - 6*r**3 + 14. Factor p(j).
3*j**2*(j - 6)
Suppose -5*f - 4 = -19. Suppose -10 = f*l - 25. Factor 3*c**l - 2*c**4 - 2*c**4 - 2*c - c**5 + 4*c**2.
2*c*(c - 1)**3*(c + 1)
Let z(f) be the first derivative of 2*f**3/3 - 18*f**2 + 162*f + 19. Let z(y) = 0. Calculate y.
9
Let j(q) be the second derivative of 0 + 0*q**4 + 0*q**3 - q + 3/2*q**2 + 1/60*q**5. Let d(z) be the first derivative of j(z). Factor d(n).
n**2
Solve -3*t**3 + 15*t**2 - 43 - 20*t**2 - 149 - 144*t - 31*t**2 = 0.
-4
Let g(y) be the second derivative of y**6/10 - 9*y**5/20 - y**4/2 + 6*y**3 - 12*y**2 - 31*y. Factor g(f).
3*(f - 2)**2*(f - 1)*(f + 2)
Let v(m) be the first derivative of -1/3*m**6 - 2/3*m**3 + 2/5*m**5 + 0*m**2 + 2 + 1/2*m**4 + 0*m. Factor v(h).
-2*h**2*(h - 1)**2*(h + 1)
Let q(y) be the third derivative of -y**5/18 - y**4/18 + y**2. Factor q(m).
-2*m*(5*m + 2)/3
Let k = -25 + -17. Let t be (-1)/3 - 38/k. Fact