et u be 10/3*(-3)/(-15). Determine k so that 0 - 2/9*k**5 + 4/9*k - 2/3*k**2 - 2/9*k**3 + u*k**4 = 0.
-1, 0, 1, 2
Let w(n) be the first derivative of 2*n**5/65 - 2*n**3/13 + 2*n**2/13 + 5. Factor w(g).
2*g*(g - 1)**2*(g + 2)/13
Let s(u) be the first derivative of -u**6/180 - u**5/60 + u**3 - 3. Let m(n) be the third derivative of s(n). Factor m(f).
-2*f*(f + 1)
Let o(c) = 9*c**2 + 7*c - 7. Let a(k) be the third derivative of -2/3*k**3 + 0 + 1/12*k**5 - k**2 + 1/6*k**4 + 0*k. Let y(l) = -7*a(l) + 4*o(l). Factor y(f).
f**2
Let d(f) = f**4 + 5*f**3 + 2*f**2 - 4*f. Let w(p) = 5*p**4 + 21*p**3 + 9*p**2 - 16*p. Let u(l) = 9*d(l) - 2*w(l). Factor u(t).
-t*(t - 2)**2*(t + 1)
Let d(o) be the third derivative of 1/18*o**4 + 2*o**2 + 0 - 2/9*o**3 + 0*o - 1/180*o**5. Let d(b) = 0. Calculate b.
2
Let u(p) be the first derivative of -5*p**4 - 16*p**3 - 8*p**2 - 5. What is i in u(i) = 0?
-2, -2/5, 0
Let b(i) = 5*i**4 + i**3 - 13*i**2 - 9*i - 3. Let k(o) = -o**4 - o**3 + o**2 + o + 1. Let g(w) = -2*b(w) - 6*k(w). Solve g(d) = 0.
-1, 0, 3
Let u be (-2 + 4)*83/10. Let f = 17 - u. Factor -1/5*n**3 + f*n**4 + 1/5*n + 0 - 2/5*n**2.
n*(n - 1)*(n + 1)*(2*n - 1)/5
Let g(r) be the third derivative of -7/60*r**5 + 0*r + 0 + 0*r**3 + 1/12*r**4 - r**2. Factor g(m).
-m*(7*m - 2)
Let x(r) be the second derivative of -r**7/11340 - r**6/1620 - r**5/540 - r**4/12 + 2*r. Let l(i) be the third derivative of x(i). Solve l(o) = 0.
-1
Factor -2*z - 2/3*z**3 + 2/3*z**4 + 0 - 10/3*z**2.
2*z*(z - 3)*(z + 1)**2/3
Let d(l) be the first derivative of 5*l**5/4 - 45*l**4/8 + 121*l**3/12 - 9*l**2 + 4*l - 2. Factor d(h).
(h - 1)**2*(5*h - 4)**2/4
Let t(q) be the first derivative of -1/10*q**2 + 3/10*q**4 - 2/5*q + 4 + 7/15*q**3. Factor t(j).
(j + 1)*(2*j - 1)*(3*j + 2)/5
Suppose -5*k + 3*c = -3, 0 = k + 7*c - 2*c + 5. Let 2*r**2 - 56*r**3 + 0 + 55*r**3 + k = 0. Calculate r.
0, 2
Factor 38/5*y**2 + 0 + 4/5*y + 34/5*y**3.
2*y*(y + 1)*(17*y + 2)/5
Let g be (-6)/9 + 8/3. Factor -5*k**4 + 7*k**4 - g*k**2 - 4*k + 2*k**3 + 2*k**3 + 0*k**3.
2*k*(k - 1)*(k + 1)*(k + 2)
Suppose 4*c = -14 + 34. Let o = c + -5. Find p such that -4 + 6*p + o*p**3 - 4*p**3 + p**3 + p**3 = 0.
-2, 1
Let j be (-6)/12*3/(-18). Let a(q) be the second derivative of -j*q**4 + 0*q**2 + 0 + 0*q**3 + 2*q. Factor a(h).
-h**2
Let a(x) be the second derivative of x**7/21 + x**6/15 - 3*x**5/10 - x**4/6 + 2*x**3/3 - 2*x. Factor a(q).
2*q*(q - 1)**2*(q + 1)*(q + 2)
Suppose 0*t - 4/5 + 3*t**3 + 19/5*t**2 = 0. What is t?
-1, -2/3, 2/5
Suppose 2*i - 2*n - 3 = -3*n, 5*i = -4*n + 6. Let 1 - m**2 + m - i + m + 0*m = 0. What is m?
1
Let s = 170 - 166. Let q(m) be the third derivative of 0*m**3 + 0*m**5 - 1/90*m**6 + 0*m**s + 1/315*m**7 + 0 + 0*m + 2*m**2. Factor q(w).
