0*s = -s - 0*s. Let b(n) be the third derivative of 0*n + 4*n**2 + 1/6*n**5 + 0*n**3 - 1/6*n**4 + s. Factor b(x).
2*x*(5*x - 2)
Suppose -5*x + 33 = d, x - 5*d - 31 = -2*x. Let i be x*3/42*4. Factor 50/3*p**5 - 46/3*p**i + 38/3*p**3 + 8/3 + 110/3*p**4 - 16/3*p.
2*(p + 1)**3*(5*p - 2)**2/3
Let n(o) be the first derivative of -3*o**4/16 - o**3/8 + 3*o**2/4 + o + 2. Let s(b) be the first derivative of n(b). Factor s(q).
-3*(q + 1)*(3*q - 2)/4
Factor 3/8 + 1/8*l**2 - 1/2*l.
(l - 3)*(l - 1)/8
Let c(l) be the first derivative of 2*l**6/15 + 3*l**5/5 + 2*l**4/3 + 3*l + 4. Let g(i) be the first derivative of c(i). Factor g(b).
4*b**2*(b + 1)*(b + 2)
Let k = 61 - 25. Let f be (-44)/(-10) - k/9. Determine q, given that -6/5*q + 4/5*q**2 + 2/5*q**5 - 6/5*q**4 + f + 4/5*q**3 = 0.
-1, 1
Suppose -6*m = 8*m + m. Solve l**5 + m*l - 7/4*l**3 + 0 - 1/2*l**2 + 5/4*l**4 = 0.
-2, -1/4, 0, 1
Let j be 2 - ((-6)/(-2) - -4). Let s(k) = -5*k**3 + 2*k**2 + 3*k + 1. Let v(w) = 5*w**3 - 3*w**2 - 4*w. Let y(c) = j*v(c) - 4*s(c). Find a, given that y(a) = 0.
-1, 2/5, 2
Let g(r) be the first derivative of 4*r**5/15 + 2*r**4/3 - 4*r**3/9 - 4*r**2/3 - 45. Factor g(j).
4*j*(j - 1)*(j + 1)*(j + 2)/3
Determine v, given that -6*v + 4*v**2 + 0*v**2 - 3*v - v**2 = 0.
0, 3
Let q(s) be the first derivative of -s**5/5 - s**4/6 + 7*s**3/9 - s**2/3 + 19. Determine c, given that q(c) = 0.
-2, 0, 1/3, 1
Find n, given that 2/5*n + 6/5*n**2 + 1/10*n**5 + 0 + 3/5*n**4 + 13/10*n**3 = 0.
-2, -1, 0
Let g = 59/45 + -10/9. Let m = 97 - 94. Determine y so that -1/5*y**m + 1/5*y + 1/5*y**2 - g = 0.
-1, 1
Let k(n) be the first derivative of -n**5/50 + 2*n**4/15 - 4*n**3/15 - 2*n - 3. Let j(a) be the first derivative of k(a). Factor j(d).
-2*d*(d - 2)**2/5
Suppose 4*g - 165 - 51 = 0. Let a be 12/g - (-4)/9. Suppose 0 - 2/3*t + a*t**2 = 0. Calculate t.
0, 1
Let t(d) = -8*d**2 - 41*d + 40. Let h(k) = -4*k**2 - 20*k + 20. Let u(b) = 9*h(b) - 4*t(b). Determine x so that u(x) = 0.
-5, 1
Let g(y) = y**4 + 9*y**3 - 11*y**2 - 4*y - 5. Suppose 0 = m, -d + 5*m + 7 = 2. Let o(p) = -5*p**3 + 6*p**2 + 2*p + 3. Let a(t) = d*o(t) + 3*g(t). Factor a(z).
z*(z - 1)*(z + 1)*(3*z + 2)
Let y(r) be the second derivative of r**6/120 + r**5/30 + r**4/24 - 3*r**2/2 - 2*r. Let o(h) be the first derivative of y(h). Find g such that o(g) = 0.
-1, 0
Let n(k) = 3*k**4 + 4*k**3 - k**2 - 2. Let o(t) = 7*t**4 + 9*t**3 - 3*t**2 - 5. Let s(y) = -5*n(y) + 2*o(y). Factor s(a).
-a**2*(a + 1)**2
Let y(t) = -32*t**3 + 62*t**2 - 62*t - 2. Let q(r) = 11*r**3 - 21*r**2 + 21*r + 1. Let m(k) = -17*q(k) - 6*y(k). Suppose m(l) = 0. Calculate l.
1
Let w = -15/22 + 13/11. Let s = -1/5 - -7/10. Solve -y - w - s*y**2 = 0.
-1
Let d be 92/28 - 2/7. Suppose x = d*x + 4*h - 24, 0 = h - 5. Factor j**3 - x*j**3 - 2*j - j + 2 + 2*j**3.
(j - 1)**2*(j + 2)
Let q = 1175/7 + -167. Let q*w**3 - 8/7 + 0*w + 2*w**2 = 0. What is w?
-2, -1, 2/3
Factor -p + 1/4*p**2 + 1.
(p - 2)**2/4
Let n(o) be the second derivative of -o**6/20 - o**5/8 - o**4/12 - 8*o. Factor n(w).
-w**2*(w + 1)*(3*w + 2)/2
Let d = -14 + 16. Factor 2*h**2 - 2*h**4 - 4*h**3 - h**d + 2*h**3 + 3*h**4.
h**2*(h - 1)**2
Factor 0*y + 0*y**2 - 24*y**3 + 0 - 12*y**4 - 3/2*y**5.
-3*y**3*(y + 4)**2/2
Let a(n) be the second derivative of n**5/240 - n**4/16 + 3*n**3/8 + 3*n**2/2 - 8*n. Let j(f) be the first derivative of a(f). Suppose j(o) = 0. What is o?
3
Let j(m) = 25*m**2 + 11*m - 10. Let w(p) = 51*p**2 + 21*p - 21. Let i(f) = 9*j(f) - 4*w(f). Solve i(c) = 0.
-1, 2/7
Let l = -3 + 5. Factor 0*u**l + 0*u - 4*u - 8 - 4*u - 2*u**2.
-2*(u + 2)**2
Suppose -3*z + 5 = i - 2, 5*z - 3*i = 7. Let -1/2*n**3 - 1/2 + 1/2*n**z + 1/2*n = 0. What is n?
-1, 1
Let z(y) = -y**3 - y**2 + y - 8. Let s be z(0). Let p = s - -13. Determine w, given that w**2 - 6*w + 2*w**p - 1 - 6*w**2 + 6*w**4 + 4*w**3 + w**2 - 1 = 0.
-1, 1
Let h(q) = -2*q**2 + q + 4. Let u be h(0). Factor 0*g**3 + 4/7*g**u - 4/7*g**2 + 2/7*g**5 - 2/7*g + 0.
2*g*(g - 1)*(g + 1)**3/7
Let p(g) = 6*g**3 - 4*g**2 + 4*g + 1. Let n(q) = 0*q**3 - 4*q**3 - q + 3*q**3 + 2*q**2 - q**2. Let a(m) = -21*n(m) - 3*p(m). Factor a(r).
3*(r - 1)**3
Let p = 163 + -160. Let s(y) be the first derivative of -3/10*y**5 + p + 0*y + 9/8*y**4 + 0*y**2 - y**3. Find x, given that s(x) = 0.
0, 1, 2
Suppose 6*v - 8 = 2*v. Let x(s) be the second derivative of -1/10*s**5 + 2*s**v + 1/3*s**3 - 1/3*s**4 + 0 - s. Factor x(w).
-2*(w - 1)*(w + 1)*(w + 2)
Let w(h) be the third derivative of h**6/720 - h**5/180 + h**4/144 - 23*h**2. Determine z so that w(z) = 0.
0, 1
Let u(z) be the third derivative of -z**6/900 + z**5/75 - z**4/20 + z**3/2 - 5*z**2. Let k(l) be the first derivative of u(l). Let k(c) = 0. Calculate c.
1, 3
Determine j, given that -16*j + 12*j**3 + 4*j**4 + 8*j**4 - 16*j**4 = 0.
-1, 0, 2
Factor 4 - 10*m**3 + 16*m**3 + 6*m - 8*m**3.
-2*(m - 2)*(m + 1)**2
Let b be 0/(-1*(-3 + 4)). Let m be b + 21/9 - 2. Factor 0*q - 1/3*q**4 + 2/3*q**3 + 0 - m*q**2.
-q**2*(q - 1)**2/3
Factor -b + b**2 - 2*b**3 - 3*b**2 + 0*b**4 + 3*b + 2*b**4.
2*b*(b - 1)**2*(b + 1)
Let s be (-2)/8 + 42/8. Let a(p) be the second derivative of -p + 1/60*p**6 + 0*p**3 + 0 + 0*p**2 - 1/48*p**4 - 1/80*p**s. Solve a(w) = 0.
-1/2, 0, 1
Let d(m) = -m**3 + 1. Let y(p) = p**3 - 7*p**2 - 14*p. Let k(t) = -6*d(t) + 2*y(t). Solve k(u) = 0.
-1, -1/4, 3
Let h be 6/(-3) + 5 - (-63)/(-28). Factor -45/2*j**2 + 27/4*j - h - 99/4*j**4 + 69/2*j**3 + 27/4*j**5.
3*(j - 1)**3*(3*j - 1)**2/4
Let d = -104 - -316/3. Find g, given that 0 + 2/3*g + 2/3*g**3 - d*g**2 = 0.