2*w**3*(w - 2)/3
Let l(j) be the first derivative of -4*j**5/5 + 4*j**3 - 4*j**2 - 34. Find v such that l(v) = 0.
-2, 0, 1
Let l(m) = -m**5 - m**4 - m**2. Let j(o) = 10*o**5 + 10*o**4 - 22*o**3 - 38*o**2 - 22*o - 4. Let v(f) = -j(f) - 2*l(f). Suppose v(x) = 0. What is x?
-1, -1/2, 2
Let a(c) be the third derivative of -c**6/240 - 7*c**5/120 - 11*c**4/48 - 5*c**3/12 - 5*c**2 + 1. Solve a(d) = 0.
-5, -1
Let r(u) be the first derivative of u**3/4 - 9*u**2/4 + 27*u/4 + 6. What is v in r(v) = 0?
3
Let h(i) be the third derivative of i**5/15 - i**4/3 + 4*i**2. Factor h(w).
4*w*(w - 2)
Let v(y) = y + 2. Let a be v(2). Suppose 3*q + 16 = 5*f, -q + 4*f = -0*f + 17. Suppose -2*s**a + 2*s**q - 2*s**5 - 2*s + 2*s + 0*s + 2*s**2 = 0. What is s?
-1, 0, 1
Let a = 2 - 5/3. Let l = -50 + 151/3. Factor -1/3*s + a*s**3 - 1/3 + l*s**2.
(s - 1)*(s + 1)**2/3
Let s be 3 - (93/33 - 0). Determine u, given that 2/11*u**3 + 0 - 4/11*u + s*u**2 = 0.
-2, 0, 1
Let a(z) = 3*z**2 + 8*z - 1. Let u be a(-10). Let o = u - 150. Let -2 + 28*m - 25*m**4 - 69*m**2 - 3 + 1 + m**3 + o*m**3 = 0. What is m?
2/5, 1
Let l(k) be the third derivative of -k**5/40 + 3*k**4/4 - 11*k**3/4 - 2*k**2 + 1. Factor l(f).
-3*(f - 11)*(f - 1)/2
Suppose 5*r - 24 = -3*t, 0*t - 12 = -2*t - 2*r. Factor -2*c**2 - 2 - 3*c + 2*c**2 + 2*c**t + c + 2*c**2.
2*(c - 1)*(c + 1)**2
Let y = 357 - 1774/5. Let w(f) be the first derivative of -2 + f**2 + 1/2*f**6 + 0*f + y*f**5 + 15/4*f**4 + 3*f**3. What is q in w(q) = 0?
-1, -2/3, 0
Suppose 5*z**4 - 5/4*z**5 - 5*z**2 + 0 + 5*z - 15/4*z**3 = 0. Calculate z.
-1, 0, 1, 2
Suppose 1 = 2*q + 4*c + 5, -5*q = c - 8. Let h = 8/59 + 46/531. Factor 2/9*z**q - 4/9 - h*z.
2*(z - 2)*(z + 1)/9
Let b = -222 - -1118/5. Let c = -5 + 7. What is g in b + 2/5*g**3 + 2*g**c + 16/5*g = 0?
-2, -1
Find d such that 0*d + 0 - 6/7*d**2 + 3/7*d**4 - 3/7*d**3 = 0.
-1, 0, 2
Suppose 0*v**2 - 5*v**2 + 53 + 25*v - 53 = 0. Calculate v.
0, 5
Let o(q) be the first derivative of 8*q**3/3 - 5*q**2 + 2*q - 6. Suppose o(x) = 0. Calculate x.
1/4, 1
Let g(i) = -20*i**2 + 66*i. Let q(j) = 4*j**2 - 13*j. Suppose -2*r - 2 = -4*w, 2*w + 5*r = 4*w + 19. Let c(s) = w*g(s) + 14*q(s). Factor c(m).
-4*m*(m - 4)
Factor 0 + 0*f + 2/15*f**3 - 4/15*f**2.
2*f**2*(f - 2)/15
Let r = -4442/13 + 342. Solve 0*i + r*i**2 + 6/13*i**4 + 0 - 14/13*i**3 = 0 for i.
0, 1/3, 2
Suppose -8*n = 6*n - 98. Let u(m) be the third derivative of 0*m**6 + 1/1344*m**8 - 1/420*m**n - m**2 + 0*m**3 - 1/96*m**4 + 1/120*m**5 + 0 + 0*m. Factor u(a).
a*(a - 1)**3*(a + 1)/4
Let 1/11 + 1/11*v**2 + 2/11*v = 0. Calculate v.
-1
Let c(a) be the first derivative of 2*a**5/35 + a**4/7 + 6. Suppose c(d) = 0. Calculate d.