0, 1
Let z = 38/3 - 12. Let p = -2/103 + 109/309. Solve -p - z*a - 1/3*a**2 = 0 for a.
-1
Let o = 98 - 93. Let l(m) be the third derivative of 0*m + 4*m**2 - 3/5*m**o + 0 + 2/3*m**3 + 5/12*m**4. Factor l(q).
-2*(2*q - 1)*(9*q + 2)
Let t be -3 + (2/1 - -1). Let q(r) = r**2 - r + 2. Let d be q(t). Let 0 + 2/3*p**d + 2/3*p**4 + 0*p - 4/3*p**3 = 0. Calculate p.
0, 1
Suppose 6 = -3*o, 3*o = -3*n + 2*o + 4. Let r be 5/n*24/20. Factor 1/4*q**4 + 0 + 1/4*q**2 + 0*q + 1/2*q**r.
q**2*(q + 1)**2/4
Suppose -3*m - 5 = -2*b, 4*b + 0*m - 11 = 5*m. Factor 3*j**2 - 5*j**2 + 8*j - 2*j - b + 0.
-2*(j - 2)*(j - 1)
Suppose -2*m - p = -5, -3*m - 5*p = -6 - 5. Let s(g) be the second derivative of 1/9*g**3 + 2/9*g**m + 3*g + 1/54*g**4 + 0. Factor s(o).
2*(o + 1)*(o + 2)/9
Let h be 8/(-14) + -7 + (-318)/(-42). Find w, given that 0*w + 1/3*w**4 - 2/3*w**2 + h - 1/3*w**3 = 0.
-1, 0, 2
Find g, given that -3*g**2 + 3*g**3 - g**2 + 7*g**2 - g - 3 - 2*g = 0.
-1, 1
Let h = -1/34 + 379/170. Suppose 0 + 6/5*b**2 - 1/5*b - h*b**3 + 6/5*b**4 = 0. Calculate b.
0, 1/3, 1/2, 1
Let i(z) = 1. Let d(u) = -4*u**5 - 12*u**4 - 12*u**3 - 4*u**2 - 4. Let g(f) = -d(f) - 4*i(f). Solve g(p) = 0 for p.
-1, 0
Suppose -21*q**2 + 2*q**2 + 15*q + 20*q**5 - 25*q**2 + 84*q**3 - 68*q**4 - 7*q = 0. What is q?
0, 2/5, 1
Let l(y) be the second derivative of -y**6/60 + 2*y**5/15 - y**4/3 + 5*y**2/2 + 4*y. Let v(d) be the first derivative of l(d). Factor v(j).
-2*j*(j - 2)**2
Factor -9/7 - 1/7*h**2 + 6/7*h.
-(h - 3)**2/7
Let n = 895 + -893. Factor 0 - 1/2*o**4 - 3/2*o**3 - o**n + 0*o.
-o**2*(o + 1)*(o + 2)/2
Let k(n) be the second derivative of -n**6/280 + n**5/20 - 15*n**4/56 + 9*n**3/14 + 5*n**2 - 5*n. Let w(j) be the first derivative of k(j). Factor w(r).
-3*(r - 3)**2*(r - 1)/7
Let d be ((-14)/(-4) + -3)*10. Suppose z = d*z. Factor 1/2*n**2 + z*n + 0.
n**2/2
Factor 0 + 3/4*j**2 + 3*j.
3*j*(j + 4)/4
Let m(l) = -l - 7. Let t be m(-7). Let k(q) be the second derivative of -1/9*q**4 - 1/45*q**6 + 0*q**3 - 3*q + 0 + 1/10*q**5 + t*q**2. Factor k(y).
-2*y**2*(y - 2)*(y - 1)/3
Let s(x) = 3*x**2 - 9*x - 5. Let j(b) = -2*b**2 + 4*b + 2. Let q(o) = 7*j(o) + 4*s(o). Factor q(m).
-2*(m + 1)*(m + 3)
Let i(o) be the third derivative of 5*o**7/231 - o**6/66 + o**5/330 - 6*o**2. Suppose i(m) = 0. What is m?
0, 1/5
Factor 0*c**2 + 2/15 + 4/15*c - 2/15*c**4 - 4/15*c**3.
-2*(c - 1)*(c + 1)**3/15
Let u(j) be the third derivative of 0 + 1/90*j**5 + 0*j - 3*j**2 + 0*j**3 - 1/36*j**4. Factor u(l).
2*l*(l - 1)/3
Let d(l) be the first derivative of 3*l**5/35 - 3*l**4/7 + 6*l**3/7 - 6*l**2/7 + 3*l/7 - 14. Suppose d(r) = 0. What is r?
1
Let p(q) be the third derivative of 9*q**5/10 - q**4 + 4*q**3/9 + 5*q**2. Factor p(b).
2*(9*b - 2)**2/3
Let s be (-6)/126*4/(-25).