-2, 0
Let l be 1*(-5)/25*2/(-3). Let b(v) be the first derivative of l*v**3 - 1/5*v**2 + 0*v - 2. Factor b(k).
2*k*(k - 1)/5
Let n(b) be the third derivative of -b**5/100 + 4*b**2. Factor n(v).
-3*v**2/5
Let i(m) be the third derivative of m**8/1400 + m**7/1050 - m**6/900 - m**3/3 - 2*m**2. Let j(r) be the first derivative of i(r). Suppose j(s) = 0. Calculate s.
-1, 0, 1/3
Let m = 19 - 30. Let q = -9 - m. Determine j so that -1/2*j**q - 6*j + 2 + 15/2*j**3 = 0.
-1, 2/5, 2/3
Suppose -6 = -3*p + 24. Let a be 12/(-20)*p/(-8). Solve -1/2*f + 1/4 - a*f**2 = 0 for f.
-1, 1/3
Let j(k) = k**2 - 23*k + 62. Let d be j(20). Factor -3/4*b**3 - 9/4*b + 9/4*b**d + 3/4.
-3*(b - 1)**3/4
Let j(s) be the third derivative of -s**6/30 + s**5/15 + s**4/6 - 2*s**3/3 - 3*s**2. Factor j(b).
-4*(b - 1)**2*(b + 1)
Suppose -3 = -u + l, 4*l + 21 = 5*u + 7. Factor -5*t**u + 13*t**3 - 10*t**2 + 6*t - 34*t**3.
-3*t*(t + 1)*(7*t - 2)
Suppose 3*k = 3*q + 2*q + 31, -15 = 3*q. Let h(i) = -4*i + 59. Let g be h(14). Determine s, given that -1 - 3/2*s**k - 7/2*s**g + 5/2*s**4 + 7/2*s = 0.
-1, 2/5, 1
Suppose -5 = -10*t - 5. Let r(v) be the second derivative of t*v**2 + v - 1/6*v**4 + 2/27*v**3 + 0. Solve r(m) = 0 for m.
0, 2/9
Let u = 12 - 10. Let m be (-4)/(-10) + 13/5. Factor 0*q + 2*q**4 + 0*q + m*q**3 + 2*q**u - 7*q**3.
2*q**2*(q - 1)**2
Suppose 0 + 0*j - 2/13*j**2 + 2/13*j**4 + 2/13*j**5 - 2/13*j**3 = 0. Calculate j.
-1, 0, 1
Let f(q) be the first derivative of 0*q + 1/2*q**4 + 0*q**3 - q**2 - 1. Factor f(b).
2*b*(b - 1)*(b + 1)
Let v = -66 - -71. Let o(u) be the second derivative of 1/50*u**v - u + 0*u**2 - 1/15*u**4 + 0 + 1/15*u**3. Solve o(w) = 0.
0, 1
Let s be (-6)/4*56/(-6). Suppose s = 2*u - 2*b + 4, 5*u - b = 13. Suppose 0 + 2/3*y**5 + 10/3*y**3 + 0*y - 8/3*y**4 - 4/3*y**u = 0. What is y?
0, 1, 2
Let z = -11 - -9. Let a be (-5)/25*35/z. Determine j, given that -j - 5/2*j**3 + 0 - a*j**2 = 0.
-1, -2/5, 0
Find c, given that 0 - 2/17*c + 4/17*c**4 + 0*c**3 - 4/17*c**2 + 2/17*c**5 = 0.
-1, 0, 1
Let y(b) be the first derivative of b**6/180 + b**5/120 - b**4/72 - b**3/36 + 2*b + 3. Let g(t) be the first derivative of y(t). Factor g(v).
v*(v - 1)*(v + 1)**2/6
Let q(l) be the third derivative of l**7/8820 + l**6/840 + l**5/210 - l**4/8 + 3*l**2. Let v(x) be the second derivative of q(x). Factor v(w).
2*(w + 1)*(w + 2)/7
Let b(x) = -x**2 - 9*x - 8. Let n(p) = -p**2 - 13*p - 12. Let q(d) = 7*b(d) - 5*n(d). Let q(v) = 0. What is v?
-1, 2
Factor 0*i**2 + 2/13*i**3 - 6/13*i + 4/13.
2*(i - 1)**2*(i + 2)/13
Let q(i) be the first derivative of -4/3*i**3 + 7 + 0*i + i**2 + 1/2*i**4. Factor q(p).
2*p*(p - 1)**2
Let j(s) be the third derivative of s**6/540 - s**4/36 + s**3/3 + s**2. Let f(r) be the first derivative of j(r). Determine g, given that f(g) = 0.
-1, 1
Solve 0 - 1/11*x**5 - 2/11*x**4 + 1/11*x + 0*x**3 + 2/11*x*